{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b218a709",
   "metadata": {
    "papermill": {
     "duration": 0.005723,
     "end_time": "2026-03-18T17:33:45.879362+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:45.873639+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Model Fitting Tutorial\n",
    "\n",
    "This notebook provides a comprehensive guide to fitting epidemic models to data using the `epimodels.fitting` module.\n",
    "\n",
    "## Overview\n",
    "\n",
    "The fitting module provides:\n",
    "1. **Dataset**: Register and validate observed data with state variable mappings\n",
    "2. **Loss Functions**: Multiple options (SSE, Poisson, Negative Binomial, etc.)\n",
    "3. **Optimizers**: Scipy, JAX, and Nevergrad backends\n",
    "4. **ModelFitter**: Main API for fitting models to data\n",
    "\n",
    "We'll cover:\n",
    "- Generating synthetic data for testing\n",
    "- Basic fitting workflow\n",
    "- Data registration and validation\n",
    "- Comparing loss functions and optimizers\n",
    "- Advanced features: fixed parameters, initial condition fitting, profile likelihood"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf601506",
   "metadata": {
    "papermill": {
     "duration": 0.003817,
     "end_time": "2026-03-18T17:33:45.889761+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:45.885944+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 1. Setup and Imports"
   ]
  },
  {
   "cell_type": "code",
   "id": "bc2e26e5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:45.899243Z",
     "iopub.status.busy": "2026-03-18T17:33:45.898956Z",
     "iopub.status.idle": "2026-03-18T17:33:47.385494Z",
     "shell.execute_reply": "2026-03-18T17:33:47.384756Z"
    },
    "papermill": {
     "duration": 1.491965,
     "end_time": "2026-03-18T17:33:47.386435+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:45.894470+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:34:07.738835849Z",
     "start_time": "2026-03-30T17:34:04.983845192Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import display\n",
    "\n",
    "from epimodels.continuous.models import SIR, SEIR, SIRS\n",
    "from epimodels.fitting import (\n",
    "    Dataset,\n",
    "    DataSeries,\n",
    "    ParameterSpec,\n",
    "    ModelFitter,\n",
    "    FittingResult,\n",
    "    fit_model,\n",
    "    SumOfSquaredErrors,\n",
    "    WeightedSSE,\n",
    "    PoissonLikelihood,\n",
    "    NegativeBinomialLikelihood,\n",
    "    NormalLikelihood,\n",
    "    HuberLoss,\n",
    "    ScipyOptimizer,\n",
    "    MultiStartOptimizer,\n",
    ")\n",
    "\n",
    "np.random.seed(42)\n",
    "plt.style.use('seaborn-v0_8-whitegrid')\n",
    "%matplotlib inline"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "id": "0850fa0e",
   "metadata": {
    "papermill": {
     "duration": 0.003487,
     "end_time": "2026-03-18T17:33:47.393660+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:47.390173+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 2. Generating Synthetic Data\n",
    "\n",
    "Before fitting, we need data. Let's generate synthetic data from an SIR model with known parameters, then add realistic noise."
   ]
  },
  {
   "cell_type": "code",
   "id": "5e8b1b1b2de81176",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:05.440400089Z",
     "start_time": "2026-03-30T17:35:04.521397123Z"
    }
   },
   "source": [
    "# True parameters\n",
    "TRUE_BETA = 0.4\n",
    "TRUE_GAMMA = 0.1\n",
    "TOTAL_POPULATION = 10000\n",
    "INITIAL_INFECTED = 50\n",
    "\n",
    "# Generate ground truth data\n",
    "ground_truth_model = SIR()\n",
    "ground_truth_model(\n",
    "    inits=[TOTAL_POPULATION - INITIAL_INFECTED, INITIAL_INFECTED, 0],\n",
    "    trange=[0, 100],\n",
    "    totpop=TOTAL_POPULATION,\n",
    "    params={'beta': TRUE_BETA, 'gamma': TRUE_GAMMA},\n",
    ")\n",
    "\n",
    "# Extract time series\n",
    "true_times = ground_truth_model.traces['time']\n",
    "true_I = ground_truth_model.traces['I']\n",
    "true_R = ground_truth_model.traces['R']\n",
    "\n",
    "print(f\"Ground truth parameters: beta={TRUE_BETA}, gamma={TRUE_GAMMA}\")\n",
    "print(f\"R0 = {TRUE_BETA / TRUE_GAMMA:.1f}\")\n",
    "print(f\"Time points: {len(true_times)}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ground truth parameters: beta=0.4, gamma=0.1\n",
      "R0 = 4.0\n",
      "Time points: 19\n"
     ]
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "code",
   "id": "eff0b887f23c1ca2",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:06.736350074Z",
     "start_time": "2026-03-30T17:35:05.829166445Z"
    }
   },
   "source": [
    "ground_truth_model.plot_traces()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 5
  },
  {
   "cell_type": "code",
   "id": "c682d39ba40836ba",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:09.310398187Z",
     "start_time": "2026-03-30T17:35:08.069996483Z"
    }
   },
   "source": [
    "# Add realistic noise to simulate observations\n",
    "# Using Poisson noise (appropriate for count data)\n",
    "observed_I = np.random.poisson(lam=true_I).astype(float)\n",
    "observed_R = np.random.poisson(lam=true_R).astype(float)\n",
    "\n",
    "# Ensure non-negative\n",
    "observed_I = np.maximum(observed_I, 0)\n",
    "observed_R = np.maximum(observed_R, 0)\n",
    "\n",
    "# Plot ground truth vs observed\n",
    "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
    "\n",
    "axes[0].plot(true_times, true_I, 'b-', label='Ground Truth I', linewidth=2)\n",
    "axes[0].plot(true_times, observed_I, 'ro', label='Observed I', markersize=3, alpha=0.7)\n",
    "axes[0].set_xlabel('Time (days)')\n",
    "axes[0].set_ylabel('Number of Infected')\n",
    "axes[0].set_title('Infectious Population')\n",
    "axes[0].legend()\n",
    "\n",
    "axes[1].plot(true_times, true_R, 'g-', label='Ground Truth R', linewidth=2)\n",
    "axes[1].plot(true_times, observed_R, 'mo', label='Observed R', markersize=3, alpha=0.7)\n",
    "axes[1].set_xlabel('Time (days)')\n",
    "axes[1].set_ylabel('Number of Recovered')\n",
    "axes[1].set_title('Recovered Population')\n",
    "axes[1].legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1400x500 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "id": "b6da8fc0",
   "metadata": {
    "papermill": {
     "duration": 0.004058,
     "end_time": "2026-03-18T17:33:47.906161+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:47.902103+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 3. Basic Fitting Workflow\n",
    "\n",
    "The basic workflow consists of:\n",
    "1. Create a `Dataset` and register observed data\n",
    "2. Define `ParameterSpec` for parameters to fit\n",
    "3. Create a `ModelFitter` with model, data, and specifications\n",
    "4. Call `fit()` and analyze results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c77ecbc",
   "metadata": {
    "papermill": {
     "duration": 0.004308,
     "end_time": "2026-03-18T17:33:47.914778+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:47.910470+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 3.1 Register Data with Dataset"
   ]
  },
  {
   "cell_type": "code",
   "id": "c951dae8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:47.924396Z",
     "iopub.status.busy": "2026-03-18T17:33:47.924159Z",
     "iopub.status.idle": "2026-03-18T17:33:47.928122Z",
     "shell.execute_reply": "2026-03-18T17:33:47.927478Z"
    },
    "papermill": {
     "duration": 0.009555,
     "end_time": "2026-03-18T17:33:47.928593+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:47.919038+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:11.672019162Z",
     "start_time": "2026-03-30T17:35:11.244352335Z"
    }
   },
   "source": [
    "# Create a fresh model for fitting\n",
    "model = SIR()\n",
    "\n",
    "# Create dataset and register observed data\n",
    "dataset = Dataset(model)\n",
    "\n",
    "# Register the 'I' compartment data\n",
    "dataset.register(\n",
    "    name='infected',\n",
    "    values=observed_I,\n",
    "    times=true_times,\n",
    "    state_variable='I',\n",
    "    time_unit='days',\n",
    ")\n",
    "\n",
    "# Validate the dataset\n",
    "validation_result = dataset.validate(total_population=TOTAL_POPULATION)\n",
    "print(f\"Dataset valid: {validation_result.is_valid}\")\n",
    "print(f\"Time range: {dataset.time_range}\")\n",
    "print(dataset)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset valid: True\n",
      "Time range: (0.0, 100.0)\n",
      "Dataset(n_series=1, variables=['I'], time_range=(0.0, 100.0))\n"
     ]
    }
   ],
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "id": "d86215ec",
   "metadata": {
    "papermill": {
     "duration": 0.005179,
     "end_time": "2026-03-18T17:33:47.938975+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:47.933796+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 3.2 Define Parameters to Fit"
   ]
  },
  {
   "cell_type": "code",
   "id": "d34623cf",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:47.953800Z",
     "iopub.status.busy": "2026-03-18T17:33:47.953540Z",
     "iopub.status.idle": "2026-03-18T17:33:47.958183Z",
     "shell.execute_reply": "2026-03-18T17:33:47.957448Z"
    },
    "papermill": {
     "duration": 0.013121,
     "end_time": "2026-03-18T17:33:47.958867+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:47.945746+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:14.971182209Z",
     "start_time": "2026-03-30T17:35:14.246672920Z"
    }
   },
   "source": [
    "# Define parameter specifications\n",
    "param_specs = [\n",
    "    ParameterSpec(\n",
    "        name='beta',\n",
    "        bounds=(0.1, 1.0),\n",
    "        initial=0.5,  # Initial guess\n",
    "    ),\n",
    "    ParameterSpec(\n",
    "        name='gamma',\n",
    "        bounds=(0.01, 0.5),\n",
    "        initial=0.2,  # Initial guess\n",
    "    ),\n",
    "]\n",
    "\n",
    "print(\"Parameters to fit:\")\n",
    "for spec in param_specs:\n",
    "    print(f\"  {spec.name}: bounds={spec.bounds}, initial={spec.initial}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters to fit:\n",
      "  beta: bounds=(0.1, 1.0), initial=0.5\n",
      "  gamma: bounds=(0.01, 0.5), initial=0.2\n"
     ]
    }
   ],
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "id": "65dac467",
   "metadata": {
    "papermill": {
     "duration": 0.00424,
     "end_time": "2026-03-18T17:33:47.967432+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:47.963192+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 3.3 Create Fitter and Fit"
   ]
  },
  {
   "cell_type": "code",
   "id": "1d47ba22",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:47.976522Z",
     "iopub.status.busy": "2026-03-18T17:33:47.976300Z",
     "iopub.status.idle": "2026-03-18T17:33:48.062433Z",
     "shell.execute_reply": "2026-03-18T17:33:48.060619Z"
    },
    "papermill": {
     "duration": 0.092128,
     "end_time": "2026-03-18T17:33:48.063465+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:47.971337+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:16.636628287Z",
     "start_time": "2026-03-30T17:35:15.877802312Z"
    }
   },
   "source": [
    "# Create the fitter\n",
    "fitter = ModelFitter(\n",
    "    model=model,\n",
    "    dataset=dataset,\n",
    "    parameters_to_fit=param_specs,\n",
    "    total_population=TOTAL_POPULATION,\n",
    "    optimizer=ScipyOptimizer(method='L-BFGS-B', max_iterations=200),\n",
    ")\n",
    "\n",
    "# Perform the fit\n",
    "result = fitter.fit()\n",
    "\n",
    "# Display results\n",
    "print(\"\\n\" + \"=\"*50)\n",
    "print(\"FITTING RESULTS\")\n",
    "print(\"=\"*50)\n",
    "print(f\"Convergence: {result.convergence}\")\n",
    "print(f\"Number of evaluations: {result.n_evaluations}\")\n",
    "print(f\"Final loss: {result.best_loss:.2f}\")\n",
    "print(\"\\nFitted parameters:\")\n",
    "for param, value in result.best_params.items():\n",
    "    true_val = TRUE_BETA if param == 'beta' else TRUE_GAMMA\n",
    "    error = abs(value - true_val) / true_val * 100\n",
    "    print(f\"  {param}: {value:.4f} (true: {true_val}, error: {error:.1f}%)\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "==================================================\n",
      "FITTING RESULTS\n",
      "==================================================\n",
      "Convergence: True\n",
      "Number of evaluations: 60\n",
      "Final loss: 2860.33\n",
      "\n",
      "Fitted parameters:\n",
      "  beta: 0.4067 (true: 0.4, error: 1.7%)\n",
      "  gamma: 0.1008 (true: 0.1, error: 0.8%)\n"
     ]
    }
   ],
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "id": "d783ae9e",
   "metadata": {
    "papermill": {
     "duration": 0.007095,
     "end_time": "2026-03-18T17:33:48.078062+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.070967+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 3.4 Visualize Fit Results"
   ]
  },
  {
   "cell_type": "code",
   "id": "41aa0527",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:48.097625Z",
     "iopub.status.busy": "2026-03-18T17:33:48.096861Z",
     "iopub.status.idle": "2026-03-18T17:33:48.423885Z",
     "shell.execute_reply": "2026-03-18T17:33:48.423272Z"
    },
    "papermill": {
     "duration": 0.337926,
     "end_time": "2026-03-18T17:33:48.424700+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.086774+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:17.812437068Z",
     "start_time": "2026-03-30T17:35:17.046746023Z"
    }
   },
   "source": [
    "# Plot observed vs fitted\n",
    "fitted_model = result.fitted_model\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "\n",
    "# Observed data\n",
    "ax.plot(true_times, observed_I, 'ro', label='Observed I', markersize=4, alpha=0.7)\n",
    "\n",
    "# Ground truth\n",
    "ax.plot(true_times, true_I, 'b-', label='Ground Truth', linewidth=2, alpha=0.5)\n",
    "\n",
    "# Fitted model\n",
    "if fitted_model is not None and fitted_model.traces:\n",
    "    ax.plot(fitted_model.traces['time'], fitted_model.traces['I'], \n",
    "            'g--', label='Fitted', linewidth=2)\n",
    "\n",
    "ax.set_xlabel('Time (days)', fontsize=12)\n",
    "ax.set_ylabel('Number of Infected', fontsize=12)\n",
    "ax.set_title('Model Fitting Results', fontsize=14)\n",
    "ax.legend(fontsize=11)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 10
  },
  {
   "cell_type": "markdown",
   "id": "80ac673b",
   "metadata": {
    "papermill": {
     "duration": 0.004384,
     "end_time": "2026-03-18T17:33:48.434516+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.430132+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 4. Data Registration and Validation\n",
    "\n",
    "The `Dataset` class provides robust data handling with validation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "867a6d67",
   "metadata": {
    "papermill": {
     "duration": 0.004954,
     "end_time": "2026-03-18T17:33:48.444067+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.439113+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 4.1 Registering Multiple Data Series"
   ]
  },
  {
   "cell_type": "code",
   "id": "2da153ce",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:48.454175Z",
     "iopub.status.busy": "2026-03-18T17:33:48.453984Z",
     "iopub.status.idle": "2026-03-18T17:33:48.457292Z",
     "shell.execute_reply": "2026-03-18T17:33:48.456739Z"
    },
    "papermill": {
     "duration": 0.009618,
     "end_time": "2026-03-18T17:33:48.458287+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.448669+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:21.021252922Z",
     "start_time": "2026-03-30T17:35:20.479753661Z"
    }
   },
   "source": [
    "# Register both I and R compartments\n",
    "model2 = SIR()\n",
    "dataset2 = Dataset(model2)\n",
    "\n",
    "dataset2.register(\n",
    "    name='infected',\n",
    "    values=observed_I,\n",
    "    times=true_times,\n",
    "    state_variable='I',\n",
    ").register(\n",
    "    name='recovered',\n",
    "    values=observed_R,\n",
    "    times=true_times,\n",
    "    state_variable='R',\n",
    ")\n",
    "\n",
    "print(f\"Registered series: {list(dataset2.series.keys())}\")\n",
    "print(f\"State variables mapped: {list(set(s.state_variable for s in dataset2.series.values()))}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Registered series: ['infected', 'recovered']\n",
      "State variables mapped: ['I', 'R']\n"
     ]
    }
   ],
   "execution_count": 11
  },
  {
   "cell_type": "markdown",
   "id": "9f27ce34",
   "metadata": {
    "papermill": {
     "duration": 0.0046,
     "end_time": "2026-03-18T17:33:48.467518+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.462918+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 4.2 Validation Errors"
   ]
  },
  {
   "cell_type": "code",
   "id": "dccdf306",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:48.481757Z",
     "iopub.status.busy": "2026-03-18T17:33:48.481511Z",
     "iopub.status.idle": "2026-03-18T17:33:48.486162Z",
     "shell.execute_reply": "2026-03-18T17:33:48.485218Z"
    },
    "papermill": {
     "duration": 0.014684,
     "end_time": "2026-03-18T17:33:48.488131+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.473447+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:23.759317345Z",
     "start_time": "2026-03-30T17:35:23.550665570Z"
    }
   },
   "source": [
    "# Example: Invalid state variable\n",
    "from epimodels.fitting import DataValidationError\n",
    "\n",
    "model_test = SIR()\n",
    "dataset_test = Dataset(model_test)\n",
    "\n",
    "dataset_test.register(\n",
    "    name='invalid',\n",
    "    values=observed_I,\n",
    "    times=true_times,\n",
    "    state_variable='X',  # 'X' doesn't exist in SIR model\n",
    ")\n",
    "\n",
    "validation = dataset_test.validate()\n",
    "print(f\"Valid: {validation.is_valid}\")\n",
    "print(f\"Errors: {validation.errors}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valid: False\n",
      "Errors: [\"Series 'invalid': state variable 'X' not found in model. Available: ['I', 'S', 'R']\", \"Data mapped to non-existent variables: ['X']\"]\n"
     ]
    }
   ],
   "execution_count": 12
  },
  {
   "cell_type": "markdown",
   "id": "175f9025",
   "metadata": {
    "papermill": {
     "duration": 0.004939,
     "end_time": "2026-03-18T17:33:48.499924+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.494985+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 4.3 Time Unit Handling"
   ]
  },
  {
   "cell_type": "code",
   "id": "bbf82539",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:48.510382Z",
     "iopub.status.busy": "2026-03-18T17:33:48.510190Z",
     "iopub.status.idle": "2026-03-18T17:33:48.514242Z",
     "shell.execute_reply": "2026-03-18T17:33:48.513570Z"
    },
    "papermill": {
     "duration": 0.010377,
     "end_time": "2026-03-18T17:33:48.515032+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.504655+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:25.659131916Z",
     "start_time": "2026-03-30T17:35:25.420083770Z"
    }
   },
   "source": [
    "# Data with different time units\n",
    "model3 = SIR()\n",
    "dataset3 = Dataset(model3)\n",
    "\n",
    "# Register with weeks instead of days\n",
    "weeks = true_times / 7.0\n",
    "\n",
    "dataset3.register(\n",
    "    name='infected_weekly',\n",
    "    values=observed_I,\n",
    "    times=weeks,\n",
    "    state_variable='I',\n",
    "    time_unit='weeks',\n",
    ")\n",
    "\n",
    "print(f\"Dataset time unit: {dataset3.time_unit}\")\n",
    "print(f\"Series time unit: {dataset3.series['infected_weekly'].time_unit}\")\n",
    "print(f\"Time range: {dataset3.time_range}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset time unit: weeks\n",
      "Series time unit: weeks\n",
      "Time range: (0.0, 14.285714285714286)\n"
     ]
    }
   ],
   "execution_count": 13
  },
  {
   "cell_type": "markdown",
   "id": "f7d5289e",
   "metadata": {
    "papermill": {
     "duration": 0.005664,
     "end_time": "2026-03-18T17:33:48.525750+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.520086+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 4.4 DataFrame Integration"
   ]
  },
  {
   "cell_type": "code",
   "id": "c8de9eca",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:48.538774Z",
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     "shell.execute_reply": "2026-03-18T17:33:48.551318Z"
    },
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     "duration": 0.021153,
     "end_time": "2026-03-18T17:33:48.552493+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.531340+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:28.477927090Z",
     "start_time": "2026-03-30T17:35:27.748761825Z"
    }
   },
   "source": [
    "import pandas as pd\n",
    "\n",
    "# Create a DataFrame with observations\n",
    "df = pd.DataFrame({\n",
    "    'day': true_times,\n",
    "    'cases': observed_I,\n",
    "    'recoveries': observed_R,\n",
    "})\n",
    "\n",
    "print(\"Sample data:\")\n",
    "display(df.head(10))\n",
    "\n",
    "# Register from DataFrame\n",
    "model_df = SIR()\n",
    "dataset_df = Dataset(model_df)\n",
    "\n",
    "dataset_df.register_from_dataframe(\n",
    "    df=df,\n",
    "    time_column='day',\n",
    "    mapping={'cases': 'I', 'recoveries': 'R'},\n",
    "    time_unit='days',\n",
    ")\n",
    "\n",
    "print(f\"\\nRegistered from DataFrame: {list(dataset_df.series.keys())}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample data:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "         day   cases  recoveries\n",
       "0   0.000000    47.0         0.0\n",
       "1   0.000283    55.0         0.0\n",
       "2   0.003111    42.0         0.0\n",
       "3   0.031395    53.0         0.0\n",
       "4   0.314235    63.0         1.0\n",
       "5   2.552370    96.0        24.0\n",
       "6   6.256865   302.0        84.0\n",
       "7  10.862630  1062.0       354.0\n",
       "8  16.573157  3099.0      1564.0\n",
       "9  22.737625  3986.0      3898.0"
      ],
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>day</th>\n",
       "      <th>cases</th>\n",
       "      <th>recoveries</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>47.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.000283</td>\n",
       "      <td>55.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.003111</td>\n",
       "      <td>42.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.031395</td>\n",
       "      <td>53.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.314235</td>\n",
       "      <td>63.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2.552370</td>\n",
       "      <td>96.0</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6.256865</td>\n",
       "      <td>302.0</td>\n",
       "      <td>84.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>10.862630</td>\n",
       "      <td>1062.0</td>\n",
       "      <td>354.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>16.573157</td>\n",
       "      <td>3099.0</td>\n",
       "      <td>1564.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>22.737625</td>\n",
       "      <td>3986.0</td>\n",
       "      <td>3898.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Registered from DataFrame: ['cases', 'recoveries']\n"
     ]
    }
   ],
   "execution_count": 14
  },
  {
   "cell_type": "markdown",
   "id": "861975af",
   "metadata": {
    "papermill": {
     "duration": 0.006459,
     "end_time": "2026-03-18T17:33:48.564447+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.557988+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 5. Loss Functions\n",
    "\n",
    "Different loss functions are appropriate for different data types and noise models."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1916862c",
   "metadata": {
    "papermill": {
     "duration": 0.005162,
     "end_time": "2026-03-18T17:33:48.574465+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.569303+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 5.1 Available Loss Functions"
   ]
  },
  {
   "cell_type": "code",
   "id": "9c574798",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:48.585982Z",
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     "shell.execute_reply": "2026-03-18T17:33:48.588521Z"
    },
    "papermill": {
     "duration": 0.010518,
     "end_time": "2026-03-18T17:33:48.589832+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.579314+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:33.654851877Z",
     "start_time": "2026-03-30T17:35:33.389468939Z"
    }
   },
   "source": [
    "loss_functions = {\n",
    "    'SSE': SumOfSquaredErrors(),\n",
    "    'Poisson': PoissonLikelihood(),\n",
    "    'NegBinom': NegativeBinomialLikelihood(dispersion=5.0),\n",
    "    'Normal': NormalLikelihood(),\n",
    "    'Huber': HuberLoss(delta=10.0),\n",
    "}\n",
    "\n",
    "print(\"Available loss functions:\")\n",
    "for name, lf in loss_functions.items():\n",
    "    print(f\"  - {name}: {lf.__class__.__name__}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Available loss functions:\n",
      "  - SSE: SumOfSquaredErrors\n",
      "  - Poisson: PoissonLikelihood\n",
      "  - NegBinom: NegativeBinomialLikelihood\n",
      "  - Normal: NormalLikelihood\n",
      "  - Huber: HuberLoss\n"
     ]
    }
   ],
   "execution_count": 15
  },
  {
   "cell_type": "markdown",
   "id": "652aa5df",
   "metadata": {
    "papermill": {
     "duration": 0.004706,
     "end_time": "2026-03-18T17:33:48.599782+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.595076+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 5.2 Comparing Loss Functions"
   ]
  },
  {
   "cell_type": "code",
   "id": "8aaec140",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:48.610623Z",
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     "shell.execute_reply": "2026-03-18T17:33:49.496380Z"
    },
    "papermill": {
     "duration": 0.895151,
     "end_time": "2026-03-18T17:33:49.499605+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:48.604454+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:37.333248410Z",
     "start_time": "2026-03-30T17:35:35.506127376Z"
    }
   },
   "source": [
    "# Fit with different loss functions\n",
    "results_comparison = {}\n",
    "\n",
    "for name, loss_fn in loss_functions.items():\n",
    "    print(f\"Fitting with {name}...\")\n",
    "    \n",
    "    fitter_comp = ModelFitter(\n",
    "        model=SIR(),\n",
    "        dataset=dataset,  # Using single-series dataset from earlier\n",
    "        parameters_to_fit=param_specs,\n",
    "        total_population=TOTAL_POPULATION,\n",
    "        loss_fn=loss_fn,\n",
    "        optimizer=ScipyOptimizer(method='L-BFGS-B', max_iterations=100),\n",
    "    )\n",
    "    \n",
    "    result = fitter_comp.fit()\n",
    "    results_comparison[name] = result"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting with SSE...\n",
      "Fitting with Poisson...\n",
      "Fitting with NegBinom...\n",
      "Fitting with Normal...\n",
      "Fitting with Huber...\n"
     ]
    }
   ],
   "execution_count": 16
  },
  {
   "cell_type": "code",
   "id": "b824b3d4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:49.518899Z",
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     "shell.execute_reply": "2026-03-18T17:33:49.523687Z"
    },
    "papermill": {
     "duration": 0.018747,
     "end_time": "2026-03-18T17:33:49.526675+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:49.507928+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:37.633576408Z",
     "start_time": "2026-03-30T17:35:37.337385526Z"
    }
   },
   "source": [
    "# Compare results\n",
    "print(\"\\n\" + \"=\"*70)\n",
    "print(\"LOSS FUNCTION COMPARISON\")\n",
    "print(\"=\"*70)\n",
    "print(f\"{'Loss Function':<15} {'beta':>10} {'gamma':>10} {'R0':>10} {'Loss':>12}\")\n",
    "print(\"-\"*70)\n",
    "print(f\"{'TRUE VALUES':<15} {TRUE_BETA:>10.4f} {TRUE_GAMMA:>10.4f} {TRUE_BETA/TRUE_GAMMA:>10.2f} {'-':>12}\")\n",
    "print(\"-\"*70)\n",
    "\n",
    "for name, result in results_comparison.items():\n",
    "    beta = result.best_params['beta']\n",
    "    gamma = result.best_params['gamma']\n",
    "    r0 = beta / gamma\n",
    "    print(f\"{name:<15} {beta:>10.4f} {gamma:>10.4f} {r0:>10.2f} {result.best_loss:>12.2f}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "======================================================================\n",
      "LOSS FUNCTION COMPARISON\n",
      "======================================================================\n",
      "Loss Function         beta      gamma         R0         Loss\n",
      "----------------------------------------------------------------------\n",
      "TRUE VALUES         0.4000     0.1000       4.00            -\n",
      "----------------------------------------------------------------------\n",
      "SSE                 0.4067     0.1008       4.03      2860.33\n",
      "Poisson             0.4057     0.1008       4.03       143.37\n",
      "NegBinom            0.3994     0.1007       3.97       201.01\n",
      "Normal              0.4067     0.1008       4.03        74.61\n",
      "Huber               0.4056     0.1007       4.03      1068.47\n"
     ]
    }
   ],
   "execution_count": 17
  },
  {
   "cell_type": "markdown",
   "id": "34f1cd70",
   "metadata": {
    "papermill": {
     "duration": 0.007731,
     "end_time": "2026-03-18T17:33:49.552608+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:49.544877+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 5.3 When to Use Each Loss Function\n",
    "\n",
    "| Loss Function | Best For | Assumptions |\n",
    "|--------------|----------|-------------|\n",
    "| **SSE** | General purpose | Gaussian errors |\n",
    "| **Poisson** | Count data | Mean = Variance |\n",
    "| **Negative Binomial** | Overdispersed counts | Variance > Mean |\n",
    "| **Normal** | Continuous measurements | Known or estimated σ |\n",
    "| **Huber** | Data with outliers | Robust to outliers |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c291e76a",
   "metadata": {
    "papermill": {
     "duration": 0.006318,
     "end_time": "2026-03-18T17:33:49.568966+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:49.562648+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 6. Optimizers\n",
    "\n",
    "The module supports multiple optimization backends."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ded1c08f",
   "metadata": {
    "papermill": {
     "duration": 0.007943,
     "end_time": "2026-03-18T17:33:49.585639+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:49.577696+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 6.1 Scipy Methods"
   ]
  },
  {
   "cell_type": "code",
   "id": "025f3d16",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:49.598820Z",
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    },
    "papermill": {
     "duration": 2.043262,
     "end_time": "2026-03-18T17:33:51.634639+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:49.591377+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:47.315016525Z",
     "start_time": "2026-03-30T17:35:44.469855047Z"
    }
   },
   "source": [
    "# Compare scipy optimization methods\n",
    "scipy_methods = ['L-BFGS-B', 'Nelder-Mead', 'Powell', 'differential_evolution']\n",
    "optimizer_results = {}\n",
    "\n",
    "for method in scipy_methods:\n",
    "    print(f\"Testing {method}...\")\n",
    "    \n",
    "    optimizer = ScipyOptimizer(method=method, max_iterations=100)\n",
    "    \n",
    "    fitter_opt = ModelFitter(\n",
    "        model=SIR(),\n",
    "        dataset=dataset,\n",
    "        parameters_to_fit=param_specs,\n",
    "        total_population=TOTAL_POPULATION,\n",
    "        optimizer=optimizer,\n",
    "    )\n",
    "    \n",
    "    result = fitter_opt.fit()\n",
    "    optimizer_results[method] = result"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing L-BFGS-B...\n",
      "Testing Nelder-Mead...\n",
      "Testing Powell...\n",
      "Testing differential_evolution...\n"
     ]
    }
   ],
   "execution_count": 18
  },
  {
   "cell_type": "code",
   "id": "f60d8af6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:51.648281Z",
     "iopub.status.busy": "2026-03-18T17:33:51.648042Z",
     "iopub.status.idle": "2026-03-18T17:33:51.652280Z",
     "shell.execute_reply": "2026-03-18T17:33:51.651759Z"
    },
    "papermill": {
     "duration": 0.01218,
     "end_time": "2026-03-18T17:33:51.653062+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:51.640882+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:47.849869172Z",
     "start_time": "2026-03-30T17:35:47.400746516Z"
    }
   },
   "source": [
    "# Compare optimizer performance\n",
    "print(\"\\n\" + \"=\"*80)\n",
    "print(\"OPTIMIZER COMPARISON\")\n",
    "print(\"=\"*80)\n",
    "print(f\"{'Method':<25} {'beta':>10} {'gamma':>10} {'Evals':>8} {'Converged':>10}\")\n",
    "print(\"-\"*80)\n",
    "\n",
    "for method, result in optimizer_results.items():\n",
    "    beta = result.best_params['beta']\n",
    "    gamma = result.best_params['gamma']\n",
    "    print(f\"{method:<25} {beta:>10.4f} {gamma:>10.4f} {result.n_evaluations:>8} {str(result.convergence):>10}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "================================================================================\n",
      "OPTIMIZER COMPARISON\n",
      "================================================================================\n",
      "Method                          beta      gamma    Evals  Converged\n",
      "--------------------------------------------------------------------------------\n",
      "L-BFGS-B                      0.4067     0.1008       60       True\n",
      "Nelder-Mead                   0.4067     0.1008       60       True\n",
      "Powell                        0.4067     0.1008       60       True\n",
      "differential_evolution        0.4067     0.1008     1164       True\n"
     ]
    }
   ],
   "execution_count": 19
  },
  {
   "cell_type": "markdown",
   "id": "771f8490",
   "metadata": {
    "papermill": {
     "duration": 0.005877,
     "end_time": "2026-03-18T17:33:51.666029+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:51.660152+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 6.2 Multi-Start Optimization\n",
    "\n",
    "For robust results, especially with local minima, use multi-start optimization."
   ]
  },
  {
   "cell_type": "code",
   "id": "d9d1f77c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:51.679107Z",
     "iopub.status.busy": "2026-03-18T17:33:51.678888Z",
     "iopub.status.idle": "2026-03-18T17:33:52.840284Z",
     "shell.execute_reply": "2026-03-18T17:33:52.839574Z"
    },
    "papermill": {
     "duration": 1.168798,
     "end_time": "2026-03-18T17:33:52.840977+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:51.672179+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:52.621553702Z",
     "start_time": "2026-03-30T17:35:50.917926016Z"
    }
   },
   "source": [
    "# Multi-start optimization\n",
    "base_optimizer = ScipyOptimizer(method='L-BFGS-B', max_iterations=50)\n",
    "multi_start = MultiStartOptimizer(\n",
    "    base_optimizer=base_optimizer,\n",
    "    n_starts=5,\n",
    "    sampling_method='latin_hypercube',\n",
    "    seed=42,\n",
    ")\n",
    "\n",
    "fitter_ms = ModelFitter(\n",
    "    model=SIR(),\n",
    "    dataset=dataset,\n",
    "    parameters_to_fit=param_specs,\n",
    "    total_population=TOTAL_POPULATION,\n",
    "    optimizer=multi_start,\n",
    ")\n",
    "\n",
    "result_ms = fitter_ms.fit()\n",
    "\n",
    "print(f\"Multi-start optimization results:\")\n",
    "print(f\"  beta: {result_ms.best_params['beta']:.4f}\")\n",
    "print(f\"  gamma: {result_ms.best_params['gamma']:.4f}\")\n",
    "print(f\"  Total evaluations: {result_ms.n_evaluations}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Multi-start optimization results:\n",
      "  beta: 0.4067\n",
      "  gamma: 0.1008\n",
      "  Total evaluations: 477\n"
     ]
    }
   ],
   "execution_count": 20
  },
  {
   "cell_type": "markdown",
   "id": "bb89587d",
   "metadata": {
    "papermill": {
     "duration": 0.005488,
     "end_time": "2026-03-18T17:33:52.852767+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:52.847279+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 7. Advanced Features\n",
    "\n",
    "### 7.1 Fixed Parameters\n",
    "\n",
    "Sometimes we know some parameters and only want to fit others."
   ]
  },
  {
   "cell_type": "code",
   "id": "52d6823a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:52.864067Z",
     "iopub.status.busy": "2026-03-18T17:33:52.863851Z",
     "iopub.status.idle": "2026-03-18T17:33:52.956460Z",
     "shell.execute_reply": "2026-03-18T17:33:52.955724Z"
    },
    "papermill": {
     "duration": 0.099036,
     "end_time": "2026-03-18T17:33:52.957102+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:52.858066+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:35:56.524117028Z",
     "start_time": "2026-03-30T17:35:56.239043894Z"
    }
   },
   "source": [
    "# Fix gamma and only fit beta\n",
    "fitter_fixed = ModelFitter(\n",
    "    model=SIR(),\n",
    "    dataset=dataset,\n",
    "    parameters_to_fit=[\n",
    "        ParameterSpec(name='beta', bounds=(0.1, 1.0), initial=0.5),\n",
    "    ],\n",
    "    total_population=TOTAL_POPULATION,\n",
    "    fixed_params={'gamma': TRUE_GAMMA},  # Fix gamma at true value\n",
    ")\n",
    "\n",
    "result_fixed = fitter_fixed.fit()\n",
    "\n",
    "print(\"Fitting with fixed gamma:\")\n",
    "print(f\"  Fitted beta: {result_fixed.best_params['beta']:.4f} (true: {TRUE_BETA})\")\n",
    "print(f\"  Fixed gamma: {TRUE_GAMMA}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting with fixed gamma:\n",
      "  Fitted beta: 0.4064 (true: 0.4)\n",
      "  Fixed gamma: 0.1\n"
     ]
    }
   ],
   "execution_count": 21
  },
  {
   "cell_type": "markdown",
   "id": "766d99a6",
   "metadata": {
    "papermill": {
     "duration": 0.007554,
     "end_time": "2026-03-18T17:33:52.971058+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:52.963504+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 7.2 Log-Scale Parameter Transformation\n",
    "\n",
    "For parameters spanning orders of magnitude, log-scale transformation can improve optimization."
   ]
  },
  {
   "cell_type": "code",
   "id": "5bad4d4103171be8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-30T17:36:47.074252091Z",
     "start_time": "2026-03-30T17:36:46.926440863Z"
    }
   },
   "source": [
    "# =noisy_I,# Parameters with log-scale transformation\n",
    "param_specs_log = [\n",
    "    ParameterSpec(\n",
    "        name='beta',\n",
    "        bounds=(0.01, 1.0),\n",
    "        initial=0.3,\n",
    "        log_scale=True,  # Search in log space\n",
    "    ),\n",
    "    ParameterSpec(\n",
    "        name='gamma',\n",
    "        bounds=(0.01, 0.5),\n",
    "        initial=0.1,\n",
    "        log_scale=True,  # Search in log space\n",
    "    ),\n",
    "]\n",
    "\n",
    "print(\"Log-scale parameter specs:\")\n",
    "for spec in param_specs_log:\n",
    "    print(f\"  {spec.name}: bounds={spec.bounds}, log_scale={spec.log_scale}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log-scale parameter specs:\n",
      "  beta: bounds=(0.01, 1.0), log_scale=True\n",
      "  gamma: bounds=(0.01, 0.5), log_scale=True\n"
     ]
    }
   ],
   "execution_count": 23
  },
  {
   "cell_type": "markdown",
   "id": "fabc91c8",
   "metadata": {
    "papermill": {
     "duration": 0.008252,
     "end_time": "2026-03-18T17:33:53.003298+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:52.995046+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 7.3 Profile Likelihood for Confidence Intervals"
   ]
  },
  {
   "cell_type": "code",
   "id": "63f699cd",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:53.132904Z",
     "iopub.status.busy": "2026-03-18T17:33:53.132581Z",
     "iopub.status.idle": "2026-03-18T17:33:54.114984Z",
     "shell.execute_reply": "2026-03-18T17:33:54.114411Z"
    },
    "papermill": {
     "duration": 0.991469,
     "end_time": "2026-03-18T17:33:54.115451+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:53.123982+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:36:52.481851905Z",
     "start_time": "2026-03-30T17:36:51.349691304Z"
    }
   },
   "source": [
    "# Compute profile likelihood for beta\n",
    "profile_result = fitter.profile_likelihood(\n",
    "    param_name='beta',\n",
    "    n_points=20,\n",
    "    threshold=3.84,  # Chi-squared 95% CI for 1 df\n",
    ")\n",
    "\n",
    "print(\"Profile likelihood analysis for beta:\")\n",
    "print(f\"  Minimum loss: {profile_result['min_loss']:.2f}\")\n",
    "print(f\"  95% CI threshold: {profile_result['threshold_loss']:.2f}\")\n",
    "print(f\"  Confidence interval: {profile_result['confidence_interval']}\")"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Profile likelihood analysis for beta:\n",
      "  Minimum loss: 283984.09\n",
      "  95% CI threshold: 283986.01\n",
      "  Confidence interval: (np.float64(0.43157894736842106), np.float64(0.43157894736842106))\n"
     ]
    }
   ],
   "execution_count": 24
  },
  {
   "cell_type": "code",
   "id": "16032f91",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:54.127935Z",
     "iopub.status.busy": "2026-03-18T17:33:54.127746Z",
     "iopub.status.idle": "2026-03-18T17:33:54.255679Z",
     "shell.execute_reply": "2026-03-18T17:33:54.255182Z"
    },
    "papermill": {
     "duration": 0.135007,
     "end_time": "2026-03-18T17:33:54.256474+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:54.121467+00:00",
     "status": "completed"
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-30T17:36:55.751804185Z",
     "start_time": "2026-03-30T17:36:55.205149946Z"
    }
   },
   "source": [
    "# Plot profile likelihood\n",
    "fig, ax = plt.subplots(figsize=(10, 6))\n",
    "\n",
    "ax.plot(profile_result['values'], profile_result['losses'], 'b-', linewidth=2)\n",
    "ax.axhline(y=profile_result['threshold_loss'], color='r', linestyle='--', \n",
    "           label=f\"95% CI threshold\")\n",
    "ax.axvline(x=TRUE_BETA, color='g', linestyle=':', label=f\"True beta = {TRUE_BETA}\")\n",
    "\n",
    "# Shade CI region\n",
    "ci = profile_result['confidence_interval']\n",
    "if ci[0] is not None and ci[1] is not None:\n",
    "    ax.axvspan(ci[0], ci[1], alpha=0.2, color='blue', label=f\"95% CI: [{ci[0]:.3f}, {ci[1]:.3f}]\")\n",
    "\n",
    "ax.set_xlabel('beta', fontsize=12)\n",
    "ax.set_ylabel('Loss', fontsize=12)\n",
    "ax.set_title('Profile Likelihood for beta', fontsize=14)\n",
    "ax.legend(fontsize=10)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 25
  },
  {
   "cell_type": "markdown",
   "id": "ic_fitting_section",
   "metadata": {
    "papermill": {
     "duration": 0.005,
     "end_time": "2026-03-18T17:33:54.000",
     "exception": false,
     "start_time": "2026-03-18T17:33:53.995",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 7.4 Fitting Initial Conditions\n",
    "\n",
    "By default, initial conditions are estimated from the first data point and kept fixed. You can also fit initial conditions alongside model parameters using `fit_initial_conditions=True`.\n",
    "\n",
    "For more control, use `InitialConditionSpec` to specify:\n",
    "- `bounds`: Search range for the initial value\n",
    "- `initial`: Starting value for optimization\n",
    "- `fixed`: If `True`, the IC is held fixed during fitting\n",
    "\n",
    "This allows you to fix some initial conditions (e.g., S[0] = N - I[0] - R[0]) while fitting others."
   ]
  },
  {
   "cell_type": "code",
   "id": "ic_fitting_example",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-30T17:38:19.152917691Z",
     "start_time": "2026-03-30T17:38:17.508041351Z"
    }
   },
   "source": [
    "# Example: Fit initial conditions for I and R, but fix S based on total population\n",
    "from epimodels.fitting import InitialConditionSpec\n",
    "\n",
    "# Create dataset with both I and R observations\n",
    "model_ic = SIR()\n",
    "dataset_ic = Dataset(model_ic)\n",
    "dataset_ic.register(\n",
    "    name='infected',\n",
    "    values=observed_I,\n",
    "    times=true_times,\n",
    "    state_variable='I',\n",
    ").register(\n",
    "    name='recovered',\n",
    "    values=observed_R,\n",
    "    times=true_times,\n",
    "    state_variable='R',\n",
    ")\n",
    "\n",
    "# Specify IC fitting: fix S[0], fit I[0] and R[0]\n",
    "# S[0] will be computed as: TOTAL_POPULATION - I[0] - R[0]\n",
    "ic_specs = [\n",
    "    InitialConditionSpec(\n",
    "        state_variable='S',\n",
    "        bounds=(TOTAL_POPULATION - 100, TOTAL_POPULATION),\n",
    "        initial=TOTAL_POPULATION - INITIAL_INFECTED,\n",
    "        fixed=False,  # Fixed - will be computed from other ICs\n",
    "    ),\n",
    "    InitialConditionSpec(\n",
    "        state_variable='I',\n",
    "        bounds=(1, 500),\n",
    "        initial=INITIAL_INFECTED,\n",
    "        fixed=True,  # Will be fitted\n",
    "    ),\n",
    "    InitialConditionSpec(\n",
    "        state_variable='R',\n",
    "        bounds=(0, 100),\n",
    "        initial=0,\n",
    "        fixed=False,  # Will be fitted\n",
    "    ),\n",
    "]\n",
    "\n",
    "# Create fitter with IC fitting enabled\n",
    "fitter_ic = ModelFitter(\n",
    "    model=model_ic,\n",
    "    dataset=dataset_ic,\n",
    "    parameters_to_fit=[\n",
    "        ParameterSpec(name='beta', bounds=(0.1, 1.0), initial=0.5),\n",
    "        ParameterSpec(name='gamma', bounds=(0.01, 0.5), initial=0.2),\n",
    "    ],\n",
    "    total_population=TOTAL_POPULATION,\n",
    "    fit_initial_conditions=True,\n",
    "    initial_condition_specs=ic_specs,\n",
    ")\n",
    "\n",
    "# Fit the model\n",
    "result_ic = fitter_ic.fit()\n",
    "\n",
    "print(\"Fitting with initial conditions:\")\n",
    "print(f\"  Fitted beta: {result_ic.best_params['beta']:.4f} (true: {TRUE_BETA})\")\n",
    "print(f\"  Fitted gamma: {result_ic.best_params['gamma']:.4f} (true: {TRUE_GAMMA})\")\n",
    "print(f\"  Fitted I[0]: {result_ic.best_initial_conditions[1]:.1f} (true: {INITIAL_INFECTED})\")\n",
    "print(f\"  Fitted R[0]: {result_ic.best_initial_conditions[2]:.1f} (true: 0)\")\n",
    "print(f\"  Fixed S[0]: {result_ic.best_initial_conditions[0]:.1f}\")"
   ],
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10150.0) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10149.99999999) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10037.678751579851) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10037.678751589852) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10011.246044332569) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10011.24604434257) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10011.246044342568) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.25094652309) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.250946533091) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.25094653309) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.002172119051) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.002172129052) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10149.962619408532) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10149.962619398531) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10149.962619418533) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10079.858433258289) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10079.85843326829) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10079.858433268288) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10044.806554293556) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10044.806554303557) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10027.280668121946) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10027.280668131947) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10018.517738323637) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10018.517738333638) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10014.13699951408) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10014.13699952408) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10011.946748875098) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10011.946748885099) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10011.946748885097) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10141.878067286249) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10141.87806729625) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10141.878067276248) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10075.8206951335) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10075.8206951435) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10075.820695143499) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.094218228329) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.09421823833) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.04010036447) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.04010037447) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.013041433149) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.01304144315) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.008441414833) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.008441424834) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.857593866049) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.85759387605) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.857593876048) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.428552967584) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.428552977584) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.214032547216) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.214032557216) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.106772344796) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.106772354797) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.053142358962) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.053142368963) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.026327366257) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.026327376258) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.026327376256) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.85884101824) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.858841028241) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.429176746948) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.429176756948) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.214344624053) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.214344634054) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.106928565787) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.106928575788) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.053220540518) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.053220550519) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.053220550517) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.026366528082) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.026366538083) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.02636653808) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.861086708797) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.861086718798) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.430299663643) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.430299673644) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.21490615387) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.21490616387) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.214906163868) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.107209418502) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.107209428503) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.053361051625) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.053361061626) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.0264369209) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.0264369309) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.012974855574) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.012974865575) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.012974865573) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.001440781833) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n",
      "/home/fccoelho/Documentos/Software_projects/epimodels/epimodels/fitting/base.py:412: RuntimeWarning: Model evaluation failed: Sum of initial conditions (10010.001440791833) exceeds total population (10000)\n",
      "  warnings.warn(f\"Model evaluation failed: {e}\", RuntimeWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting with initial conditions:\n",
      "  Fitted beta: 0.4037 (true: 0.4)\n",
      "  Fitted gamma: 0.0986 (true: 0.1)\n",
      "  Fitted I[0]: 50.0 (true: 50)\n",
      "  Fitted R[0]: 6.7 (true: 0)\n",
      "  Fixed S[0]: 9953.3\n"
     ]
    }
   ],
   "execution_count": 26
  },
  {
   "cell_type": "markdown",
   "id": "6e8bf8a4",
   "metadata": {
    "papermill": {
     "duration": 0.00697,
     "end_time": "2026-03-18T17:33:54.269524+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:54.262554+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 8. Practical Example: Handling Noisy and Missing Data\n",
    "\n",
    "Real-world data often has noise, outliers, and missing observations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d188bd0",
   "metadata": {
    "papermill": {
     "duration": 0.006186,
     "end_time": "2026-03-18T17:33:54.281666+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:54.275480+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 8.1 Generate Realistic Noisy Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d3cdf548fcf216df",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T18:31:28.689892994Z",
     "start_time": "2026-03-18T18:31:28.525633729Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sampled 20 time points from 100 total\n",
      "Added outliers at indices: [5, 10, 15]\n"
     ]
    }
   ],
   "source": [
    "# Generate data with more realistic noise\n",
    "np.random.seed(123)\n",
    "\n",
    "# Ground truth with more time points\n",
    "ground_truth = SIR()\n",
    "ground_truth(\n",
    "    inits=[TOTAL_POPULATION - INITIAL_INFECTED, INITIAL_INFECTED, 0],\n",
    "    trange=[0, 80],\n",
    "    totpop=TOTAL_POPULATION,\n",
    "    params={'beta': 0.35, 'gamma': 0.12},\n",
    ")\n",
    "\n",
    "# Create denser time points for sampling\n",
    "full_times = np.linspace(0, 80, 100)\n",
    "from scipy.interpolate import interp1d\n",
    "interp_I = interp1d(ground_truth.traces['time'], ground_truth.traces['I'], kind='linear', fill_value='extrapolate')\n",
    "full_I = interp_I(full_times)\n",
    "\n",
    "# Sample every 5 days (realistic observation frequency)\n",
    "sample_indices = np.arange(0, len(full_times), 5)\n",
    "sample_times = full_times[sample_indices]\n",
    "sample_I = full_I[sample_indices]\n",
    "\n",
    "# Add noise with some outliers\n",
    "noisy_I = sample_I + np.random.normal(0, 50, size=len(sample_I))\n",
    "\n",
    "# Add a few outliers (indices within range)\n",
    "n_samples = len(sample_times)\n",
    "outlier_indices = [min(5, n_samples-1), min(10, n_samples-1), min(15, n_samples-1)]\n",
    "outlier_indices = [i for i in outlier_indices if i < n_samples]\n",
    "noisy_I[outlier_indices] += np.random.uniform(200, 400, size=len(outlier_indices))\n",
    "\n",
    "# Ensure non-negative\n",
    "noisy_I = np.maximum(noisy_I, 0)\n",
    "\n",
    "print(f\"Sampled {len(sample_times)} time points from {len(full_times)} total\")\n",
    "print(f\"Added outliers at indices: {outlier_indices}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "2cc20190e87e326a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T18:31:30.153762393Z",
     "start_time": "2026-03-18T18:31:29.818932905Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the noisy data\n",
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "\n",
    "ax.plot(full_times, full_I, \n",
    "        'b-', label='Ground Truth', linewidth=2, alpha=0.7)\n",
    "ax.plot(sample_times, noisy_I, 'ro', label='Noisy Observations', markersize=6)\n",
    "if outlier_indices:\n",
    "    ax.plot(sample_times[outlier_indices], noisy_I[outlier_indices], \n",
    "            'g^', label='Outliers', markersize=10)\n",
    "\n",
    "ax.set_xlabel('Time (days)', fontsize=12)\n",
    "ax.set_ylabel('Number of Infected', fontsize=12)\n",
    "ax.set_title('Noisy Data with Outliers', fontsize=14)\n",
    "ax.legend(fontsize=11)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daa5d2b4",
   "metadata": {
    "papermill": {
     "duration": 0.006498,
     "end_time": "2026-03-18T17:33:54.462021+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:54.455523+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### 8.2 Compare SSE vs Huber Loss on Noisy Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "d543e1ee",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T18:33:53.639807535Z",
     "start_time": "2026-03-18T18:33:53.535107378Z"
    },
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:54.476549Z",
     "iopub.status.busy": "2026-03-18T17:33:54.476343Z",
     "iopub.status.idle": "2026-03-18T17:33:54.580908Z",
     "shell.execute_reply": "2026-03-18T17:33:54.580275Z"
    },
    "papermill": {
     "duration": 0.112884,
     "end_time": "2026-03-18T17:33:54.581678+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:54.468794+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Comparison on noisy data with outliers:\n",
      "  True:     beta=0.35, gamma=0.12\n",
      "  SSE:      beta=0.400, gamma=0.150\n",
      "  Huber:    beta=0.400, gamma=0.150\n"
     ]
    }
   ],
   "source": [
    "# Create dataset with noisy data\n",
    "noisy_dataset = Dataset(SIR())\n",
    "noisy_dataset.register(\n",
    "    name='noisy_infected',\n",
    "    values=noisy_I,\n",
    "    times=sample_times,\n",
    "    state_variable='I',\n",
    ")\n",
    "\n",
    "# Parameters to fit\n",
    "noisy_params = [\n",
    "    ParameterSpec(name='beta', bounds=(0.1, 0.8), initial=0.4),\n",
    "    ParameterSpec(name='gamma', bounds=(0.05, 0.3), initial=0.15),\n",
    "]\n",
    "\n",
    "# Fit with SSE\n",
    "fitter_sse = ModelFitter(\n",
    "    model=SIR(),\n",
    "    dataset=noisy_dataset,\n",
    "    parameters_to_fit=noisy_params,\n",
    "    total_population=TOTAL_POPULATION,\n",
    "    loss_fn=SumOfSquaredErrors(),\n",
    ")\n",
    "result_sse = fitter_sse.fit()\n",
    "\n",
    "# Fit with Huber loss (robust to outliers)\n",
    "fitter_huber = ModelFitter(\n",
    "    model=SIR(),\n",
    "    dataset=noisy_dataset,\n",
    "    parameters_to_fit=noisy_params,\n",
    "    total_population=TOTAL_POPULATION,\n",
    "    loss_fn=HuberLoss(delta=50.0),\n",
    ")\n",
    "result_huber = fitter_huber.fit()\n",
    "\n",
    "print(\"Comparison on noisy data with outliers:\")\n",
    "print(f\"  True:     beta=0.35, gamma=0.12\")\n",
    "print(f\"  SSE:      beta={result_sse.best_params['beta']:.3f}, gamma={result_sse.best_params['gamma']:.3f}\")\n",
    "print(f\"  Huber:    beta={result_huber.best_params['beta']:.3f}, gamma={result_huber.best_params['gamma']:.3f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "a4e46479",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T18:35:00.839113511Z",
     "start_time": "2026-03-18T18:35:00.578253863Z"
    },
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:54.602010Z",
     "iopub.status.busy": "2026-03-18T17:33:54.601796Z",
     "iopub.status.idle": "2026-03-18T17:33:54.752356Z",
     "shell.execute_reply": "2026-03-18T17:33:54.751913Z"
    },
    "papermill": {
     "duration": 0.161535,
     "end_time": "2026-03-18T17:33:54.753039+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:54.591504+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize comparison\n",
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "\n",
    "# Observations\n",
    "ax.plot(sample_times, noisy_I, 'ro', label='Noisy Observations', markersize=6, alpha=0.7)\n",
    "\n",
    "# Ground truth\n",
    "ax.plot(full_times, full_I, \n",
    "        'b-', label='Ground Truth', linewidth=2)\n",
    "\n",
    "# SSE fit\n",
    "if result_sse.fitted_model and result_sse.fitted_model.traces:\n",
    "    ax.plot(result_sse.fitted_model.traces['time'], result_sse.fitted_model.traces['I'],\n",
    "            'g--', label=f\"SSE Fit (β={result_sse.best_params['beta']:.3f})\", linewidth=2)\n",
    "\n",
    "# Huber fit\n",
    "if result_huber.fitted_model and result_huber.fitted_model.traces:\n",
    "    ax.plot(result_huber.fitted_model.traces['time'], result_huber.fitted_model.traces['I'],\n",
    "            'm:', label=f\"Huber Fit (β={result_huber.best_params['beta']:.3f})\", linewidth=2)\n",
    "\n",
    "ax.set_xlabel('Time (days)', fontsize=12)\n",
    "ax.set_ylabel('Number of Infected', fontsize=12)\n",
    "ax.set_title('Robust Fitting with Outliers: SSE vs Huber Loss', fontsize=14)\n",
    "ax.legend(fontsize=10)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b7cee27",
   "metadata": {
    "papermill": {
     "duration": 0.007807,
     "end_time": "2026-03-18T17:33:54.767781+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:54.759974+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 9. Convenience Function\n",
    "\n",
    "For quick fitting, use the `fit_model` convenience function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "9c180e94",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-18T18:35:55.569534554Z",
     "start_time": "2026-03-18T18:35:55.281644022Z"
    },
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:54.782298Z",
     "iopub.status.busy": "2026-03-18T17:33:54.782056Z",
     "iopub.status.idle": "2026-03-18T17:33:54.900276Z",
     "shell.execute_reply": "2026-03-18T17:33:54.899756Z"
    },
    "papermill": {
     "duration": 0.126547,
     "end_time": "2026-03-18T17:33:54.901219+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:54.774672+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Quick fit results:\n",
      "  beta: 0.4067\n",
      "  gamma: 0.1008\n",
      "  R0: 4.03\n"
     ]
    }
   ],
   "source": [
    "# Quick fit with convenience function\n",
    "result_quick = fit_model(\n",
    "    model=SIR(),\n",
    "    data={'I': observed_I},\n",
    "    times=true_times,\n",
    "    params_to_fit={'beta': (0.1, 1.0), 'gamma': (0.01, 0.5)},\n",
    "    total_population=TOTAL_POPULATION,\n",
    "    variable_mapping={'I': 'I'},\n",
    ")\n",
    "\n",
    "print(\"Quick fit results:\")\n",
    "print(f\"  beta: {result_quick.best_params['beta']:.4f}\")\n",
    "print(f\"  gamma: {result_quick.best_params['gamma']:.4f}\")\n",
    "print(f\"  R0: {result_quick.best_params['beta'] / result_quick.best_params['gamma']:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "228b14e4",
   "metadata": {
    "papermill": {
     "duration": 0.011247,
     "end_time": "2026-03-18T17:33:54.924195+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:54.912948+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## 10. Summary and Best Practices\n",
    "\n",
    "### Key Takeaways\n",
    "\n",
    "1. **Data Registration**: Always validate your dataset before fitting\n",
    "2. **Loss Functions**: Choose based on your data type:\n",
    "   - SSE for general use\n",
    "   - Poisson/NegBinom for count data\n",
    "   - Huber for data with outliers\n",
    "\n",
    "3. **Optimizers**:\n",
    "   - L-BFGS-B for fast, local optimization (good initial guess)\n",
    "   - Differential evolution for global optimization\n",
    "   - Multi-start for robustness\n",
    "\n",
    "4. **Parameter Scaling**: Use `log_scale=True` for parameters spanning orders of magnitude\n",
    "\n",
    "5. **Validation**: Use profile likelihood for confidence intervals\n",
    "\n",
    "### Common Pitfalls\n",
    "\n",
    "- **Poor initial guesses**: Can lead to local minima\n",
    "- **Wrong loss function**: SSE on count data can over-weight high values\n",
    "- **Too narrow bounds**: May exclude true parameter values\n",
    "- **Ignoring validation**: Data issues should be caught early"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "975c98f0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-03-18T17:33:54.947182Z",
     "iopub.status.busy": "2026-03-18T17:33:54.946933Z",
     "iopub.status.idle": "2026-03-18T17:33:54.950358Z",
     "shell.execute_reply": "2026-03-18T17:33:54.949680Z"
    },
    "papermill": {
     "duration": 0.01557,
     "end_time": "2026-03-18T17:33:54.951141+00:00",
     "exception": false,
     "start_time": "2026-03-18T17:33:54.935571+00:00",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "============================================================\n",
      "Tutorial complete!\n",
      "============================================================\n"
     ]
    }
   ],
   "source": [
    "# Clean up\n",
    "print(\"\\n\" + \"=\"*60)\n",
    "print(\"Tutorial complete!\")\n",
    "print(\"=\"*60)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "epimodels (3.12.11)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
  },
  "papermill": {
   "default_parameters": {},
   "duration": 10.564421,
   "end_time": "2026-03-18T17:33:55.574500+00:00",
   "environment_variables": {},
   "exception": null,
   "input_path": "docs/Examples/Model_Fitting.ipynb",
   "output_path": "/tmp/Model_Fitting_executed.ipynb",
   "parameters": {},
   "start_time": "2026-03-18T17:33:45.010079+00:00",
   "version": "2.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}