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   "source": [
    "# Graphical model assessment: Predictive regression\n",
    "\n",
    "[Dataset download](https://s3.amazonaws.com/bebi103.caltech.edu/data/good_invitro_droplet_data.csv)\n",
    "\n",
    "<hr>"
   ]
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       "      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n",
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Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    const el = document.getElementById(\"a2bb2927-a8d3-4de0-9dce-bfb124627bb5\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error(url) {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (let i = 0; i < css_urls.length; i++) {\n      const url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (let i = 0; i < js_urls.length; i++) {\n      const url = js_urls[i];\n      const element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.2.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-3.2.1.min.js\", \"https://unpkg.com/@holoviz/panel@1.2.1/dist/panel.min.js\"];\n  const css_urls = [];\n\n  const inline_js = [    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\nfunction(Bokeh) {\n    }\n  ];\n\n  function run_inline_js() {\n    if (root.Bokeh !== undefined || force === true) {\n          for (let i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\nif (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      const cell = $(document.getElementById(\"a2bb2927-a8d3-4de0-9dce-bfb124627bb5\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import warnings\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.optimize\n",
    "import scipy.stats as st\n",
    "\n",
    "import bebi103\n",
    "\n",
    "import bokeh.io\n",
    "import bokeh.plotting\n",
    "bokeh.io.output_notebook()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "We have just seen how a predictive ECDF can be used to graphically assess a model for the case of repeated measurements drawn out of a generative distribution. Now, we turn to a model that involves a regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The data set and models\n",
    "\n",
    "We again use the data set from [Good and coworkers](https://dx.doi.org/10.1126%2Fscience.1243147) that we used in our lessons on [model building](../22/model_building.ipynb) and [regression](../22/regression.ipynb). In the experiment, Good and coworkers measured the length of mitotic spindles in droplets of varying diameter.\n",
    "\n",
    "Let's take a quick look at the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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fa-info-circle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]}]}]},{\"type\":\"model\",\"name\":\"Notification\",\"properties\":[{\"name\":\"background\",\"kind\":\"Any\",\"default\":null},{\"name\":\"duration\",\"kind\":\"Any\",\"default\":3000},{\"name\":\"icon\",\"kind\":\"Any\",\"default\":null},{\"name\":\"message\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"notification_type\",\"kind\":\"Any\",\"default\":null},{\"name\":\"_destroyed\",\"kind\":\"Any\",\"default\":false}]},{\"type\":\"model\",\"name\":\"TemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"BootstrapTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"MaterialTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]}]}};\n",
       "  const render_items = [{\"docid\":\"6c5b98d1-04ca-4139-8d76-5430aa26561c\",\"roots\":{\"p1002\":\"bb29dabc-edc8-4f9e-8bea-22bb4cc2ef69\"},\"root_ids\":[\"p1002\"]}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "p1002"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.read_csv('../data/good_invitro_droplet_data.csv', comment='#')\n",
    "\n",
    "p = bokeh.plotting.figure(\n",
    "    frame_width=350,\n",
    "    frame_height=250,\n",
    "    x_axis_label='droplet diameter (µm)',\n",
    "    y_axis_label='spindle length (µm)',\n",
    ")\n",
    "\n",
    "p.circle(df['Droplet Diameter (um)'], df['Spindle Length (um)'], alpha=0.7)\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Good and coworkers proposed two models for the relationship between spindle length and droplet diameter. In the first model, the spindle length is independent of the droplet diameter and drawn out of a Normal distribution.\n",
    "\n",
    "\\begin{align}\n",
    "l_i \\sim \\text{Norm}(\\phi, \\sigma)\\;\\forall i.\n",
    "\\end{align}\n",
    "\n",
    "In the second model, the spindle length depends on the droplet diameter according to the equation below, and the spindle lengths vary from the theoretical model in a Normal fashion.\n",
    "\n",
    "\\begin{align}\n",
    "&\\mu_i = \\frac{\\gamma d_i}{\\left(1 + (\\gamma d_i/\\phi)^3\\right)^{1/3}}\\\\[1em]\n",
    "&l_i \\sim \\text{Norm}(\\mu_i, \\sigma)\\;\\forall i.\n",
    "\\end{align}\n",
    "\n",
    "These are the two models we will graphically assess, starting with the second model, which establishes a relationship between spindle length and droplet diameter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assessing the model for spindle length dependent on droplet diameter\n",
    "\n",
    "As was the case with our studies of the Singer, et al. data on mRNA counts, we do also need functions from previous lessons here to compute the MLE. You can skip this, since it is copied directly from previous lessons. The important result is that we get the MLE for the three parameters, $\\gamma$, $\\phi$, and $\\sigma$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "γ* = 0.860475\n",
      "φ* = 38.231250\n",
      "σ* = 3.753422\n"
     ]
    }
   ],
   "source": [
    "def theor_spindle_length(gamma, phi, d):\n",
    "    \"\"\"Compute spindle length using mathematical model\"\"\"\n",
    "    return gamma * d / np.cbrt(1 + (gamma * d / phi)**3)\n",
    "\n",
    "\n",
    "def log_likelihood(params, d, ell):\n",
    "    \"\"\"Log likelihood of spindle length model.\"\"\"\n",
    "    gamma, phi, sigma = params\n",
    "\n",
    "    if gamma <= 0 or gamma > 1 or phi <= 0:\n",
    "        return -np.inf\n",
    "\n",
    "    mu = theor_spindle_length(gamma, phi, d)\n",
    "    return np.sum(st.norm.logpdf(ell, mu, sigma))\n",
    "\n",
    "\n",
    "def spindle_mle(d, ell):\n",
    "    \"\"\"Compute MLE for parameters in spindle length model.\"\"\"\n",
    "    with warnings.catch_warnings():\n",
    "        warnings.simplefilter(\"ignore\")\n",
    "\n",
    "        res = scipy.optimize.minimize(\n",
    "            fun=lambda params, d, ell: -log_likelihood(params, d, ell),\n",
    "            x0=np.array([0.5, 35, 5]),\n",
    "            args=(d, ell),\n",
    "            method='Powell'\n",
    "        )\n",
    "\n",
    "    if res.success:\n",
    "        return res.x\n",
    "    else:\n",
    "        raise RuntimeError('Convergence failed with message', res.message)\n",
    "        \n",
    "\n",
    "mle_params = spindle_mle(df['Droplet Diameter (um)'].values, df['Spindle Length (um)'].values)\n",
    "\n",
    "# Take a look\n",
    "print(\"γ* = {0:f}\\nφ* = {1:f}\\nσ* = {2:f}\".format(*mle_params))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling out of the generative model\n",
    "\n",
    "As before, we want to see what kind of data sets are predicted by the generative model when parametrized by the MLEs of the parameters. We therefore need to write a function to obtain the samples. The extra wrinkle here is that we need to also provide values for the droplet diameter for which we want the samples. In this model, we assume that the droplet diameters are measured exactly and that they determine the spindle length (of course neglecting the variation we model in the residuals)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng()\n",
    "\n",
    "def sample_spindle(gamma, phi, sigma, d, size=1):\n",
    "    \"\"\"Generate samples of spindle length vs droplet diameter.\"\"\"\n",
    "    samples = np.empty((size, len(d)))\n",
    "\n",
    "    for i in range(size):\n",
    "        mu = theor_spindle_length(gamma, phi, d)\n",
    "        samples[i] = np.maximum(0, rng.normal(mu, sigma))\n",
    "\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that this function returns a array of shape `(size, len(d))`. That is, each row of the outputted array of samples corresponds to one set of measurements for prescribed droplet diameters `d`.\n",
    "\n",
    "We will generate samples for the droplet diameters going from zero to 250 microns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "d_theor = np.linspace(0, 250, 200)\n",
    "samples = sample_spindle(*mle_params, d_theor, size=10000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Making the predictive regression plot\n",
    "\n",
    "Now that we have our samples, we compute the percentiles of the spindle length for each value of $d$. We then generate the plot from these percentiles, with the data overlaid. The `bebi103.viz.predictive_regression()` function accomplishes this for us. We need to provide it with the samples of spindle length (with the shape we have already prescribed), as well as the $d$-values for which the samples were generated. We also need to provide the data as an array with two columns, the first being the diameter and the second the spindle length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
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length (\\u00b5m)\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1062\"}}}],\"below\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1054\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1055\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1056\"},\"axis_label\":\"droplet diameter (\\u00b5m)\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1057\"}}}],\"center\":[{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1058\",\"attributes\":{\"axis\":{\"id\":\"p1054\"}}},{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1063\",\"attributes\":{\"dimension\":1,\"axis\":{\"id\":\"p1059\"}}}],\"frame_width\":400,\"frame_height\":325}}],\"defs\":[{\"type\":\"model\",\"name\":\"ReactiveHTML1\"},{\"type\":\"model\",\"name\":\"FlexBox1\",\"properties\":[{\"name\":\"align_content\",\"kind\":\"Any\",\"default\":\"flex-start\"},{\"name\":\"align_items\",\"kind\":\"Any\",\"default\":\"flex-start\"},{\"name\":\"flex_direction\",\"kind\":\"Any\",\"default\":\"row\"},{\"name\":\"flex_wrap\",\"kind\":\"Any\",\"default\":\"wrap\"},{\"name\":\"justify_content\",\"kind\":\"Any\",\"default\":\"flex-start\"}]},{\"type\":\"model\",\"name\":\"FloatPanel1\",\"properties\":[{\"name\":\"config\",\"kind\":\"Any\",\"default\":{\"type\":\"map\"}},{\"name\":\"contained\",\"kind\":\"Any\",\"default\":true},{\"name\":\"position\",\"kind\":\"Any\",\"default\":\"right-top\"},{\"name\":\"offsetx\",\"kind\":\"Any\",\"default\":null},{\"name\":\"offsety\",\"kind\":\"Any\",\"default\":null},{\"name\":\"theme\",\"kind\":\"Any\",\"default\":\"primary\"},{\"name\":\"status\",\"kind\":\"Any\",\"default\":\"normalized\"}]},{\"type\":\"model\",\"name\":\"GridStack1\",\"properties\":[{\"name\":\"mode\",\"kind\":\"Any\",\"default\":\"warn\"},{\"name\":\"ncols\",\"kind\":\"Any\",\"default\":null},{\"name\":\"nrows\",\"kind\":\"Any\",\"default\":null},{\"name\":\"allow_resize\",\"kind\":\"Any\",\"default\":true},{\"name\":\"allow_drag\",\"kind\":\"Any\",\"default\":true},{\"name\":\"state\",\"kind\":\"Any\",\"default\":[]}]},{\"type\":\"model\",\"name\":\"drag1\",\"properties\":[{\"name\":\"slider_width\",\"kind\":\"Any\",\"default\":5},{\"name\":\"slider_color\",\"kind\":\"Any\",\"default\":\"black\"},{\"name\":\"value\",\"kind\":\"Any\",\"default\":50}]},{\"type\":\"model\",\"name\":\"click1\",\"properties\":[{\"name\":\"terminal_output\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"debug_name\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"clears\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"FastWrapper1\",\"properties\":[{\"name\":\"object\",\"kind\":\"Any\",\"default\":null},{\"name\":\"style\",\"kind\":\"Any\",\"default\":null}]},{\"type\":\"model\",\"name\":\"NotificationAreaBase1\",\"properties\":[{\"name\":\"js_events\",\"kind\":\"Any\",\"default\":{\"type\":\"map\"}},{\"name\":\"position\",\"kind\":\"Any\",\"default\":\"bottom-right\"},{\"name\":\"_clear\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"NotificationArea1\",\"properties\":[{\"name\":\"js_events\",\"kind\":\"Any\",\"default\":{\"type\":\"map\"}},{\"name\":\"notifications\",\"kind\":\"Any\",\"default\":[]},{\"name\":\"position\",\"kind\":\"Any\",\"default\":\"bottom-right\"},{\"name\":\"_clear\",\"kind\":\"Any\",\"default\":0},{\"name\":\"types\",\"kind\":\"Any\",\"default\":[{\"type\":\"map\",\"entries\":[[\"type\",\"warning\"],[\"background\",\"#ffc107\"],[\"icon\",{\"type\":\"map\",\"entries\":[[\"className\",\"fas fa-exclamation-triangle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]},{\"type\":\"map\",\"entries\":[[\"type\",\"info\"],[\"background\",\"#007bff\"],[\"icon\",{\"type\":\"map\",\"entries\":[[\"className\",\"fas fa-info-circle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]}]}]},{\"type\":\"model\",\"name\":\"Notification\",\"properties\":[{\"name\":\"background\",\"kind\":\"Any\",\"default\":null},{\"name\":\"duration\",\"kind\":\"Any\",\"default\":3000},{\"name\":\"icon\",\"kind\":\"Any\",\"default\":null},{\"name\":\"message\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"notification_type\",\"kind\":\"Any\",\"default\":null},{\"name\":\"_destroyed\",\"kind\":\"Any\",\"default\":false}]},{\"type\":\"model\",\"name\":\"TemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"BootstrapTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"MaterialTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]}]}};\n",
       "  const render_items = [{\"docid\":\"e5e7312d-a165-4292-8047-ec480580180d\",\"roots\":{\"p1041\":\"fc5b845a-a707-49b5-8f5d-f090565a4f9d\"},\"root_ids\":[\"p1041\"]}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "p1041"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = bebi103.viz.predictive_regression(\n",
    "    samples=samples,\n",
    "    samples_x=d_theor,\n",
    "    data=df[['Droplet Diameter (um)', 'Spindle Length (um)']].values,\n",
    "    x_axis_label='droplet diameter (µm)',\n",
    "    y_axis_label='spindle length (µm)',\n",
    "    x_range=[0, 250],\n",
    "    y_range=[0, 50],\n",
    ")\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this plot, we see that roughly 5% of the data points (there are 670 total points) lie outside the middle 95%, so the model is consistent with the measured data.\n",
    "\n",
    "In my view, **this** is how regression results should be plotted, not simple with a \"best fit line\", which does not reveal the full generative model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Viewing differences\n",
    "\n",
    "We may also wish to get a plot of how different the data are from the model. In this case, the median spindle length is subtracted off of all samples such that the median is zero. We also need to subtract it from the data to make a comparison. That means that we have to draw our samples from the generative distribution for values of the droplet diameter that were actually measured."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "  <div id=\"db719d11-4556-4ede-867b-4de8c55616a7\" data-root-id=\"p1115\" style=\"display: contents;\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "(function(root) {\n",
       "  function embed_document(root) {\n",
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hqMtgvwh3A0GR4z9P7HMDAmyzhIHgdwMjVjqmwPh7AcGoNUPOnHcCAIyz3CH8dwFQfhv3VNR3A5CNpw90VHcAwUBWfcaQdwICB279gIh3APAG5VoP2HMDIaAPa6lAdwPhssDJB4B3AlOdBHaoHHcCAK0ryfSkdwLCkzCRwUB3AFJ+2fRdfHcDME82lM0QewLwTBYVt+R3AeGVYFtMLHcA0xZA5OT4dwNDDbg0yDR7AJLPIxg41HcComgtNpPgcwIAne10z1xzAvGEhzshgHcCgOvnVmiMdwJj8mvy6ZR3AiE/hyvYmHcB0dV5OyZ8dwDgBSrFxbx3AhPRapN7NHMCsDQ8p/iwdwLCjgN+iox3A/KXoh2r5HcDs75ixRxYewMg2woI8hx3AcNxpp6IKHsAIZHw1NeEcwJAt8KLxvxzA/GIHY8rpHcAoyZMSVXodwECXIsztVh3A1OvCU8FAHcBMhOw72AgdwACoDWRJJx7AUHDoS4D/HMAMXbFZlYcdwLQNep96hB3AsDlCBmLxHcDImRVaQ1QdwKCtB1zi6BzA5AMQ6sLFHcCcIIHq0IcdwHyJ2CQpXx3A2ISu5y2tHcCE8lsUFycdwMxsWiCj+R3AZCzINGEtHcCcxvBuVGYdwODE8YZegBzAWAgtj+tfHsAw1odNx1AdwFRf0cix1R3AHBDLa2cEHsD0IXFqIOMdwOzh8VqcMx7ABLHJBkHLHcDUIO8lduIdwCj5KP/G3hzAjJqZqYXpHcCcW+UUmBIdwIxYnGfI1B3A+BFE9tx7HcAIb+Lvj24dwCBdm3V/7xzAVGDNeh28HMBEVxFBfqEcwASKxOT9Wx3A+LNFXYorHcAYqWwozbEcwIQWBVUwFh3AdO7i+SmYHcDw5Weo3jYdwFyJC8fDGh3AbD+ivlvpHMAU7T5MbXAdwLRWO7RbOh3AVPoFw4v2HMDEKdr+d+UcwDz0XwMAAB3AWHWRuCtWHcC04NFVnDYdwCw0EKjWZB3AOBIpXedkHcC095R6TTUdwPzzhUPCOx3AxDg2NzP8HMDobtbRUIodwCwzfRLkeh3AsMt6b9hPHcAYRqNQH7cdwMwnXeGbNR3A8A5FohsXHcD8xVfV41cdwHSo0GCBfh3ABAoyUz16HcAsPnOwfR8dwGA8EthsUx3AvLadg/pfHcB8IBVnyfwdwOTgInuL6B3AWFE4O+FIHcD8m/0RlTwdwICeiHXMUx3AWP309YUpHcB8/sxAAZ8dwLD8yYuuIx3AuN2GywFrHcB4dzWGRNwcwMymsCBq8R3ADG5HTS/THcDsnBo7yrccwKRHyDddIR3AKKFQPAtIHcAUrQfnqa8dwCSOU8sIVx3AjE0NXMOvHMC8clkRQY8dwOia8CUB3hzAmFdc9ALJHMB4zpYcwm0dwJR46rTgfR3A8KcC2elxHcDA/KtQ4VYdwLQAQ8L3XB3A3KN/kaEbHcD0Msu5ggYewJAaO+KQch3AJKb0R05XHcCM7a7VfK0dwMhRzehnJh3A9MwKEXXwHcBINZNqkN8dwOxu9eRuHR7AEIZuRDjFHcBs3fWi5RIewEzReV/kKx3APFOYJvlbHcD4R2hlCI8dwEwrkL6zch3AkMt/N4ksHcBoeTuRm7IdwCAuoQAzEx3AZEuvk+D6HMA4NSyTPNkdwJzfZMUPHB3A4DTV5Gx/HcAMJDbhA2cdwMzi2pMGvx3AeAzrnAGkHcBA99OVqWIdwKA8dd3Krh3AAHWbOYf5HMCMnpCmgt4cwKBODi/QeBzAQOJvSy+XHMD8j78YYK0cwMwkcfAM4hzAJM8ZEZB5HcDsDsAlT80dwHzdt1Y5Rh3A7Je8bGaPHMBMtf1/XkkdwAQOpbc+7RzAuJWicv8LHsAQlT0Usm0dwKD3xDDEhR3AkIAgHeqeHcDcmuBc+4wdwEAb8W8UyxzATPqEOKQ9HcBgnqQ8Rf0dwEA5wYOHdx3AMPcqCED3HMBMsjLbvU4dwJSJUPuGEB7AjJqE5H18HMBwiIh6nB8ewNRK24N85B3A5GQ2agR8HcC0Z2z3DogdwEAabn0KXB3AlI1D4fF7HcDo0oZlQXUdwGxu7J0JVB7ADIhOmVuuHcCIgOi3g14cwIQE+9yYtB3AEI6BbV2aHcCsPNnvzTEdwOSC/+azOh3AMAQ5LZIoHcDcO4pAStMcwIxFVMO7jR3AjJwpc0x3HcB0H3DBOxIewEQsZflyfx3AdNp3SLGJHMBMzdzriqEdwKgrK/Ee8RzAWDbSMhKUHMAMt7yGncQdwOQEsZoKgBzA+AXG93rgHcAIXmsH+jcdwETM4/sUKh3A/LK71dZTHcDc5LLxVqodwPCut98RcB3AbPs+3zbyHcAAn3QwufQcwGSN8nuf5xzAOPIz9sNTHcBI4ccS8+4cwGjbcvJIfR3AAGt52CS+HcCQLbmWDkkdwPysZ+6cwx3AON1G1KzKHcDQJXHYoC4dwGBi1xeLjB3ASKuZV50FHcCQD0QAG80dwJQvgdmFXB3AaH0wKnioHcAYoap3LMYdwFjYe8eJsxzAhBaq2X1RHcD0atDum8IdwJxG1UcsUx3ANGOs+1j4HMDs5Qw+T6YdwKxhmC26zx3A1PrFy5tPHcAohwfsExAdQPBF7bmitRxA6JPTpXFaHUDweJV84BAeQBjbFcwvZR1AIPxz6xKjHUCY6vZZrwcdQCiTMtH1nR1AcIpIAR2GHUBYjO+9zPEdQOD0ZYLznB1AWLheC9rwHECoPVZuqMQdQGgtlMme1R1AOEV3XW8qHUCAtyvMD04dQBj+kRndwBxAQCkRIrOLHUC4KqDpGO8dQIjXeKnnXx1AsG1iTFmvHUCIdLzQC+odQCiN0qvdMh1AOP0Br8eEHUBYLapM4/UcQEh1lG4kDR1AaDzvvHXTHUCIqiVVA4sdQNCwlFwuvx1ACO/pwj6BHUAoDt0evSUdQMD6hD9jsx1AUHtRmo0tHUDwpvisYbsdQMjJS7GpXx1AYLQJEFhaHkD4mdt47k4dQGDUQBtcuR1AkBHIyiTXHEAo6QO1qTcdQABU3b4F4RxAMKCgXJIgHUDg0Vh+eNkdQMD13oBGaB1AaOtgErZpHUAQkuCXt9gdQCj/lKYHiR1AmEPEVOUxHkAg6zUOxKkdQDB8/EPUnRxA6CQmMOpMHUCocwj0sRwdQKAgiXLkbB5AAFu1Je6ZHUD4OFx5D9odQNBpo0yfxRxAqMAeDVGiHUB4yTj5yXQdQKjhXkd/CR1AwGaX3dITHkCQIMW3QSIeQNDHUmISIB1AMPAf7PaMHECo8XmO98kcQCgSJ065yxxA+P4MEcpdHEAgNnMXwIUdQLANZEBdQh1A8BCwqyfwHUBoHklqcJ8dQFB8yPAoth1AKIsf00U8HUBI/AstLoodQAjeypu14x1AOGvPePMaHUBgv8I0kicdQBhYiRP9tR1AeE/r6D9WHUCAHcSsJ7kdQGDAhFu7iR1AiPSnhU0MHUDo3FsvddocQMinqYPNZh1AKPMsq4cVHkDQvN7cE34eQKgcg/+HAh5AsLCj7yZIHUCIyYXUsx0dQMgq7XQuxR1AEIikc2qDHUBw7RFhgUEdQOAFxn1zHB1AcGvyVLQVHkDw4iNLLsIdQMgtp5uOSR1AiFAuHLBiHUBYlWUY8AMdQMjC2gg5IB5AsKfvZAQNHkDgAaZWuxUeQEA0IAJ8MR5AkPBxO8/ZHEC471L2b6odQHiW4FHv2x1A4L1gJdxWHUDQjh2uPYYdQPA6knWfTh1A6Ks5CKpUHkBgxBZt79sdQOB/71I/8hxA0G1zh/nuHEDIio9RBGAdQBAlPDresBxA8DI3hS0zHUCADuqqnRceQODQa+k32BxA+LiQqJ+cHEB4oCv/weQcQJDzKONbpB1A+PA2UQiLHUCIqzXgTSEdQKhq7VnmJh5AmJPzdEJNHUA4mS7XkXwdQHjtpBFQOB1AGOQMauWHHUAwEnB351MdQLD4E3BEgh1AqMYegSOEHUDwMJ8paCMdQADGCcfH9xxA4CXQtkMrHkCAIFMz49MdQJiZrdMOBh1AMHA0PLCjHUBQaxzYGAgeQDBYOilgmBxAsLX/v6vVHUBwUWtUoKQdQCAm2ypkPx1AKP0ZValoHEAg7Bzf/jsdQGh29lmHZB1A8JBOcbU4HUAoAxay27YdQFjeBmc0Ch1A0HZXKKyWHEBwZ2s1VPYcQNhme4XlDx1AWND/pFQuHUDojDywvTcdQMBJIXweZx1A6LEEWgq3HUA43cpjWmMcQFiqm+W92x1ASLcDJy9/HEDIhjzlUIcdQAjyz1TVlB1AiC10neqKHUBgL76hW6wdQLC7yXxaGh5AEABBC7+vHUCg8bbvYYUdQPDwMbF+Vh1AsMDwLSs6HkDI/5xG1+EcQADv/O5xphxAEFeAn/7zHEDQ09JLSg8eQKiSgYClTR1AuA+uAF4oHUBwjtp7ECgdQJBi6cwTxR1A8DqWW23fHECQGOVSWuwcQJBXSkS9dB1A2Jczl5RcHUCQkygXyikdQKD6w5KSkh1AiN3c1tFxHUAAQsj4CEAeQABnmuJmdh1AqGTLsDVUHUAA6McXhgoeQLDnW6DDfB1AqCc6i+6jHUBgpQnP5A0dQLjN0FOnRB1AgP4VpR0THUCQGWGrB58dQBAh4gg3Ch5AgDM2ynogHUDoW1V9A2YdQKAuFhygwR1AwKp0mplpHEAYgszKPMwdQCjTGvRSbB1ACI28B0GHHUCwl2JF0igdQFjQOBdtLB1AgKSmfsEkHkAYKMNyS6YdQEiqkRz9OR1AAMzhKCWDHUA40Ozo0akdQDClzpu+fR1AmDHW3efEHUBIxzWr/tYdQIB9v+49kxxAmFKiI8vxHEBA6t7Ce8YdQDDlGqRLnB1AAJMlfPnPHUCIanzO3aUdQGiQli7/2B1AYMYVrPHLHEDg6gVlPSMdQGByVIlSLh1A8MC7OlhZHUDoGla+WEIdQIANXp0v2R1AYOJxBldyHUCo92JTBUIeQMA9NwceOx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\"},\"shape\":[670],\"dtype\":\"float64\",\"order\":\"little\"}]]}}},\"view\":{\"type\":\"object\",\"name\":\"CDSView\",\"id\":\"p1178\",\"attributes\":{\"filter\":{\"type\":\"object\",\"name\":\"AllIndices\",\"id\":\"p1179\"}}},\"glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1174\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"x\"},\"y\":{\"type\":\"field\",\"field\":\"y\"},\"size\":{\"type\":\"value\",\"value\":2},\"line_color\":{\"type\":\"value\",\"value\":\"orange\"},\"fill_color\":{\"type\":\"value\",\"value\":\"orange\"},\"hatch_color\":{\"type\":\"value\",\"value\":\"orange\"}}},\"nonselection_glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1175\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"x\"},\"y\":{\"type\":\"field\",\"field\":\"y\"},\"size\":{\"type\":\"value\",\"value\":2},\"line_color\":{\"type\":\"value\",\"value\":\"orange\"},\"line_alpha\":{\"type\":\"value\",\"value\":0.1},\"fill_color\":{\"type\":\"value\",\"value\":\"orange\"},\"fill_alpha\":{\"type\":\"value\",\"value\":0.1},\"hatch_color\":{\"type\":\"value\",\"value\":\"orange\"},\"hatch_alpha\":{\"type\":\"value\",\"value\":0.1}}},\"muted_glyph\":{\"type\":\"object\",\"name\":\"Circle\",\"id\":\"p1176\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"x\"},\"y\":{\"type\":\"field\",\"field\":\"y\"},\"size\":{\"type\":\"value\",\"value\":2},\"line_color\":{\"type\":\"value\",\"value\":\"orange\"},\"line_alpha\":{\"type\":\"value\",\"value\":0.2},\"fill_color\":{\"type\":\"value\",\"value\":\"orange\"},\"fill_alpha\":{\"type\":\"value\",\"value\":0.2},\"hatch_color\":{\"type\":\"value\",\"value\":\"orange\"},\"hatch_alpha\":{\"type\":\"value\",\"value\":0.2}}}}}],\"toolbar\":{\"type\":\"object\",\"name\":\"Toolbar\",\"id\":\"p1123\",\"attributes\":{\"tools\":[{\"type\":\"object\",\"name\":\"PanTool\",\"id\":\"p1137\"},{\"type\":\"object\",\"name\":\"WheelZoomTool\",\"id\":\"p1138\"},{\"type\":\"object\",\"name\":\"BoxZoomTool\",\"id\":\"p1139\",\"attributes\":{\"overlay\":{\"type\":\"object\",\"name\":\"BoxAnnotation\",\"id\":\"p1140\",\"attributes\":{\"syncable\":false,\"level\":\"overlay\",\"visible\":false,\"left_units\":\"canvas\",\"right_units\":\"canvas\",\"bottom_units\":\"canvas\",\"top_units\":\"canvas\",\"line_color\":\"black\",\"line_alpha\":1.0,\"line_width\":2,\"line_dash\":[4,4],\"fill_color\":\"lightgrey\",\"fill_alpha\":0.5}}}},{\"type\":\"object\",\"name\":\"SaveTool\",\"id\":\"p1141\"},{\"type\":\"object\",\"name\":\"ResetTool\",\"id\":\"p1142\"},{\"type\":\"object\",\"name\":\"HelpTool\",\"id\":\"p1143\"}]}},\"left\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1132\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1133\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1134\"},\"axis_label\":\"diff. spindle length (\\u00b5m)\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1135\"}}}],\"below\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1127\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1128\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1129\"},\"axis_label\":\"droplet diameter (\\u00b5m)\",\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1130\"}}}],\"center\":[{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1131\",\"attributes\":{\"axis\":{\"id\":\"p1127\"}}},{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1136\",\"attributes\":{\"dimension\":1,\"axis\":{\"id\":\"p1132\"}}}],\"frame_width\":400,\"frame_height\":325}}],\"defs\":[{\"type\":\"model\",\"name\":\"ReactiveHTML1\"},{\"type\":\"model\",\"name\":\"FlexBox1\",\"properties\":[{\"name\":\"align_content\",\"kind\":\"Any\",\"default\":\"flex-start\"},{\"name\":\"align_items\",\"kind\":\"Any\",\"default\":\"flex-start\"},{\"name\":\"flex_direction\",\"kind\":\"Any\",\"default\":\"row\"},{\"name\":\"flex_wrap\",\"kind\":\"Any\",\"default\":\"wrap\"},{\"name\":\"justify_content\",\"kind\":\"Any\",\"default\":\"flex-start\"}]},{\"type\":\"model\",\"name\":\"FloatPanel1\",\"properties\":[{\"name\":\"config\",\"kind\":\"Any\",\"default\":{\"type\":\"map\"}},{\"name\":\"contained\",\"kind\":\"Any\",\"default\":true},{\"name\":\"position\",\"kind\":\"Any\",\"default\":\"right-top\"},{\"name\":\"offsetx\",\"kind\":\"Any\",\"default\":null},{\"name\":\"offsety\",\"kind\":\"Any\",\"default\":null},{\"name\":\"theme\",\"kind\":\"Any\",\"default\":\"primary\"},{\"name\":\"status\",\"kind\":\"Any\",\"default\":\"normalized\"}]},{\"type\":\"model\",\"name\":\"GridStack1\",\"properties\":[{\"name\":\"mode\",\"kind\":\"Any\",\"default\":\"warn\"},{\"name\":\"ncols\",\"kind\":\"Any\",\"default\":null},{\"name\":\"nrows\",\"kind\":\"Any\",\"default\":null},{\"name\":\"allow_resize\",\"kind\":\"Any\",\"default\":true},{\"name\":\"allow_drag\",\"kind\":\"Any\",\"default\":true},{\"name\":\"state\",\"kind\":\"Any\",\"default\":[]}]},{\"type\":\"model\",\"name\":\"drag1\",\"properties\":[{\"name\":\"slider_width\",\"kind\":\"Any\",\"default\":5},{\"name\":\"slider_color\",\"kind\":\"Any\",\"default\":\"black\"},{\"name\":\"value\",\"kind\":\"Any\",\"default\":50}]},{\"type\":\"model\",\"name\":\"click1\",\"properties\":[{\"name\":\"terminal_output\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"debug_name\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"clears\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"FastWrapper1\",\"properties\":[{\"name\":\"object\",\"kind\":\"Any\",\"default\":null},{\"name\":\"style\",\"kind\":\"Any\",\"default\":null}]},{\"type\":\"model\",\"name\":\"NotificationAreaBase1\",\"properties\":[{\"name\":\"js_events\",\"kind\":\"Any\",\"default\":{\"type\":\"map\"}},{\"name\":\"position\",\"kind\":\"Any\",\"default\":\"bottom-right\"},{\"name\":\"_clear\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"NotificationArea1\",\"properties\":[{\"name\":\"js_events\",\"kind\":\"Any\",\"default\":{\"type\":\"map\"}},{\"name\":\"notifications\",\"kind\":\"Any\",\"default\":[]},{\"name\":\"position\",\"kind\":\"Any\",\"default\":\"bottom-right\"},{\"name\":\"_clear\",\"kind\":\"Any\",\"default\":0},{\"name\":\"types\",\"kind\":\"Any\",\"default\":[{\"type\":\"map\",\"entries\":[[\"type\",\"warning\"],[\"background\",\"#ffc107\"],[\"icon\",{\"type\":\"map\",\"entries\":[[\"className\",\"fas fa-exclamation-triangle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]},{\"type\":\"map\",\"entries\":[[\"type\",\"info\"],[\"background\",\"#007bff\"],[\"icon\",{\"type\":\"map\",\"entries\":[[\"className\",\"fas fa-info-circle\"],[\"tagName\",\"i\"],[\"color\",\"white\"]]}]]}]}]},{\"type\":\"model\",\"name\":\"Notification\",\"properties\":[{\"name\":\"background\",\"kind\":\"Any\",\"default\":null},{\"name\":\"duration\",\"kind\":\"Any\",\"default\":3000},{\"name\":\"icon\",\"kind\":\"Any\",\"default\":null},{\"name\":\"message\",\"kind\":\"Any\",\"default\":\"\"},{\"name\":\"notification_type\",\"kind\":\"Any\",\"default\":null},{\"name\":\"_destroyed\",\"kind\":\"Any\",\"default\":false}]},{\"type\":\"model\",\"name\":\"TemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"BootstrapTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]},{\"type\":\"model\",\"name\":\"MaterialTemplateActions1\",\"properties\":[{\"name\":\"open_modal\",\"kind\":\"Any\",\"default\":0},{\"name\":\"close_modal\",\"kind\":\"Any\",\"default\":0}]}]}};\n",
       "  const render_items = [{\"docid\":\"78766aa6-9f83-497c-b4bf-3251537530f0\",\"roots\":{\"p1115\":\"db719d11-4556-4ede-867b-4de8c55616a7\"},\"root_ids\":[\"p1115\"]}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
       "  }\n",
       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
       "  } else {\n",
       "    let attempts = 0;\n",
       "    const timer = setInterval(function(root) {\n",
       "      if (root.Bokeh !== undefined) {\n",
       "        clearInterval(timer);\n",
       "        embed_document(root);\n",
       "      } else {\n",
       "        attempts++;\n",
       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
       "        }\n",
       "      }\n",
       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
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     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "p1115"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = sample_spindle(*mle_params, df['Droplet Diameter (um)'].values, size=10000)\n",
    "\n",
    "p = bebi103.viz.predictive_regression(\n",
    "    samples=samples,\n",
    "    samples_x=df['Droplet Diameter (um)'].values,\n",
    "    data=df[['Droplet Diameter (um)', 'Spindle Length (um)']].values,\n",
    "    diff=True,\n",
    "    x_axis_label='droplet diameter (µm)',\n",
    "    y_axis_label='diff. spindle length (µm)',\n",
    "    x_range=[df['Droplet Diameter (um)'].values.min(), df['Droplet Diameter (um)'].values.max()],\n",
    ")\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Importantly, there does not seem to be any systematic way in which the measurements deviate from the model. In other words, whether a data point lies outside the 80% envelope and whether it lies above or below looks independent of droplet diameter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graphical assessment of the Normal model\n",
    "\n",
    "As we have learned, the MLE for the parameters for the Normal model are the same as the plug-in estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi = np.mean(df['Spindle Length (um)'])\n",
    "sigma = np.std(df['Spindle Length (um)'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then draw our samples directly out of a Normal distribution with location parameter $\\phi^*$ and scale parameter $\\sigma^*$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = rng.normal(phi, sigma, size=(5000, len(df)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the samples, we can again make a predictive regression plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
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       "  const render_items = [{\"docid\":\"add09510-51e6-4d30-913a-e85abd5ae424\",\"roots\":{\"p1188\":\"fbedc744-9320-4280-ba03-d75fd86a6b2f\"},\"root_ids\":[\"p1188\"]}];\n",
       "  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n",
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       "  if (root.Bokeh !== undefined) {\n",
       "    embed_document(root);\n",
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       "    let attempts = 0;\n",
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       "        if (attempts > 100) {\n",
       "          clearInterval(timer);\n",
       "          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n",
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       "    }, 10, root)\n",
       "  }\n",
       "})(window);"
      ],
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "p1188"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = bebi103.viz.predictive_regression(\n",
    "    samples=samples,\n",
    "    samples_x=df['Droplet Diameter (um)'].values,\n",
    "    percentiles=[68, 80, 95],\n",
    "    data=df[['Droplet Diameter (um)', 'Spindle Length (um)']].values,\n",
    "    x_axis_label='droplet diameter (µm)',\n",
    "    y_axis_label='spindle length (µm)',\n",
    "    x_range=[df['Droplet Diameter (um)'].values.min(), df['Droplet Diameter (um)'].values.max()],\n",
    ")\n",
    "\n",
    "bokeh.io.show(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, I have also included the 80% envelope. Again, only about 5% of the data points lie outside the 95% envelope. However, the data points tend to fall below the 80% envelope only for small droplet diameters and above only for large droplet diameters, suggesting that the model is missing the droplet-diameter dependence."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## General method of graphical predictive model assessment\n",
    "\n",
    "When using both predictive ECDFs and predictive regression curves, we did the same procedure, which you can imagine generalizing.\n",
    "\n",
    "1. Compute the MLE of the parameters for the generative model in question.\n",
    "2. Use the MLE to parametrize the model and generate many data sets out of the model.\n",
    "3. Make a plot showing percentile regions of the generated data sets.\n",
    "4. Overlay the measured data set.\n",
    "5. Evaluate how many of the measured data points lie outside the percentile regions of the generated data sets.\n",
    "\n",
    "Predictive ECDFs and regression curves are just two (often used) examples of this prescription, and you can develop your own as is useful for the model and data set you are working with."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computing environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.11.4\n",
      "IPython version      : 8.12.2\n",
      "\n",
      "numpy     : 1.24.3\n",
      "pandas    : 2.0.3\n",
      "scipy     : 1.11.1\n",
      "bokeh     : 3.2.1\n",
      "bebi103   : 0.1.15\n",
      "jupyterlab: 4.0.5\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -v -p numpy,pandas,scipy,bokeh,bebi103,jupyterlab"
   ]
  }
 ],
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