ricardoV94/PyMC workflow.ipynb

## PyMC workflow.ipynb
{
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   "source": [
    "import arviz as az\n",
    "import pymc as pm\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng(sum(map(ord, \"Alex is chilling\")))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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   "source": [
    "with pm.Model() as m:\n",
    "    x = pm.MutableData(\"x\", np.linspace(-5, 5, 50))\n",
    "    \n",
    "    b0 = pm.Normal(\"b0\")\n",
    "    b1 = pm.Normal(\"b1\")\n",
    "    \n",
    "    noise = pm.HalfNormal(\"noise\")\n",
    "    y = pm.Normal(\"y\", pm.math.sigmoid(b0 + b1 * x), sigma=noise)\n",
    "        \n",
    "pm.model_to_graphviz(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [b0, b1, y]\n"
     ]
    }
   ],
   "source": [
    "with pm.do(m, {noise: 1.0}) as prior_m:\n",
    "    prior_pred = pm.sample_prior_predictive(1, random_seed=rng).isel(chain=0, draw=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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    "pm.model_to_graphviz(prior_m)"
   ]
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     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [b0, b1, noise]\n"
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       "      100.00% [4000/4000 00:05&lt;00:00 Sampling 2 chains, 0 divergences]\n",
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     "text": [
      "Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 5 seconds.\n",
      "We recommend running at least 4 chains for robust computation of convergence diagnostics\n"
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   "source": [
    "with pm.observe(m, {y: prior_pred.prior[\"y\"]}) as observed_m:\n",
    "    posterior = pm.sample(random_seed=rng)"
   ]
  },
  {
   "cell_type": "code",
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       "<title>b1&#45;&gt;y</title>\n",
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       "</g>\n",
       "<!-- noise -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>noise</title>\n",
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       "<text text-anchor=\"middle\" x=\"312.97\" y=\"-199.32\" font-family=\"Times,serif\" font-size=\"14.00\">~</text>\n",
       "<text text-anchor=\"middle\" x=\"312.97\" y=\"-182.07\" font-family=\"Times,serif\" font-size=\"14.00\">HalfNormal</text>\n",
       "</g>\n",
       "<!-- noise&#45;&gt;y -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>noise&#45;&gt;y</title>\n",
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       "<!-- b0 -->\n",
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       "<title>b0</title>\n",
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       "<text text-anchor=\"middle\" x=\"449.97\" y=\"-216.57\" font-family=\"Times,serif\" font-size=\"14.00\">b0</text>\n",
       "<text text-anchor=\"middle\" x=\"449.97\" y=\"-199.32\" font-family=\"Times,serif\" font-size=\"14.00\">~</text>\n",
       "<text text-anchor=\"middle\" x=\"449.97\" y=\"-182.07\" font-family=\"Times,serif\" font-size=\"14.00\">Normal</text>\n",
       "</g>\n",
       "<!-- b0&#45;&gt;y -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>b0&#45;&gt;y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M413.82,-174.98C406.79,-170.2 399.32,-165.56 391.97,-161.75 339.62,-134.59 275.6,-113.24 230.33,-99.94\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"231.4,-96.32 220.82,-96.9 229.45,-103.04 231.4,-96.32\"/>\n",
       "</g>\n",
       "<!-- x -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>x</title>\n",
       "<path fill=\"lightgrey\" stroke=\"black\" d=\"M212.47,-233.87C212.47,-233.87 127.47,-233.87 127.47,-233.87 121.47,-233.87 115.47,-227.87 115.47,-221.87 115.47,-221.87 115.47,-186.12 115.47,-186.12 115.47,-180.12 121.47,-174.12 127.47,-174.12 127.47,-174.12 212.47,-174.12 212.47,-174.12 218.47,-174.12 224.47,-180.12 224.47,-186.12 224.47,-186.12 224.47,-221.87 224.47,-221.87 224.47,-227.87 218.47,-233.87 212.47,-233.87\"/>\n",
       "<text text-anchor=\"middle\" x=\"169.97\" y=\"-216.57\" font-family=\"Times,serif\" font-size=\"14.00\">x</text>\n",
       "<text text-anchor=\"middle\" x=\"169.97\" y=\"-199.32\" font-family=\"Times,serif\" font-size=\"14.00\">~</text>\n",
       "<text text-anchor=\"middle\" x=\"169.97\" y=\"-182.07\" font-family=\"Times,serif\" font-size=\"14.00\">MutableData</text>\n",
       "</g>\n",
       "<!-- x&#45;&gt;y -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>x&#45;&gt;y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M170.71,-173.71C170.99,-162.57 171.32,-149.53 171.64,-136.9\"/>\n",
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       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x7fe176511090>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.model_to_graphviz(observed_m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 2208x552 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_posterior(\n",
    "    posterior, \n",
    "    ref_val=[\n",
    "        prior_pred.prior[\"b0\"].values,\n",
    "        prior_pred.prior[\"b1\"].values,\n",
    "        prior_pred.constant_data[\"noise\"].values,\n",
    "    ],\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling: [y]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       "    /* Turns off some styling */\n",
       "    progress {\n",
       "        /* gets rid of default border in Firefox and Opera. */\n",
       "        border: none;\n",
       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "        background-size: auto;\n",
       "    }\n",
       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
       "    }\n",
       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "        background: #F44336;\n",
       "    }\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "      <progress value='2000' class='' max='2000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [2000/2000 00:00&lt;00:00]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with pm.do(observed_m, {\"x\": [-1, 0, 1], \"b1\": m[\"b1\"] / 2}, prune_vars=True) as post_pred_model:\n",
    "    posterior_pred = pm.sample_posterior_predictive(posterior, random_seed=rng)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 8.1.0 (20230707.2238)\n",
       " -->\n",
       "<!-- Pages: 1 -->\n",
       "<svg width=\"546pt\" height=\"258pt\"\n",
       " viewBox=\"0.00 0.00 545.72 257.87\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 253.87)\">\n",
       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-253.87 541.72,-253.87 541.72,4 -4,4\"/>\n",
       "<g id=\"clust1\" class=\"cluster\">\n",
       "<title>cluster3</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M153.75,-8C153.75,-8 259.75,-8 259.75,-8 265.75,-8 271.75,-14 271.75,-20 271.75,-20 271.75,-229.87 271.75,-229.87 271.75,-235.87 265.75,-241.87 259.75,-241.87 259.75,-241.87 153.75,-241.87 153.75,-241.87 147.75,-241.87 141.75,-235.87 141.75,-229.87 141.75,-229.87 141.75,-20 141.75,-20 141.75,-14 147.75,-8 153.75,-8\"/>\n",
       "<text text-anchor=\"middle\" x=\"259.25\" y=\"-15.95\" font-family=\"Times,serif\" font-size=\"14.00\">3</text>\n",
       "</g>\n",
       "<!-- b1 -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>b1</title>\n",
       "<polygon fill=\"none\" stroke=\"black\" points=\"113.5,-233.87 0,-233.87 0,-174.12 113.5,-174.12 113.5,-233.87\"/>\n",
       "<text text-anchor=\"middle\" x=\"56.75\" y=\"-216.57\" font-family=\"Times,serif\" font-size=\"14.00\">b1</text>\n",
       "<text text-anchor=\"middle\" x=\"56.75\" y=\"-199.32\" font-family=\"Times,serif\" font-size=\"14.00\">~</text>\n",
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       "<!-- b1&#45;&gt;y -->\n",
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       "<!-- b0&#45;&gt;y -->\n",
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       "<title>b0&#45;&gt;y</title>\n",
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       "<title>x</title>\n",
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       "<text text-anchor=\"middle\" x=\"206.75\" y=\"-199.32\" font-family=\"Times,serif\" font-size=\"14.00\">~</text>\n",
       "<text text-anchor=\"middle\" x=\"206.75\" y=\"-182.07\" font-family=\"Times,serif\" font-size=\"14.00\">ConstantData</text>\n",
       "</g>\n",
       "<!-- x&#45;&gt;y -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>x&#45;&gt;y</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M207.74,-173.71C208.11,-162.57 208.55,-149.53 208.98,-136.9\"/>\n",
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       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.graphs.Digraph at 0x7fe17596a0d0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.model_to_graphviz(post_pred_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(\n",
    "    posterior_pred.constant_data[\"x\"],\n",
    "    posterior_pred.posterior_predictive[\"y\"].mean([\"chain\", \"draw\"]), \n",
    "    marker=\"o\",\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "pymc-dev",
   "language": "python",
   "name": "pymc-dev"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}