{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2a6f87e3-0d3c-4da4-90c6-eb9e00bd1e29",
   "metadata": {},
   "source": [
    "# Optimization Tutorial\n",
    "\n",
    "Trey V. Wenger (c) August 2024\n",
    "\n",
    "Here we demonstrate how to determine the optimal number of components for a `YPlusModel` model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ed4fe22b-ecee-424a-bcb9-c7b29cfa12f9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-06-22T01:55:45.529239Z",
     "start_time": "2024-06-22T01:55:43.485984Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pymc version: 5.16.2\n",
      "bayes_spec version: 1.7.2+4.gfef408d\n",
      "bayes_yplus version: 1.3.1+0.gb4f2b7d.dirty\n"
     ]
    }
   ],
   "source": [
    "# General imports    \n",
    "import os\n",
    "import pickle\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",
    "print(\"pymc version:\", pm.__version__)\n",
    "\n",
    "import bayes_spec\n",
    "print(\"bayes_spec version:\", bayes_spec.__version__)\n",
    "\n",
    "import bayes_yplus\n",
    "print(\"bayes_yplus version:\", bayes_yplus.__version__)\n",
    "\n",
    "# Notebook configuration\n",
    "pd.options.display.max_rows = None"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10a63f40",
   "metadata": {},
   "source": [
    "## Simulating Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2fe2541d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from bayes_spec import SpecData\n",
    "\n",
    "# spectral axis definition\n",
    "spec_axis = np.linspace(-200.0, 100.0, 251) # km s-1\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 = 1.0 # mK\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 = noise * np.random.randn(len(spec_axis)) # mK\n",
    "\n",
    "# The data can be named anything. We name our data \"observation\"\n",
    "observation = SpecData(\n",
    "    spec_axis,\n",
    "    brightness_data,\n",
    "    noise,\n",
    "    xlabel=r\"$V_{\\rm LSR}$ (km s$^{-1}$)\",\n",
    "    ylabel=\"Brightness Temperature (mK)\",\n",
    ")\n",
    "dummy_data = {\"observation\": observation}\n",
    "\n",
    "from bayes_yplus import YPlusModel\n",
    "\n",
    "# Initialize and define the model\n",
    "n_clouds = 3\n",
    "baseline_degree = 1\n",
    "model = YPlusModel(\n",
    "    dummy_data,\n",
    "    n_clouds=n_clouds,\n",
    "    baseline_degree=baseline_degree,\n",
    "    seed=1234,\n",
    "    verbose=True\n",
    ")\n",
    "model.add_priors(\n",
    "    prior_H_area = 1000.0, # width of the H_area prior (mK km s-1)\n",
    "    prior_H_center = [0.0, 25.0], # mean and width of H_center prior (km s-1)\n",
    "    prior_H_fwhm = [25.0, 10.0], # mean and width of H FWHM prior (km s-1)\n",
    "    prior_He_H_fwhm_ratio = [1.0, 0.1], # mean and width of He/H FWHM ratio prior\n",
    "    prior_yplus = 0.05, # width of yplus prior\n",
    "    prior_rms = None, # do not infer spectral rms\n",
    "    prior_baseline_coeffs = None, # use default baseline priors\n",
    "    ordered = False, # do not assume ordered components\n",
    ")\n",
    "model.add_likelihood()\n",
    "\n",
    "sim_brightness = model.model.observation.eval({\n",
    "    \"H_area\": [800.0, 1000.0, 1200.0],\n",
    "    \"H_center\": [-30.0, 5.0, 25.0],\n",
    "    \"H_fwhm\": [20.0, 25.0, 30.0],\n",
    "    \"He_H_fwhm_ratio\": [1.1, 1.0, 0.9],\n",
    "    \"yplus\": [0.1, 0.15, 0.05],\n",
    "    \"baseline_observation_norm\": [-2.0, 1.5], # normalized baseline coefficients\n",
    "})\n",
    "\n",
    "# Plot the simulated data\n",
    "plt.plot(dummy_data[\"observation\"].spectral, sim_brightness, 'k-')\n",
    "plt.xlabel(dummy_data[\"observation\"].xlabel)\n",
    "_ = plt.ylabel(dummy_data[\"observation\"].ylabel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "711c7b91",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "observation 251\n"
     ]
    }
   ],
   "source": [
    "# Now we pack the simulated spectrum into a new SpecData instance\n",
    "observation = SpecData(\n",
    "    spec_axis,\n",
    "    sim_brightness,\n",
    "    noise,\n",
    "    xlabel=r\"$V_{\\rm LSR}$ (km s$^{-1}$)\",\n",
    "    ylabel=\"Brightness Temperature (mK)\",\n",
    ")\n",
    "data = {\"observation\": observation}\n",
    "\n",
    "for label, dataset in data.items():\n",
    "    print(label, len(dataset.spectral))\n",
    "    # HACK: normalize data by noise\n",
    "    dataset._brightness_offset = np.median(dataset.brightness)\n",
    "    dataset._brightness_scale = dataset.noise"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4221bb69-9ae1-41c1-878c-719a255e837b",
   "metadata": {},
   "source": [
    "## Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "519f9cf7-31f3-410b-84cf-51f8e4f5a4ed",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-06-22T01:55:45.831760Z",
     "start_time": "2024-06-22T01:55:45.788818Z"
    }
   },
   "outputs": [],
   "source": [
    "from bayes_spec import Optimize\n",
    "\n",
    "# Initialize optimizer\n",
    "opt = Optimize(\n",
    "    YPlusModel,  # model definition\n",
    "    data,  # data dictionary\n",
    "    max_n_clouds=5,  # maximum number of clouds\n",
    "    baseline_degree=baseline_degree,  # polynomial baseline degree\n",
    "    seed=1234,  # random seed\n",
    "    verbose=True,  # verbosity\n",
    ")\n",
    "\n",
    "# Define each model\n",
    "opt.add_priors(\n",
    "    prior_H_area = 1000.0, # width of the H_area prior (mK km s-1)\n",
    "    prior_H_center = [0.0, 25.0], # mean and width of H_center prior (km s-1)\n",
    "    prior_H_fwhm = [25.0, 10.0], # mean and width of H FWHM prior (km s-1)\n",
    "    prior_He_H_fwhm_ratio = [1.0, 0.1], # mean and width of He/H FWHM ratio prior\n",
    "    prior_yplus = 0.05, # width of yplus prior\n",
    "    prior_rms = None, # do not infer spectral rms\n",
    "    prior_baseline_coeffs = None, # use default baseline priors\n",
    "    ordered = False, # do not assume ordered components\n",
    ")\n",
    "opt.add_likelihood()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "89d44baa-5328-4b5b-9418-b76f53f5360d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-06-22T01:55:45.979648Z",
     "start_time": "2024-06-22T01:55:45.833211Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Null hypothesis BIC = 5.501e+04\n",
      "Approximating n_cloud = 1 posterior...\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d24d5a6f4c8a43c69c249f9c59064387",
       "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"
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      "text/plain": []
     },
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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\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 3600\n",
      "Interrupted at 3,599 [3%]: Average Loss = 9,463.5\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "fd46f6a869024fbab9f5ac4b68780ba9",
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      "text/plain": [
       "Output()"
      ]
     },
     "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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     },
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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\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_cloud = 1 BIC = 1.078e+04\n",
      "\n",
      "Approximating n_cloud = 2 posterior...\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "60f5a3cadcb5415b817448604e9b03d4",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
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     "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"
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     },
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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\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 5300\n",
      "Interrupted at 5,299 [5%]: Average Loss = 5,273.1\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c50cd0515a454628bb6d18399833b1e2",
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      "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"
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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\">\n",
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      ],
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       "\n"
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     "metadata": {},
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_cloud = 2 BIC = 1.095e+03\n",
      "\n",
      "Approximating n_cloud = 3 posterior...\n"
     ]
    },
    {
     "data": {
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       "model_id": "c64cfa32ae354dfaad2b2e96f83f44b2",
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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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    },
    {
     "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\">\n",
       "</pre>\n"
      ],
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       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 4900\n",
      "Interrupted at 4,899 [4%]: Average Loss = 5,591.2\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "53fec10d1736463b98efc95edd63bca7",
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       "Output()"
      ]
     },
     "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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     },
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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\">\n",
       "</pre>\n"
      ],
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       "\n"
      ]
     },
     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_cloud = 3 BIC = 8.448e+02\n",
      "\n",
      "Approximating n_cloud = 4 posterior...\n"
     ]
    },
    {
     "data": {
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       "model_id": "36ab2f28af2e43348c87de7cb6aa0d56",
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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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      ],
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       "\n"
      ]
     },
     "metadata": {},
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 5100\n",
      "Interrupted at 5,099 [5%]: Average Loss = 6,333.1\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2e8ea8492c0c4acb8d3d3ab82f287c2c",
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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"
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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\">\n",
       "</pre>\n"
      ],
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       "\n"
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     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_cloud = 4 BIC = 8.626e+02\n",
      "\n",
      "Approximating n_cloud = 5 posterior...\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "75863ae150f5466bba95a286357b3ec2",
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       "version_minor": 0
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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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       "</pre>\n"
      ],
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       "\n"
      ]
     },
     "metadata": {},
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 4900\n",
      "Interrupted at 4,899 [4%]: Average Loss = 8,077.3\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b13f89a1778a4939933d3f046904b6c2",
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       "version_minor": 0
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      "text/plain": [
       "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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     "data": {
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      ],
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       "\n"
      ]
     },
     "metadata": {},
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    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n_cloud = 5 BIC = 9.093e+02\n",
      "\n",
      "Sampling best model (n_cloud = 3)...\n",
      "Initializing NUTS using custom advi+adapt_diag strategy\n"
     ]
    },
    {
     "data": {
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       "model_id": "8c34906d740a41febbc4924d2db6efa3",
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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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      ],
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       "\n"
      ]
     },
     "metadata": {},
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    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Convergence achieved at 4900\n",
      "Interrupted at 4,899 [4%]: Average Loss = 5,591.2\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [baseline_observation_norm, H_center_norm, H_area_norm, H_fwhm, He_H_fwhm_ratio, yplus_norm]\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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     "data": {
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       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 49 seconds.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adding log-likelihood to trace\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0d5f7bd799d94e77a5e53a546dc35cc0",
       "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"
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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\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GMM converged to unique solution\n"
     ]
    }
   ],
   "source": [
    "fit_kwargs = {\n",
    "    \"rel_tolerance\": 0.01,\n",
    "    \"abs_tolerance\": 0.05,\n",
    "    \"learning_rate\": 1e-2,\n",
    "}\n",
    "sample_kwargs = {\n",
    "    \"chains\": 4,\n",
    "    \"cores\": 4,\n",
    "    \"init_kwargs\": fit_kwargs,\n",
    "    \"nuts_kwargs\": {\"target_accept\": 0.8},\n",
    "}\n",
    "opt.optimize(bic_threshold=10.0, sample_kwargs=sample_kwargs, fit_kwargs=fit_kwargs, approx=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "81448d20",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>H_center[0]</th>\n",
       "      <td>-29.956</td>\n",
       "      <td>0.107</td>\n",
       "      <td>-30.154</td>\n",
       "      <td>-29.750</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2550.0</td>\n",
       "      <td>2600.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>H_center[1]</th>\n",
       "      <td>23.939</td>\n",
       "      <td>1.218</td>\n",
       "      <td>21.681</td>\n",
       "      <td>26.268</td>\n",
       "      <td>0.048</td>\n",
       "      <td>0.034</td>\n",
       "      <td>656.0</td>\n",
       "      <td>1167.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>H_center[2]</th>\n",
       "      <td>4.453</td>\n",
       "      <td>0.709</td>\n",
       "      <td>3.116</td>\n",
       "      <td>5.803</td>\n",
       "      <td>0.027</td>\n",
       "      <td>0.019</td>\n",
       "      <td>678.0</td>\n",
       "      <td>1093.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>H_area[0]</th>\n",
       "      <td>796.558</td>\n",
       "      <td>10.231</td>\n",
       "      <td>777.035</td>\n",
       "      <td>815.408</td>\n",
       "      <td>0.257</td>\n",
       "      <td>0.182</td>\n",
       "      <td>1585.0</td>\n",
       "      <td>2157.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>H_area[1]</th>\n",
       "      <td>1289.133</td>\n",
       "      <td>122.922</td>\n",
       "      <td>1054.824</td>\n",
       "      <td>1519.116</td>\n",
       "      <td>4.838</td>\n",
       "      <td>3.426</td>\n",
       "      <td>649.0</td>\n",
       "      <td>1235.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>H_area[2]</th>\n",
       "      <td>883.763</td>\n",
       "      <td>121.603</td>\n",
       "      <td>652.021</td>\n",
       "      <td>1111.094</td>\n",
       "      <td>4.790</td>\n",
       "      <td>3.389</td>\n",
       "      <td>648.0</td>\n",
       "      <td>1217.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>yplus[0]</th>\n",
       "      <td>0.080</td>\n",
       "      <td>0.011</td>\n",
       "      <td>0.061</td>\n",
       "      <td>0.101</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2586.0</td>\n",
       "      <td>2329.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>yplus[1]</th>\n",
       "      <td>0.053</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.035</td>\n",
       "      <td>0.072</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1408.0</td>\n",
       "      <td>1839.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>yplus[2]</th>\n",
       "      <td>0.157</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.128</td>\n",
       "      <td>0.184</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1076.0</td>\n",
       "      <td>1334.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>H_amplitude[0]</th>\n",
       "      <td>37.546</td>\n",
       "      <td>0.361</td>\n",
       "      <td>36.876</td>\n",
       "      <td>38.220</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.003</td>\n",
       "      <td>5902.0</td>\n",
       "      <td>3061.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>H_amplitude[1]</th>\n",
       "      <td>39.173</td>\n",
       "      <td>2.219</td>\n",
       "      <td>34.767</td>\n",
       "      <td>43.175</td>\n",
       "      <td>0.087</td>\n",
       "      <td>0.061</td>\n",
       "      <td>658.0</td>\n",
       "      <td>1139.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>H_amplitude[2]</th>\n",
       "      <td>34.548</td>\n",
       "      <td>3.576</td>\n",
       "      <td>27.889</td>\n",
       "      <td>41.333</td>\n",
       "      <td>0.138</td>\n",
       "      <td>0.098</td>\n",
       "      <td>674.0</td>\n",
       "      <td>1176.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>He_amplitude[0]</th>\n",
       "      <td>2.873</td>\n",
       "      <td>0.342</td>\n",
       "      <td>2.242</td>\n",
       "      <td>3.515</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>3754.0</td>\n",
       "      <td>2956.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>He_amplitude[1]</th>\n",
       "      <td>2.079</td>\n",
       "      <td>0.451</td>\n",
       "      <td>1.232</td>\n",
       "      <td>2.918</td>\n",
       "      <td>0.014</td>\n",
       "      <td>0.010</td>\n",
       "      <td>988.0</td>\n",
       "      <td>1649.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>He_amplitude[2]</th>\n",
       "      <td>5.532</td>\n",
       "      <td>0.413</td>\n",
       "      <td>4.729</td>\n",
       "      <td>6.281</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.006</td>\n",
       "      <td>2179.0</td>\n",
       "      <td>2236.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>He_center[0]</th>\n",
       "      <td>-152.106</td>\n",
       "      <td>0.107</td>\n",
       "      <td>-152.304</td>\n",
       "      <td>-151.900</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2550.0</td>\n",
       "      <td>2600.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>He_center[1]</th>\n",
       "      <td>-98.211</td>\n",
       "      <td>1.218</td>\n",
       "      <td>-100.469</td>\n",
       "      <td>-95.882</td>\n",
       "      <td>0.048</td>\n",
       "      <td>0.034</td>\n",
       "      <td>656.0</td>\n",
       "      <td>1167.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>He_center[2]</th>\n",
       "      <td>-117.697</td>\n",
       "      <td>0.709</td>\n",
       "      <td>-119.034</td>\n",
       "      <td>-116.347</td>\n",
       "      <td>0.027</td>\n",
       "      <td>0.019</td>\n",
       "      <td>678.0</td>\n",
       "      <td>1093.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>He_fwhm[0]</th>\n",
       "      <td>20.920</td>\n",
       "      <td>1.647</td>\n",
       "      <td>17.965</td>\n",
       "      <td>24.138</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.022</td>\n",
       "      <td>2948.0</td>\n",
       "      <td>2825.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>He_fwhm[1]</th>\n",
       "      <td>31.167</td>\n",
       "      <td>3.042</td>\n",
       "      <td>25.794</td>\n",
       "      <td>37.202</td>\n",
       "      <td>0.062</td>\n",
       "      <td>0.044</td>\n",
       "      <td>2391.0</td>\n",
       "      <td>2912.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>He_fwhm[2]</th>\n",
       "      <td>23.350</td>\n",
       "      <td>1.688</td>\n",
       "      <td>20.151</td>\n",
       "      <td>26.568</td>\n",
       "      <td>0.043</td>\n",
       "      <td>0.031</td>\n",
       "      <td>1526.0</td>\n",
       "      <td>2201.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>He_area[0]</th>\n",
       "      <td>63.922</td>\n",
       "      <td>8.645</td>\n",
       "      <td>48.028</td>\n",
       "      <td>80.516</td>\n",
       "      <td>0.173</td>\n",
       "      <td>0.123</td>\n",
       "      <td>2484.0</td>\n",
       "      <td>2195.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>He_area[1]</th>\n",
       "      <td>69.112</td>\n",
       "      <td>17.041</td>\n",
       "      <td>38.654</td>\n",
       "      <td>102.230</td>\n",
       "      <td>0.566</td>\n",
       "      <td>0.400</td>\n",
       "      <td>901.0</td>\n",
       "      <td>1435.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>He_area[2]</th>\n",
       "      <td>137.528</td>\n",
       "      <td>14.567</td>\n",
       "      <td>109.802</td>\n",
       "      <td>164.366</td>\n",
       "      <td>0.438</td>\n",
       "      <td>0.310</td>\n",
       "      <td>1107.0</td>\n",
       "      <td>1973.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     mean       sd    hdi_3%   hdi_97%  mcse_mean  mcse_sd  \\\n",
       "H_center[0]       -29.956    0.107   -30.154   -29.750      0.002    0.001   \n",
       "H_center[1]        23.939    1.218    21.681    26.268      0.048    0.034   \n",
       "H_center[2]         4.453    0.709     3.116     5.803      0.027    0.019   \n",
       "H_area[0]         796.558   10.231   777.035   815.408      0.257    0.182   \n",
       "H_area[1]        1289.133  122.922  1054.824  1519.116      4.838    3.426   \n",
       "H_area[2]         883.763  121.603   652.021  1111.094      4.790    3.389   \n",
       "yplus[0]            0.080    0.011     0.061     0.101      0.000    0.000   \n",
       "yplus[1]            0.053    0.010     0.035     0.072      0.000    0.000   \n",
       "yplus[2]            0.157    0.015     0.128     0.184      0.000    0.000   \n",
       "H_amplitude[0]     37.546    0.361    36.876    38.220      0.005    0.003   \n",
       "H_amplitude[1]     39.173    2.219    34.767    43.175      0.087    0.061   \n",
       "H_amplitude[2]     34.548    3.576    27.889    41.333      0.138    0.098   \n",
       "He_amplitude[0]     2.873    0.342     2.242     3.515      0.006    0.004   \n",
       "He_amplitude[1]     2.079    0.451     1.232     2.918      0.014    0.010   \n",
       "He_amplitude[2]     5.532    0.413     4.729     6.281      0.009    0.006   \n",
       "He_center[0]     -152.106    0.107  -152.304  -151.900      0.002    0.001   \n",
       "He_center[1]      -98.211    1.218  -100.469   -95.882      0.048    0.034   \n",
       "He_center[2]     -117.697    0.709  -119.034  -116.347      0.027    0.019   \n",
       "He_fwhm[0]         20.920    1.647    17.965    24.138      0.030    0.022   \n",
       "He_fwhm[1]         31.167    3.042    25.794    37.202      0.062    0.044   \n",
       "He_fwhm[2]         23.350    1.688    20.151    26.568      0.043    0.031   \n",
       "He_area[0]         63.922    8.645    48.028    80.516      0.173    0.123   \n",
       "He_area[1]         69.112   17.041    38.654   102.230      0.566    0.400   \n",
       "He_area[2]        137.528   14.567   109.802   164.366      0.438    0.310   \n",
       "\n",
       "                 ess_bulk  ess_tail  r_hat  \n",
       "H_center[0]        2550.0    2600.0   1.00  \n",
       "H_center[1]         656.0    1167.0   1.01  \n",
       "H_center[2]         678.0    1093.0   1.01  \n",
       "H_area[0]          1585.0    2157.0   1.00  \n",
       "H_area[1]           649.0    1235.0   1.01  \n",
       "H_area[2]           648.0    1217.0   1.01  \n",
       "yplus[0]           2586.0    2329.0   1.00  \n",
       "yplus[1]           1408.0    1839.0   1.00  \n",
       "yplus[2]           1076.0    1334.0   1.00  \n",
       "H_amplitude[0]     5902.0    3061.0   1.00  \n",
       "H_amplitude[1]      658.0    1139.0   1.01  \n",
       "H_amplitude[2]      674.0    1176.0   1.01  \n",
       "He_amplitude[0]    3754.0    2956.0   1.00  \n",
       "He_amplitude[1]     988.0    1649.0   1.00  \n",
       "He_amplitude[2]    2179.0    2236.0   1.00  \n",
       "He_center[0]       2550.0    2600.0   1.00  \n",
       "He_center[1]        656.0    1167.0   1.01  \n",
       "He_center[2]        678.0    1093.0   1.01  \n",
       "He_fwhm[0]         2948.0    2825.0   1.00  \n",
       "He_fwhm[1]         2391.0    2912.0   1.00  \n",
       "He_fwhm[2]         1526.0    2201.0   1.00  \n",
       "He_area[0]         2484.0    2195.0   1.00  \n",
       "He_area[1]          901.0    1435.0   1.00  \n",
       "He_area[2]         1107.0    1973.0   1.00  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.summary(opt.best_model.trace.solution_0, var_names=model.cloud_deterministics)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f977c993",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [observation]\n"
     ]
    },
    {
     "data": {
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       "model_id": "97781cb6d8da46968ebe7c8b266b51c8",
       "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"
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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\">\n",
       "</pre>\n"
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      "text/plain": [
       "\n"
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     "output_type": "display_data"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 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",
    "_ = plot_predictive(opt.best_model.data, posterior.posterior_predictive)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9d012837",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}