{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "049ed0ad",
   "metadata": {},
   "source": [
    "# Optimization Tutorial\n",
    "\n",
    "Trey V. Wenger (c) July 2025\n",
    "\n",
    "Here we demonstrate how to optimize the number of cloud components in a `HFSRatioModel` model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f1c46dd4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-05T19:59:06.989214Z",
     "start_time": "2024-08-05T19:59:04.772064Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pytensor version: 2.30.3\n",
      "pymc version: 5.22.0\n",
      "arviz version: 0.22.0dev\n",
      "bayes_spec version: 1.9.0\n",
      "bayes_hfs version: 1+0.gc6f9e00.dirty\n"
     ]
    }
   ],
   "source": [
    "# General imports    \n",
    "import time\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import arviz as az\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import pymc as pm\n",
    "\n",
    "import pytensor\n",
    "print(\"pytensor version:\", pytensor.__version__)\n",
    "\n",
    "print(\"pymc version:\", pm.__version__)\n",
    "print(\"arviz version:\", az.__version__)\n",
    "\n",
    "import bayes_spec\n",
    "print(\"bayes_spec version:\", bayes_spec.__version__)\n",
    "\n",
    "import bayes_hfs\n",
    "print(\"bayes_hfs version:\", bayes_hfs.__version__)\n",
    "\n",
    "# Notebook configuration\n",
    "pd.options.display.max_rows = None"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "095dcef8-0068-4fa2-810b-964f7fa525e6",
   "metadata": {},
   "source": [
    "## Preparing Molecule Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e927c983-f6d2-486e-bad2-2cae733c5061",
   "metadata": {},
   "outputs": [],
   "source": [
    "from bayes_hfs import get_molecule_data, supplement_molecule_data\n",
    "import pickle\n",
    "\n",
    "try:\n",
    "    all_mol_data_12CN, all_mol_metadata_12CN = get_molecule_data(\"CN, v=0,1\", fmin=100.0, fmax=200.0)\n",
    "    with open(\"mol_data_12CN.pkl\", \"wb\") as f:\n",
    "        pickle.dump(all_mol_data_12CN, f)\n",
    "    with open(\"mol_metadata_12CN.pkl\", \"wb\") as f:\n",
    "        pickle.dump(all_mol_metadata_12CN, f)\n",
    "except:\n",
    "    with open(\"mol_data_12CN.pkl\", \"rb\") as f:\n",
    "        all_mol_data_12CN = pickle.load(f)\n",
    "    with open(\"mol_metadata_12CN.pkl\", \"rb\") as f:\n",
    "        all_mol_metadata_12CN = pickle.load(f)\n",
    "\n",
    "# Keep only Kl = 0 transitions\n",
    "all_mol_data_12CN = all_mol_data_12CN[all_mol_data_12CN[\"Kl\"] == 0]\n",
    "\n",
    "# Add GLO\n",
    "all_mol_data_12CN[\"GLO\"] = 2 * all_mol_data_12CN[\"F1l\"]\n",
    "\n",
    "try:\n",
    "    all_mol_data_13CN, all_mol_metadata_13CN = get_molecule_data(\"C-13-N\", fmin=100.0, fmax=200.0)\n",
    "    with open(\"mol_data_13CN.pkl\", \"wb\") as f:\n",
    "        pickle.dump(all_mol_data_13CN, f)\n",
    "    with open(\"mol_metadata_13CN.pkl\", \"wb\") as f:\n",
    "        pickle.dump(all_mol_metadata_13CN, f)\n",
    "except:\n",
    "    with open(\"mol_data_13CN.pkl\", \"rb\") as f:\n",
    "        all_mol_data_13CN = pickle.load(f)\n",
    "    with open(\"mol_metadata_13CN.pkl\", \"rb\") as f:\n",
    "        all_mol_metadata_13CN = pickle.load(f)\n",
    "\n",
    "# Add GLO\n",
    "all_mol_data_13CN[\"GLO\"] = 2 * all_mol_data_13CN[\"F1l\"] + 1\n",
    "\n",
    "mol_data_12CN = supplement_molecule_data(all_mol_data_12CN, all_mol_metadata_12CN)\n",
    "mol_data_13CN = supplement_molecule_data(all_mol_data_13CN, all_mol_metadata_13CN)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70d808d8",
   "metadata": {},
   "source": [
    "## Model Definition and Simulated Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "da706708",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-05T19:59:10.588998Z",
     "start_time": "2024-08-05T19:59:06.991731Z"
    }
   },
   "outputs": [],
   "source": [
    "from bayes_spec import SpecData\n",
    "from bayes_hfs import HFSRatioModel\n",
    "\n",
    "# spectral axis definition\n",
    "freq_axis_12CN_1 = np.arange(113110.0, 113200.0, 0.2) # MHz\n",
    "freq_axis_12CN_2 = np.arange(113470.0, 113530.0, 0.2) # MHz\n",
    "freq_axis_13CN_1 = np.arange(108620.0, 108670.0, 0.2) # MHz\n",
    "freq_axis_13CN_2 = np.arange(108770.0, 108810.0, 0.2) # MHz\n",
    "\n",
    "# data noise can either be a scalar (assumed constant noise across the spectrum)\n",
    "# or an array of the same length as the data\n",
    "noise = 0.001 # K\n",
    "\n",
    "# brightness data. In this case, we just throw in some random data for now\n",
    "# since we are only doing this in order to simulate some actual data.\n",
    "brightness_data_12CN_1 = noise * np.random.randn(len(freq_axis_12CN_1)) # K\n",
    "brightness_data_12CN_2 = noise * np.random.randn(len(freq_axis_12CN_2)) # K\n",
    "brightness_data_13CN_1 = noise * np.random.randn(len(freq_axis_13CN_1)) # K\n",
    "brightness_data_13CN_2 = noise * np.random.randn(len(freq_axis_13CN_2)) # K\n",
    "\n",
    "# CNRatioModel expects observation names to contain either \"12CN\" or \"13CN\"\n",
    "observation_12CN_1 = SpecData(\n",
    "    freq_axis_12CN_1,\n",
    "    brightness_data_12CN_1,\n",
    "    noise,\n",
    "    xlabel=r\"LSRK Frequency (MHz)\",\n",
    "    ylabel=r\"CN $T_B$ (K)\",\n",
    ")\n",
    "observation_12CN_2 = SpecData(\n",
    "    freq_axis_12CN_2,\n",
    "    brightness_data_12CN_2,\n",
    "    noise,\n",
    "    xlabel=r\"LSRK Frequency (MHz)\",\n",
    "    ylabel=r\"CN $T_B$ (K)\",\n",
    ")\n",
    "observation_13CN_1 = SpecData(\n",
    "    freq_axis_13CN_1,\n",
    "    brightness_data_13CN_1,\n",
    "    noise,\n",
    "    xlabel=r\"LSRK Frequency (MHz)\",\n",
    "    ylabel=r\"$^{13}$CN $T_B$ (K)\",\n",
    ")\n",
    "observation_13CN_2 = SpecData(\n",
    "    freq_axis_13CN_2,\n",
    "    brightness_data_13CN_2,\n",
    "    noise,\n",
    "    xlabel=r\"LSRK Frequency (MHz)\",\n",
    "    ylabel=r\"$^{13}$CN $T_B$ (K)\",\n",
    ")\n",
    "dummy_data = {\n",
    "    \"12CN-1\": observation_12CN_1,\n",
    "    \"12CN-2\": observation_12CN_2,\n",
    "    \"13CN-1\": observation_13CN_1,\n",
    "    \"13CN-2\": observation_13CN_2,\n",
    "}\n",
    "\n",
    "# association each dataset with the related species\n",
    "mol_keys = {\n",
    "    \"12CN\": [\"12CN-1\", \"12CN-2\"],\n",
    "    \"13CN\": [\"13CN-1\", \"13CN-2\"],\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e183b304-a87b-4c53-83c6-03476a556585",
   "metadata": {},
   "outputs": [],
   "source": [
    "from bayes_hfs import HFSRatioModel\n",
    "from bayes_hfs import physics\n",
    "\n",
    "# Initialize and define the model\n",
    "n_clouds = 3 # number of cloud components\n",
    "baseline_degree = 0 # polynomial baseline degree\n",
    "model = HFSRatioModel(\n",
    "    mol_data_12CN, # molecular data for species 1\n",
    "    mol_data_13CN, # molecular data for species 2\n",
    "    mol_keys, # dataset association\n",
    "    dummy_data,\n",
    "    bg_temp = 2.7, # assumed background temperature (K)\n",
    "    Beff = 1.0, # beam efficiency\n",
    "    Feff = 1.0, # forward efficiency\n",
    "    n_clouds=n_clouds,\n",
    "    baseline_degree=baseline_degree,\n",
    "    seed=1234,\n",
    "    verbose=True\n",
    ")\n",
    "model.add_priors(\n",
    "    prior_log10_Ntot1 = [13.5, 0.5], # mean and width of log10 total column density prior of first species (cm-2)\n",
    "    prior_ratio = 0.1, # width of the column density ratio between the second and first species\n",
    "    prior_fwhm2 = 1.0, # width of FWHM^2 prior (km2 s-2)\n",
    "    prior_velocity = [-3.0, 3.0], # upper and lower limit of velocity prior (km/s)\n",
    "    prior_log10_Tex_CTEX = [0.75, 0.25], # mean and width of log10 CTEX excitation temperature prior (K)\n",
    "    assume_CTEX1 = False, # do not assume CTEX for the first species\n",
    "    assume_CTEX2 = False, # assume CTEX for the second species for speed\n",
    "    prior_log10_CTEX_variance = [-4.0, 1.0], # offset and width of log10 CTEX variance prior\n",
    "    clip_weights = 1.0e-9, # clip statistical weights between [clip_weights, 1-clip_weights]\n",
    "    clip_tau = -10.0, # clip optical depths below to prevent masers\n",
    "    prior_fwhm_L = None, # assume Gaussian line profile\n",
    "    prior_baseline_coeffs = None, # use default baseline priors\n",
    ")\n",
    "model.add_likelihood()\n",
    "\n",
    "sim_params = {\n",
    "    \"log10_Ntot_12CN\": np.array([13.8, 13.9, 14.0]),\n",
    "    \"ratio\": np.array([1.0/65.0, 1.0/60.0, 1.0/55.0]),\n",
    "    \"fwhm2\": np.array([1.0, 1.25, 1.5])**2.0,\n",
    "    \"velocity\": [-2.0, 0.0, 2.5],\n",
    "    \"log10_Tex_CTEX\": np.log10([4.46, 3.98, 3.16]),\n",
    "    \"log10_CTEX_variance\": np.array([-1.5, -2.0, -3.0]),\n",
    "    \"baseline_12CN-1_norm\": [0.0],\n",
    "    \"baseline_12CN-2_norm\": [0.0],\n",
    "    \"baseline_13CN-1_norm\": [0.0],\n",
    "    \"baseline_13CN-2_norm\": [0.0],\n",
    "}\n",
    "\n",
    "CTEX_weights_12CN = physics.calc_stat_weight(\n",
    "    model.mol1_data[\"states\"][\"deg\"][None, :],\n",
    "    model.mol1_data[\"states\"][\"E\"][None, :],\n",
    "    10.0 ** sim_params[\"log10_Tex_CTEX\"][:, None],\n",
    ").eval()\n",
    "\n",
    "CTEX_concentration_12CN = (\n",
    "    len(model.mol1_data[\"states\"][\"state\"])\n",
    "    * CTEX_weights_12CN\n",
    "    / 10.0**sim_params[\"log10_CTEX_variance\"][:, None]\n",
    ")\n",
    "\n",
    "from scipy.stats import dirichlet\n",
    "\n",
    "sim_params[\"weights_12CN\"] = np.stack([\n",
    "    dirichlet(CTEX_concentration_12CN[i]).rvs()[0] for i in range(n_clouds)\n",
    "])\n",
    "\n",
    "# add derived quantities to sim_params\n",
    "for key in model.cloud_deterministics:\n",
    "    if key not in sim_params.keys():\n",
    "        sim_params[key] = model.model[key].eval(sim_params, on_unused_input=\"ignore\")\n",
    "\n",
    "# Evaluate and save simulated observations\n",
    "sim_12CN_1 = model.model[\"12CN-1\"].eval(sim_params, on_unused_input=\"ignore\")\n",
    "sim_12CN_2 = model.model[\"12CN-2\"].eval(sim_params, on_unused_input=\"ignore\")\n",
    "sim_13CN_1 = model.model[\"13CN-1\"].eval(sim_params, on_unused_input=\"ignore\")\n",
    "sim_13CN_2 = model.model[\"13CN-2\"].eval(sim_params, on_unused_input=\"ignore\")\n",
    "\n",
    "# pack simulated data\n",
    "observation_12CN_1 = SpecData(\n",
    "    freq_axis_12CN_1,\n",
    "    sim_12CN_1,\n",
    "    noise,\n",
    "    xlabel=r\"LSRK Frequency (MHz)\",\n",
    "    ylabel=r\"CN $T_B$ (K)\",\n",
    ")\n",
    "observation_12CN_2 = SpecData(\n",
    "    freq_axis_12CN_2,\n",
    "    sim_12CN_2,\n",
    "    noise,\n",
    "    xlabel=r\"LSRK Frequency (MHz)\",\n",
    "    ylabel=r\"CN $T_B$ (K)\",\n",
    ")\n",
    "observation_13CN_1 = SpecData(\n",
    "    freq_axis_13CN_1,\n",
    "    sim_13CN_1,\n",
    "    noise,\n",
    "    xlabel=r\"LSRK Frequency (MHz)\",\n",
    "    ylabel=r\"$^{13}$CN $T_B$ (K)\",\n",
    ")\n",
    "observation_13CN_2 = SpecData(\n",
    "    freq_axis_13CN_2,\n",
    "    sim_13CN_2,\n",
    "    noise,\n",
    "    xlabel=r\"LSRK Frequency (MHz)\",\n",
    "    ylabel=r\"$^{13}$CN $T_B$ (K)\",\n",
    ")\n",
    "data = {\n",
    "    \"12CN-1\": observation_12CN_1,\n",
    "    \"12CN-2\": observation_12CN_2,\n",
    "    \"13CN-1\": observation_13CN_1,\n",
    "    \"13CN-2\": observation_13CN_2,\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0ecdcddd-9edc-4a57-81b1-a08663c693fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'log10_Ntot_12CN': array([13.8, 13.9, 14. ]),\n",
       " 'ratio': array([0.01538462, 0.01666667, 0.01818182]),\n",
       " 'fwhm2': array([1.    , 1.5625, 2.25  ]),\n",
       " 'velocity': [-2.0, 0.0, 2.5],\n",
       " 'log10_Tex_CTEX': array([0.64933486, 0.59988307, 0.49968708]),\n",
       " 'log10_CTEX_variance': array([-1.5, -2. , -3. ]),\n",
       " 'baseline_12CN-1_norm': [0.0],\n",
       " 'baseline_12CN-2_norm': [0.0],\n",
       " 'baseline_13CN-1_norm': [0.0],\n",
       " 'baseline_13CN-2_norm': [0.0],\n",
       " 'weights_12CN': array([[0.18099997, 0.35774445, 0.05141127, 0.10060146, 0.04239329,\n",
       "         0.11086714, 0.15598241],\n",
       "        [0.18391739, 0.37538564, 0.05147776, 0.0953406 , 0.04756006,\n",
       "         0.09716964, 0.14914891],\n",
       "        [0.22015952, 0.43069068, 0.03831167, 0.07664031, 0.03802426,\n",
       "         0.07752001, 0.11865354]]),\n",
       " 'log10_Ntot_13CN': array([11.98708664, 12.12184875, 12.25963731]),\n",
       " 'CTEX_weights_12CN': array([[1.99954842, 4.        , 0.59193533, 1.18327051, 0.58954346,\n",
       "         1.17923313, 1.76919492],\n",
       "        [1.99949396, 4.        , 0.51109864, 1.02161662, 0.5087849 ,\n",
       "         1.01771121, 1.52690069],\n",
       "        [1.99936267, 4.        , 0.35871387, 0.71691448, 0.35666979,\n",
       "         0.71346443, 1.07049146]]),\n",
       " 'Tex_12CN': array([[6.62377784, 4.84728125, 3.18024483],\n",
       "        [7.29549498, 5.1227256 , 3.24392405],\n",
       "        [3.48460532, 4.06018147, 3.16334071],\n",
       "        [3.66223901, 4.2517178 , 3.22631454],\n",
       "        [3.26304903, 3.72315005, 2.96168302],\n",
       "        [3.77468031, 4.02382954, 3.04074123],\n",
       "        [2.70675076, 4.08302572, 3.14052123],\n",
       "        [3.41789579, 3.88317284, 3.01669258],\n",
       "        [2.81252526, 4.2761819 , 3.20240169]]),\n",
       " 'tau_12CN': array([[0.02524333, 0.0360111 , 0.06420367],\n",
       "        [0.17973349, 0.2691383 , 0.50431054],\n",
       "        [0.28473286, 0.31504016, 0.51418762],\n",
       "        [0.33573084, 0.37674563, 0.64106031],\n",
       "        [0.38104257, 0.42733998, 0.68628587],\n",
       "        [0.88301926, 1.03135861, 1.74637405],\n",
       "        [0.32083078, 0.32311411, 0.53005213],\n",
       "        [0.26725006, 0.30419385, 0.50807069],\n",
       "        [0.03592579, 0.03636557, 0.06221058]]),\n",
       " 'tau_total_12CN': array([2.71350897, 3.11930731, 5.25675546]),\n",
       " 'TR_12CN': array([[4.27597848, 2.62918409, 1.20296471],\n",
       "        [4.91419543, 2.87859882, 1.25318148],\n",
       "        [1.44740238, 1.93265667, 1.18910571],\n",
       "        [1.59417095, 2.09880298, 1.23863245],\n",
       "        [1.26436858, 1.64130685, 1.0295351 ],\n",
       "        [1.68461726, 1.89689066, 1.09001642],\n",
       "        [0.8404223 , 1.94780861, 1.16743383],\n",
       "        [1.38876463, 1.77628294, 1.07132523],\n",
       "        [0.9174165 , 2.11549053, 1.21586649]]),\n",
       " 'CTEX_weights_13CN': array([[3.        , 0.99376119, 2.9815721 , 4.9699281 , 0.92851903,\n",
       "         0.31070072, 0.93202191, 1.55316693, 0.30874373, 0.92620269,\n",
       "         1.54373121, 0.92472116, 1.54142752, 2.15832747],\n",
       "        [3.        , 0.9930114 , 2.9793573 , 4.96631358, 0.80605378,\n",
       "         0.26984676, 0.80946217, 1.34890613, 0.26794283, 0.80380078,\n",
       "         1.33972638, 0.80236011, 1.3374862 , 1.87280054],\n",
       "        [3.        , 0.9912059 , 2.9740239 , 4.95760931, 0.57313394,\n",
       "         0.192086  , 0.57618799, 0.96013626, 0.19038061, 0.57111701,\n",
       "         0.95191395, 0.56982806, 0.94990964, 1.33015962]]),\n",
       " 'Tex_13CN': array([[3.63387014, 4.0123908 , 3.08464866],\n",
       "        [3.83675886, 4.4342716 , 3.08229104],\n",
       "        [3.84009247, 3.76818165, 3.2042096 ],\n",
       "        [3.74209719, 4.19126825, 3.15773939],\n",
       "        [4.66544699, 3.82749742, 3.11567771],\n",
       "        [4.52148561, 4.26470704, 3.07173897],\n",
       "        [5.00127202, 4.48112345, 3.08933137],\n",
       "        [5.39889112, 4.17955656, 3.20886035],\n",
       "        [5.20750875, 4.7045325 , 3.16240343],\n",
       "        [4.0212438 , 5.15561858, 3.02750414],\n",
       "        [4.02487718, 4.28049286, 3.14440333],\n",
       "        [3.89187731, 3.60468882, 2.9993573 ],\n",
       "        [4.17098129, 4.06799019, 3.15767616],\n",
       "        [4.19325594, 3.19195589, 3.24091144],\n",
       "        [4.12801426, 3.40738764, 3.11165721],\n",
       "        [4.93507743, 4.35670617, 3.05954754],\n",
       "        [4.05618042, 4.56249   , 3.11278043],\n",
       "        [4.01553487, 3.74768332, 3.06805292],\n",
       "        [3.95529061, 4.28992818, 3.1329999 ],\n",
       "        [4.40618018, 3.92832745, 3.12736718],\n",
       "        [4.18768408, 4.81107389, 3.18901639],\n",
       "        [4.46192129, 4.46628177, 3.31607163],\n",
       "        [4.2783927 , 4.38690557, 3.08338147],\n",
       "        [4.33093502, 5.06851471, 3.26663988],\n",
       "        [5.75698581, 4.81377011, 3.1490468 ],\n",
       "        [4.38657499, 4.66567441, 3.10011369],\n",
       "        [4.41108682, 3.55311919, 3.17987158],\n",
       "        [4.33931568, 3.82058713, 3.05597262]]),\n",
       " 'tau_13CN': array([[6.91016104e-05, 8.62078555e-05, 1.62414632e-04],\n",
       "        [8.13865602e-05, 1.16170996e-04, 1.98952714e-04],\n",
       "        [3.17002408e-05, 4.90748819e-05, 7.63535671e-05],\n",
       "        [1.47575919e-04, 1.80064378e-04, 3.49181577e-04],\n",
       "        [7.71761587e-05, 1.30964896e-04, 2.07535796e-04],\n",
       "        [2.17990215e-04, 2.89708089e-04, 5.72893422e-04],\n",
       "        [2.47769861e-04, 3.43972966e-04, 6.84887892e-04],\n",
       "        [7.31425101e-04, 1.29197271e-03, 2.11177097e-03],\n",
       "        [1.54527530e-03, 2.10941210e-03, 4.34270099e-03],\n",
       "        [8.23550053e-04, 9.98210130e-04, 2.27788743e-03],\n",
       "        [2.47848809e-03, 3.32640756e-03, 6.75966969e-03],\n",
       "        [1.07463295e-03, 1.45504622e-03, 2.63385994e-03],\n",
       "        [1.13999026e-03, 1.77112462e-03, 2.87381935e-03],\n",
       "        [8.52386088e-04, 1.47913347e-03, 2.13240347e-03],\n",
       "        [7.37813449e-04, 1.23676746e-03, 1.86095314e-03],\n",
       "        [3.77625764e-03, 5.59115358e-03, 1.15866992e-02],\n",
       "        [3.38711307e-03, 4.11006613e-03, 8.37106802e-03],\n",
       "        [9.41168554e-04, 1.25350083e-03, 2.32747602e-03],\n",
       "        [6.96307786e-03, 8.62039131e-03, 1.69549542e-02],\n",
       "        [3.35612901e-03, 5.45424590e-03, 8.73289194e-03],\n",
       "        [1.64511631e-03, 1.99815187e-03, 4.08158818e-03],\n",
       "        [1.15227317e-03, 1.76718272e-03, 2.94828359e-03],\n",
       "        [1.25328535e-03, 1.59472409e-03, 3.19246242e-03],\n",
       "        [8.79240704e-05, 1.04039577e-04, 2.20310632e-04],\n",
       "        [1.16316006e-05, 1.78720936e-05, 3.86220767e-05],\n",
       "        [2.82315246e-04, 3.78176622e-04, 8.07986128e-04],\n",
       "        [7.29919449e-05, 1.12072231e-04, 2.07457051e-04],\n",
       "        [1.98775501e-04, 2.92855454e-04, 5.68804114e-04]]),\n",
       " 'tau_total_13CN': array([0.03338432, 0.04615867, 0.08728389]),\n",
       " 'TR_13CN': array([[1.63769168, 1.96304246, 1.18617309],\n",
       "        [1.8108763 , 2.33556625, 1.184289  ],\n",
       "        [1.8136662 , 1.75193053, 1.28186856],\n",
       "        [1.72943434, 2.11957112, 1.24428871],\n",
       "        [2.54293543, 1.80263014, 1.21062722],\n",
       "        [2.41313236, 2.18424104, 1.17551796],\n",
       "        [2.84302083, 2.37219693, 1.18580068],\n",
       "        [3.20891541, 2.10436621, 1.28139781],\n",
       "        [3.03194919, 2.5728406 , 1.24385719],\n",
       "        [1.96259901, 2.98090426, 1.13437175],\n",
       "        [1.96568165, 2.19018492, 1.22695166],\n",
       "        [1.85033635, 1.60534487, 1.11222735],\n",
       "        [2.09347408, 2.00319904, 1.23749058],\n",
       "        [2.11306356, 1.26499364, 1.30450211],\n",
       "        [2.0557196 , 1.44064407, 1.20074399],\n",
       "        [2.77867001, 2.25756471, 1.15937469],\n",
       "        [1.99268517, 2.44131639, 1.20148997],\n",
       "        [1.9572337 , 1.72631391, 1.16600468],\n",
       "        [1.90319648, 2.19642801, 1.21615459],\n",
       "        [2.29963139, 1.87982136, 1.21163864],\n",
       "        [2.10608725, 2.66372918, 1.26092144],\n",
       "        [2.3491845 , 2.35308013, 1.3637902 ],\n",
       "        [2.18598191, 2.28226144, 1.17653557],\n",
       "        [2.23236108, 2.89813924, 1.32336919],\n",
       "        [3.53239079, 2.66305005, 1.2265218 ],\n",
       "        [2.2756973 , 2.52556554, 1.1848887 ],\n",
       "        [2.29749236, 1.55445369, 1.24843537],\n",
       "        [2.23371459, 1.78103118, 1.15001426]])}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sim_params"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20a2225f",
   "metadata": {},
   "source": [
    "## `Optimize`\n",
    "\n",
    "We use the `Optimize` class for optimization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ec488d1d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-05T19:59:10.725568Z",
     "start_time": "2024-08-05T19:59:10.599441Z"
    }
   },
   "outputs": [],
   "source": [
    "from bayes_spec import Optimize\n",
    "from bayes_hfs import HFSRatioModel\n",
    "\n",
    "# Initialize optimizer\n",
    "opt = Optimize(\n",
    "    HFSRatioModel,\n",
    "    mol_data_12CN, # molecular data for species 1\n",
    "    mol_data_13CN, # molecular data for species 2\n",
    "    mol_keys, # dataset association\n",
    "    data,\n",
    "    bg_temp = 2.7, # assumed background temperature (K)\n",
    "    Beff = 1.0, # beam efficiency\n",
    "    Feff = 1.0, # forward efficiency\n",
    "    max_n_clouds=5,\n",
    "    baseline_degree=baseline_degree,\n",
    "    seed=1234,\n",
    "    verbose=True\n",
    ")\n",
    "\n",
    "# Define each model\n",
    "opt.add_priors(\n",
    "    prior_log10_Ntot1 = [13.5, 0.5], # mean and width of log10 total column density prior of first species (cm-2)\n",
    "    prior_ratio = 0.1, # width of the column density ratio between the second and first species\n",
    "    prior_fwhm2 = 1.0, # width of FWHM^2 prior (km2 s-2)\n",
    "    prior_velocity = [-3.0, 3.0], # upper and lower limit of velocity prior (km/s)\n",
    "    prior_log10_Tex_CTEX = [0.75, 0.25], # mean and width of log10 CTEX excitation temperature prior (K)\n",
    "    assume_CTEX1 = False, # do not assume CTEX for the first species\n",
    "    assume_CTEX2 = True, # assume CTEX for the second species for speed\n",
    "    prior_log10_CTEX_variance = [-4.0, 1.0], # offset and width of log10 CTEX variance prior\n",
    "    clip_weights = 1.0e-9, # clip statistical weights between [clip_weights, 1-clip_weights]\n",
    "    clip_tau = -10.0, # clip optical depths below to prevent masers\n",
    "    prior_fwhm_L = None, # assume Gaussian line profile\n",
    "    prior_baseline_coeffs = None, # use default baseline priors\n",
    ")\n",
    "opt.add_likelihood()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b4b0d06",
   "metadata": {},
   "source": [
    "`Optimize` has created `max_n_clouds` models, where `opt.models[1]` has `n_clouds=1`, `opt.models[2]` has `n_clouds=2`, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e66910c3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-05T19:59:10.730059Z",
     "start_time": "2024-08-05T19:59:10.727121Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<bayes_hfs.hfs_ratio_model.HFSRatioModel object at 0x7bc38d9b2650>\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "print(opt.models[4])\n",
    "print(opt.models[4].n_clouds)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cc17df3",
   "metadata": {},
   "source": [
    "By default (`approx=True`), the optimization algorithm first loops over every model and approximates the posterior distribution using variational inference. This is generally a bad idea, since VI is only an approximation and tends to struggle with complex models. Instead we use `approx=False` to sample every model with MCMC. This is slower but more robust.\n",
    "\n",
    "We can supply arguments to `fit` and `sample` via dictionaries. Whichever model is the first to have a BIC within `bic_threshold` of the minimum BIC is the \"best\" model. The algorithm will terminate early if successive models have increasing BICs or fail to converge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "cf08c08c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-05T19:59:59.141293Z",
     "start_time": "2024-08-05T19:59:10.731559Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Null hypothesis BIC = 1.132e+07\n",
      "Sampling n_cloud = 1 posterior...\n",
      "Initializing NUTS using custom advi+adapt_diag strategy\n"
     ]
    },
    {
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       "model_id": "dc0620af45164011a2d9f1d40849f287",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 41000\n",
      "Interrupted at 40,999 [20%]: Average Loss = 1.8552e+17\n",
      "Multiprocess sampling (8 chains in 8 jobs)\n",
      "NUTS: [baseline_12CN-1_norm, baseline_12CN-2_norm, baseline_13CN-1_norm, baseline_13CN-2_norm, log10_Ntot_12CN_norm, ratio_norm, fwhm2_norm, velocity_norm, log10_Tex_CTEX_norm, log10_CTEX_variance_norm, weights_12CN_norm]\n"
     ]
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       "Output()"
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    },
    {
     "data": {
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 8 chains for 1_000 tune and 1_000 draw iterations (8_000 + 8_000 draws total) took 1162 seconds.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding log-likelihood to trace\n"
     ]
    },
    {
     "data": {
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       "Output()"
      ]
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
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     },
     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GMM converged to unique solution\n",
      "n_cloud = 1 solution = 0 BIC = 2.335e+06\n",
      "\n",
      "Sampling n_cloud = 2 posterior...\n",
      "Initializing NUTS using custom advi+adapt_diag strategy\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
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       "version_minor": 0
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       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 45400\n",
      "Interrupted at 45,399 [22%]: Average Loss = 7.3459e+19\n",
      "Multiprocess sampling (8 chains in 8 jobs)\n",
      "NUTS: [baseline_12CN-1_norm, baseline_12CN-2_norm, baseline_13CN-1_norm, baseline_13CN-2_norm, log10_Ntot_12CN_norm, ratio_norm, fwhm2_norm, velocity_norm, log10_Tex_CTEX_norm, log10_CTEX_variance_norm, weights_12CN_norm]\n"
     ]
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       "Output()"
      ]
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    },
    {
     "data": {
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 8 chains for 1_000 tune and 1_000 draw iterations (8_000 + 8_000 draws total) took 5737 seconds.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding log-likelihood to trace\n"
     ]
    },
    {
     "data": {
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       "Output()"
      ]
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     "metadata": {},
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
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     },
     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GMM converged to unique solution\n",
      "n_cloud = 2 solution = 0 BIC = 6.866e+05\n",
      "\n",
      "Sampling n_cloud = 3 posterior...\n",
      "Initializing NUTS using custom advi+adapt_diag strategy\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ba11fdc1774149698934949b92106ed3",
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       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 56200\n",
      "Interrupted at 56,199 [28%]: Average Loss = 4.8623e+28\n",
      "Multiprocess sampling (8 chains in 8 jobs)\n",
      "NUTS: [baseline_12CN-1_norm, baseline_12CN-2_norm, baseline_13CN-1_norm, baseline_13CN-2_norm, log10_Ntot_12CN_norm, ratio_norm, fwhm2_norm, velocity_norm, log10_Tex_CTEX_norm, log10_CTEX_variance_norm, weights_12CN_norm]\n"
     ]
    },
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       "Output()"
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
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      "text/plain": []
     },
     "metadata": {},
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 8 chains for 1_000 tune and 1_000 draw iterations (8_000 + 8_000 draws total) took 1155 seconds.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding log-likelihood to trace\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
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       "Output()"
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    },
    {
     "data": {
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
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     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There were 990 divergences in converged chains.\n",
      "GMM converged to unique solution\n",
      "6 of 8 chains appear converged.\n",
      "n_cloud = 3 solution = 0 BIC = -1.277e+04\n",
      "\n",
      "Sampling n_cloud = 4 posterior...\n",
      "Initializing NUTS using custom advi+adapt_diag strategy\n"
     ]
    },
    {
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       "Output()"
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    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
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     },
     "metadata": {},
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 65600\n",
      "Interrupted at 65,599 [32%]: Average Loss = 7.3701e+21\n",
      "Multiprocess sampling (8 chains in 8 jobs)\n",
      "NUTS: [baseline_12CN-1_norm, baseline_12CN-2_norm, baseline_13CN-1_norm, baseline_13CN-2_norm, log10_Ntot_12CN_norm, ratio_norm, fwhm2_norm, velocity_norm, log10_Tex_CTEX_norm, log10_CTEX_variance_norm, weights_12CN_norm]\n"
     ]
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       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
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     },
     "metadata": {},
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 8 chains for 1_000 tune and 1_000 draw iterations (8_000 + 8_000 draws total) took 5104 seconds.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding log-likelihood to trace\n"
     ]
    },
    {
     "data": {
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       "Output()"
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    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
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     },
     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There were 330 divergences in converged chains.\n",
      "GMM found 3 unique solutions\n",
      "Solution 0: chains [np.int64(0), np.int64(1)]\n",
      "Solution 1: chains [np.int64(3), np.int64(6), np.int64(7)]\n",
      "Solution 2: chains [np.int64(4), np.int64(5)]\n",
      "7 of 8 chains appear converged.\n",
      "n_cloud = 4 solution = 0 BIC = -1.267e+04\n",
      "n_cloud = 4 solution = 1 BIC = -1.267e+04\n",
      "n_cloud = 4 solution = 2 BIC = -1.267e+04\n",
      "\n",
      "Stopping criteria met.\n",
      "Sampling n_cloud = 5 posterior...\n",
      "Initializing NUTS using custom advi+adapt_diag strategy\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "71866095674347f69b1cc5f38139569f",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 76300\n",
      "Interrupted at 76,299 [38%]: Average Loss = 7.9475e+24\n",
      "Multiprocess sampling (8 chains in 8 jobs)\n",
      "NUTS: [baseline_12CN-1_norm, baseline_12CN-2_norm, baseline_13CN-1_norm, baseline_13CN-2_norm, log10_Ntot_12CN_norm, ratio_norm, fwhm2_norm, velocity_norm, log10_Tex_CTEX_norm, log10_CTEX_variance_norm, weights_12CN_norm]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "096add5ed5b644109f017eb7ea71b837",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 8 chains for 1_000 tune and 1_000 draw iterations (8_000 + 8_000 draws total) took 6427 seconds.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding log-likelihood to trace\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d928aec3bcf945d1a21f8b1306d1813c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There were 271 divergences in converged chains.\n",
      "No solution found!\n",
      "0 of 8 chains appear converged.\n",
      "\n",
      "Stopping criteria met.\n",
      "Stopping early.\n"
     ]
    }
   ],
   "source": [
    "fit_kwargs = {\n",
    "    \"rel_tolerance\": 0.01,\n",
    "    \"abs_tolerance\": 0.01,\n",
    "    \"learning_rate\": 0.001,\n",
    "}\n",
    "sample_kwargs = {\n",
    "    \"chains\": 8,\n",
    "    \"cores\": 8,\n",
    "    \"n_init\": 200_000,\n",
    "    \"init_kwargs\": fit_kwargs,\n",
    "    \"nuts_kwargs\": {\"target_accept\": 0.9},\n",
    "}\n",
    "solve_kwargs = {\n",
    "    \"init_params\": \"random_from_data\",\n",
    "    \"n_init\": 10,\n",
    "    \"max_iter\": 1_000,\n",
    "    \"kl_div_threshold\": 0.1,\n",
    "}\n",
    "opt.optimize(\n",
    "    bic_threshold=10.0,\n",
    "    sample_kwargs=sample_kwargs,\n",
    "    fit_kwargs=fit_kwargs,\n",
    "    solve_kwargs=solve_kwargs,\n",
    "    approx=False,\n",
    "    start_spread = {\"velocity_norm\": [0.1, 0.9]},\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0486ae8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt.best_model.n_clouds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ba72835b",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [12CN-1, 12CN-2, 13CN-1, 13CN-2]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "41f75f108e0149ed902327f03bd229e3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bayes_spec.plots import plot_predictive\n",
    "\n",
    "posterior = opt.best_model.sample_posterior_predictive(\n",
    "    thin=100, # keep one in {thin} posterior samples\n",
    ")\n",
    "axes = plot_predictive(opt.best_model.data, posterior.posterior_predictive)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "99a89912-b4ae-4f25-a1af-8005328aed12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'BIC')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(opt.bics.keys(), opt.bics.values(), 'ko')\n",
    "plt.xlabel(\"Number of Components\")\n",
    "plt.ylabel(\"BIC\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b7fc966b-4fdf-449f-8701-bd5b90869830",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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