notebooks/looking-for-lucy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Code: _Looking for Lucy_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import open3d as o3d\n",
    "import plotly.graph_objects as go\n",
    "import plotly.io as pio\n",
    "import plotly.figure_factory as ff\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load 3D data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mesh = o3d.io.read_triangle_mesh(\"../data/ship.ply\")\n",
    "tri = np.asarray(mesh.vertices)\n",
    "x = tri[:, 0]\n",
    "y = tri[:, 1]\n",
    "z = tri[:, 2]\n",
    "simplices = np.asarray(mesh.triangles)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure 1.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The ship\n",
    "fig = go.Figure(ff.create_trisurf(x=x, y=y, z=z,\n",
    "                                  simplices=simplices,\n",
    "                                  plot_edges=False,\n",
    "                                  show_colorbar=False).data)\n",
    "fig.update_traces(hoverinfo='none')\n",
    "\n",
    "# The dots\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=[-100], y=[0], z=[-60],\n",
    "                 mode='markers',\n",
    "                 hovertext='Unlikely',\n",
    "                 hoverinfo='text',\n",
    "                 showlegend=False)\n",
    ")\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=[0], y=[0], z=[-30],\n",
    "                 mode='markers',\n",
    "                 hovertext='Likely',\n",
    "                 hoverinfo='text',\n",
    "                 showlegend=False))\n",
    "\n",
    "# Viewpoint\n",
    "camera = dict(\n",
    "    eye=dict(x=-0.6, y=-1.2, z=0.2),\n",
    "    center=dict(x=0.75, y=0, z=-0.4))\n",
    "\n",
    "# Figure properties\n",
    "fig.update_layout(scene=dict(\n",
    "                    xaxis=dict(visible=False),\n",
    "                    yaxis=dict(visible=False),\n",
    "                    zaxis=dict(visible=False),\n",
    "                    aspectmode='data'),\n",
    "                  hoverlabel=dict(font_size=18),\n",
    "                  height=400,\n",
    "                  margin=dict(r=0, l=0, b=0, t=0, pad=0),\n",
    "                  scene_camera=camera)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save figure\n",
    "pio.write_html(fig,\n",
    "               file='../_includes/figures/ship.html',\n",
    "               full_html=False,\n",
    "               include_plotlyjs='cdn',\n",
    "               config=dict(displayModeBar=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure 1.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The ship\n",
    "fig = go.Figure(ff.create_trisurf(x=x, y=y, z=z-129,\n",
    "                                  simplices=simplices,\n",
    "                                  plot_edges=False,\n",
    "                                  show_colorbar=False,\n",
    "                                  colormap='rgb(255, 255, 255)').data)\n",
    "fig.update_traces(hoverinfo='none')\n",
    "\n",
    "# The bars\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=[0, 0, 0],\n",
    "                 y=[-300, -300, -300],\n",
    "                 z=[-200, -190, -180],\n",
    "                 hovertext=[\"\", \"Ocean\", \"\"],\n",
    "                 hoverinfo='text',\n",
    "                 mode='lines+text',\n",
    "                 text=[\"\", \"<b>10%</b>\", \"\"],\n",
    "                 textposition=\"middle center\",\n",
    "                 textfont=dict(size=20, color='white'),\n",
    "                 line=dict(width=120),\n",
    "                 showlegend=False))\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=[0, 0, 0],\n",
    "                 y=[0, 0, 0],\n",
    "                 z=[-200, 110, 120],\n",
    "                 hovertext=[\"\", \"Ship\", \"\"],\n",
    "                 hoverinfo='text',\n",
    "                 mode='lines+text',\n",
    "                 text=[\"\", \"<b>90%</b>\", \"\"],\n",
    "                 textposition=\"middle center\",\n",
    "                 textfont=dict(size=20, color='white'),\n",
    "                 line=dict(width=120),\n",
    "                 showlegend=False))\n",
    "\n",
    "# The x axis\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=[0, 0, 0],\n",
    "                 y=[-350, 0, 265],\n",
    "                 z=[-200, -200, -200],\n",
    "                 line=dict(color='black', width=2),\n",
    "                 mode='lines',\n",
    "                 hoverinfo='none',\n",
    "                 showlegend=False))\n",
    "\n",
    "\n",
    "# The y axis\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=[0, 0, 0],\n",
    "                 y=[265, 265, 265],\n",
    "                 z=[-200, 65, 200],\n",
    "                 line=dict(color='black', width=2),\n",
    "                 mode='lines',\n",
    "                 hoverinfo='none',\n",
    "                 showlegend=False))\n",
    "\n",
    "# The y label\n",
    "fig.update_layout(scene=dict(annotations=[dict(\n",
    "                  showarrow=False,\n",
    "                  x=0,\n",
    "                  y=265,\n",
    "                  z=0,\n",
    "                  text=\"Probability\",\n",
    "                  xanchor=\"right\",\n",
    "                  font=dict(size=16),\n",
    "                  textangle=-90)]))\n",
    "\n",
    "# Viewpoint\n",
    "camera = dict(\n",
    "    eye=dict(x=-1, y=0, z=0),\n",
    "    projection=dict(type=\"orthographic\"))\n",
    "\n",
    "# Figure properties\n",
    "fig.update_layout(scene=dict(\n",
    "                    xaxis=dict(visible=False),\n",
    "                    yaxis=dict(visible=False),\n",
    "                    zaxis=dict(visible=False),\n",
    "                    aspectmode='data'),\n",
    "                  hoverlabel=dict(font_size=18),\n",
    "                  height=600,\n",
    "                  margin=dict(r=0, l=0, b=0, t=0, pad=0),\n",
    "                  scene_camera=camera)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save figure\n",
    "pio.write_html(fig,\n",
    "               file='../_includes/figures/ship_bars.html',\n",
    "               full_html=False,\n",
    "               include_plotlyjs='cdn',\n",
    "               config=dict(scrollZoom=False,\n",
    "                           displayModeBar=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The ship\n",
    "fig = go.Figure(ff.create_trisurf(x=x, y=y, z=z,\n",
    "                                  simplices=simplices,\n",
    "                                  plot_edges=False,\n",
    "                                  show_colorbar=False,\n",
    "                                  colormap='rgb(255, 255, 255)').data)\n",
    "fig.update_traces(hoverinfo='none')\n",
    "\n",
    "# The x axis\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=[0, 0, 0],\n",
    "                 y=[-280, 0, 270],\n",
    "                 z=[-80, -80, -80],\n",
    "                 line=dict(color='black', width=2),\n",
    "                 mode='lines',\n",
    "                 hoverinfo='none',\n",
    "                 showlegend=False))\n",
    "\n",
    "annotations=[dict(\n",
    "                showarrow=False,\n",
    "                x=0,\n",
    "                y=0,\n",
    "                z=-80,\n",
    "                yanchor='top',\n",
    "                text=r'$e\\mathrm{\\ - \\ Exact\\ position}$',\n",
    "                font=dict(size=18),\n",
    "                yshift=-10)]\n",
    "\n",
    "# Vertical lines\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=np.zeros(100),\n",
    "                 y=np.ones(100) * 55,\n",
    "                 z=np.linspace(-80, 135, 100),\n",
    "                 line=dict(color='crimson', width=4, dash='dash'),\n",
    "                 mode='lines',\n",
    "                 hoverinfo='text',\n",
    "                 hovertext='20m',\n",
    "                 showlegend=False))\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=np.zeros(100),\n",
    "                 y=np.ones(100) * -55,\n",
    "                 z=np.linspace(-80, 135, 100),\n",
    "                 line=dict(color='crimson', width=4, dash='dash'),\n",
    "                 mode='lines',\n",
    "                 hoverinfo='text',\n",
    "                 hovertext='30m',\n",
    "                 showlegend=False))\n",
    "\n",
    "# Text\n",
    "annotations.append(dict(\n",
    "                showarrow=False,\n",
    "                x=0,\n",
    "                y=0,\n",
    "                z=70,\n",
    "                text=r\"$p(\\mathrm{middle}\\vert\\mathrm{ship})\\mathrm{\\ -\\ Probability}$\",\n",
    "                font=dict(color='crimson', size=18),\n",
    "                xanchor=\"right\",\n",
    "                textangle=-90))\n",
    "fig.update_layout(scene=dict(annotations=annotations))\n",
    "\n",
    "# Gaussian\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=np.zeros(100),\n",
    "                 y=np.linspace(-250, 250, 100),\n",
    "                 z=stats.norm.pdf(np.linspace(-4, 4, 100), 0, 1) * 500,\n",
    "                 line=dict(color='crimson', width=4),\n",
    "                 hovertext='Lucy?',\n",
    "                 mode='lines',\n",
    "                 hoverinfo='text',\n",
    "                 showlegend=False))\n",
    "\n",
    "# Viewpoint\n",
    "camera = dict(\n",
    "    eye=dict(x=-1, y=0, z=0),\n",
    "    projection=dict(type=\"orthographic\"))\n",
    "\n",
    "# Figure properties\n",
    "fig.update_layout(scene=dict(\n",
    "                    xaxis=dict(visible=False),\n",
    "                    yaxis=dict(visible=False),\n",
    "                    zaxis=dict(visible=False),\n",
    "                    aspectmode='data'),\n",
    "                  hoverlabel=dict(font_size=18),\n",
    "                  height=700,\n",
    "                  margin=dict(r=0, l=0, b=0, t=0, pad=0),\n",
    "                  scene_camera=camera)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save figure\n",
    "pio.write_html(fig,\n",
    "               file='../_includes/figures/ship_1dgauss.html',\n",
    "               full_html=False,\n",
    "               include_mathjax='cdn',\n",
    "               include_plotlyjs='cdn',\n",
    "               config=dict(scrollZoom=False,\n",
    "                           displayModeBar=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The ship\n",
    "fig = go.Figure(ff.create_trisurf(x=x, y=y, z=z+39,\n",
    "                                  simplices=simplices,\n",
    "                                  plot_edges=False,\n",
    "                                  show_colorbar=False,\n",
    "                                  colormap='rgb(255, 255, 255)').data)\n",
    "fig.update_traces(hoverinfo='none', opacity=0.6)\n",
    "\n",
    "# Calculating multivariate Gaussian\n",
    "X, Y = np.meshgrid(np.linspace(-1, 1, 50), np.linspace(-3, 3, 100))\n",
    "mu = np.array([0., 0.])\n",
    "Sigma = np.array([[0.15, 0], [0,  1]])\n",
    "\n",
    "pos = np.empty(X.shape + (2,))\n",
    "pos[:, :, 0] = X\n",
    "pos[:, :, 1] = Y\n",
    "\n",
    "def multivariate_gaussian(pos, mu, Sigma):\n",
    "    \"\"\"Return the multivariate Gaussian distribution on array pos.\n",
    "\n",
    "    pos is an array constructed by packing the meshed arrays of variables\n",
    "    x_1, x_2, x_3, ..., x_k into its _last_ dimension.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    n = mu.shape[0]\n",
    "    Sigma_det = np.linalg.det(Sigma)\n",
    "    Sigma_inv = np.linalg.inv(Sigma)\n",
    "    N = np.sqrt((2*np.pi)**n * Sigma_det)\n",
    "    fac = np.einsum('...k,kl,...l->...', pos-mu, Sigma_inv, pos-mu)\n",
    "\n",
    "    return np.exp(-fac / 2) / N\n",
    "\n",
    "Z = multivariate_gaussian(pos, mu, Sigma)\n",
    "\n",
    "# Plotting the Gaussian\n",
    "fig.add_trace(go.Surface(x=X*100,\n",
    "                         y=Y*100,\n",
    "                         z=Z*100,\n",
    "                         contours_z=dict(show=True,\n",
    "                                         usecolormap=True,\n",
    "                                         highlightcolor=\"limegreen\",\n",
    "                                         project_z=True,\n",
    "                                         start=0,\n",
    "                                         end=70,\n",
    "                                         size=5),\n",
    "                         showscale=False,\n",
    "                         hoverinfo='none'))\n",
    "\n",
    "# The x axis\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=[-110, -110],\n",
    "                 y=[160, 310],\n",
    "                 z=[0, 0],\n",
    "                 line=dict(color='black', width=4),\n",
    "                 mode='lines',\n",
    "                 hoverinfo='none',\n",
    "                 showlegend=False))\n",
    "\n",
    "\n",
    "# The y axis\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=[-110, 40],\n",
    "                 y=[310, 310],\n",
    "                 z=[0, 0],\n",
    "                 line=dict(color='black', width=4),\n",
    "                 mode='lines',\n",
    "                 hoverinfo='none',\n",
    "                 showlegend=False))\n",
    "\n",
    "# The labels\n",
    "annotations=[dict(showarrow=False,\n",
    "                  x=-30,\n",
    "                  y=315,\n",
    "                  z=0,\n",
    "                  text=r\"$e_y$\",\n",
    "                  xanchor=\"right\",\n",
    "                  font=dict(size=16),\n",
    "                  textangle=-90)]\n",
    "annotations.append(dict(showarrow=False,\n",
    "                        x=-120,\n",
    "                        y=240,\n",
    "                        z=0,\n",
    "                        text=r\"$e_x$\",\n",
    "                        xanchor=\"center\",\n",
    "                        font=dict(size=16)))\n",
    "fig.layout.scene.annotations = annotations\n",
    "\n",
    "# Viewpoint\n",
    "camera = dict(\n",
    "    eye=dict(x=0, y=0, z=1.3))\n",
    "\n",
    "# Figure properties\n",
    "fig.update_layout(scene=dict(\n",
    "                    xaxis=dict(visible=False),\n",
    "                    yaxis=dict(visible=False),\n",
    "                    zaxis=dict(visible=False),\n",
    "                    aspectmode='data'),\n",
    "                  height=350,\n",
    "                  margin=dict(r=0, l=0, b=0, t=0, pad=0),\n",
    "                  scene_camera=camera)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save figure\n",
    "pio.write_html(fig,\n",
    "               file='../_includes/figures/ship_2dgauss.html',\n",
    "               full_html=False,\n",
    "               include_mathjax='cdn',\n",
    "               include_plotlyjs='cdn')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figure 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The ship\n",
    "fig = go.Figure(ff.create_trisurf(x=x, y=y, z=z+39,\n",
    "                                  simplices=simplices,\n",
    "                                  plot_edges=False,\n",
    "                                  show_colorbar=False,\n",
    "                                  colormap='rgb(255, 255, 255)').data)\n",
    "fig.update_traces(hoverinfo='none')\n",
    "\n",
    "# Rear\n",
    "X,Y=np.meshgrid(np.linspace(-51, 51, 2), np.linspace(200, 260, 2))\n",
    "Z=np.ones(X.shape)  \n",
    "fig.add_trace(go.Surface(x=X, y=Y, z=Z,\n",
    "                         colorscale='greens',\n",
    "                         opacity=0.6,\n",
    "                         showscale=False,\n",
    "                         hoverinfo='text',\n",
    "                         hovertext='10%'))\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=[-20], y=[220], z=[-10],\n",
    "                 mode='text',\n",
    "                 text='<b>rear</b>',\n",
    "                 hoverinfo='none',\n",
    "                 textfont=dict(size=25, color='black'),\n",
    "                 showlegend=False))\n",
    "\n",
    "# Middle\n",
    "X,Y=np.meshgrid(np.linspace(-51, 51, 2), np.linspace(50, -50, 2))\n",
    "Z=np.ones(X.shape)  \n",
    "fig.add_trace(go.Surface(x=X, y=Y, z=Z,\n",
    "                         colorscale='reds',\n",
    "                         opacity=0.6,\n",
    "                         showscale=False,\n",
    "                         hoverinfo='text',\n",
    "                         hovertext='20%'))\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=[-20], y=[0], z=[-5],\n",
    "                 mode='text',\n",
    "                 text='<b>middle</b>',\n",
    "                 hoverinfo='none',\n",
    "                 textfont=dict(size=25, color='black'),\n",
    "                 showlegend=False))\n",
    "\n",
    "# Bow\n",
    "X,Y=np.meshgrid(np.linspace(-51, 51, 2), np.linspace(-100, -180, 2))\n",
    "Z=np.ones(X.shape)  \n",
    "fig.add_trace(go.Surface(x=X, y=Y, z=Z,\n",
    "                         colorscale='blues',\n",
    "                         opacity=0.6,\n",
    "                         showscale=False,\n",
    "                         hoverinfo='text',\n",
    "                         hovertext='20%'))\n",
    "fig.add_trace(\n",
    "    go.Scatter3d(x=[-20], y=[-140], z=[0],\n",
    "                 mode='text',\n",
    "                 text='<b>bow</b>',\n",
    "                 hoverinfo='none',\n",
    "                 textfont=dict(size=25, color='black'),\n",
    "                 showlegend=False))\n",
    "\n",
    "# Figure properties\n",
    "camera = dict(\n",
    "    eye=dict(x=-1.3, y=-1, z=1.3),\n",
    "    center=dict(x=0.2, y=-0.1, z=-0.3))\n",
    "\n",
    "# Figure properties\n",
    "fig.update_layout(scene=dict(\n",
    "                    xaxis=dict(visible=False),\n",
    "                    yaxis=dict(visible=False),\n",
    "                    zaxis=dict(visible=False),\n",
    "                    aspectmode='data'),\n",
    "                  hoverlabel=dict(font_size=18),\n",
    "                  height=500,\n",
    "                  margin=dict(r=0, l=0, b=0, t=0, pad=0),\n",
    "                  scene_camera=camera)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save figure\n",
    "pio.write_html(fig,\n",
    "               file='../_includes/figures/ship_locations.html',\n",
    "               full_html=False,\n",
    "               include_plotlyjs='cdn')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Figures for Bayes' theorem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The probability square\n",
    "fig = go.Figure()\n",
    "fig.add_shape(\n",
    "            type=\"rect\",\n",
    "            xref=\"x\",\n",
    "            yref=\"y\",\n",
    "            x0=0,\n",
    "            y0=0,\n",
    "            x1=1,\n",
    "            y1=1,\n",
    "            line=dict(color=\"RoyalBlue\"),\n",
    "            fillcolor=\"LightSkyBlue\")\n",
    "\n",
    "\n",
    "fig.add_trace(go.Scatter(x=[0.3],\n",
    "                         y=[0.5],\n",
    "                         showlegend=False,\n",
    "                         marker=dict(color='LightSkyBlue', size=100),\n",
    "                         mode='markers',\n",
    "                         hovertext=\"Probability\",\n",
    "                         hoverinfo=\"text\",\n",
    "                         hoverlabel=dict(font_size=20, align='left'),\n",
    "                         opacity=1))\n",
    "\n",
    "fig.update_layout(\n",
    "    xaxis=dict(range=[-0.1, 1.1], constrain='domain', tickmode = 'linear', tick0=0, dtick=1),\n",
    "    yaxis=dict(range=[-0.1, 1.1], scaleanchor = \"x\", scaleratio = 1, constrain='domain',\n",
    "               tickmode = 'linear', tick0=0, dtick=1),\n",
    "    margin=dict(t=0, b=0, l=0, r=0),\n",
    "    height=350,\n",
    "    template=\"plotly_white\",\n",
    "    font=dict(\n",
    "        family=\"Courier New, monospace\",\n",
    "        size=16,\n",
    "        color=\"#7f7f7f\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save figure\n",
    "pio.write_html(fig,\n",
    "               file='../_includes/figures/square.html',\n",
    "               full_html=False,\n",
    "               include_plotlyjs='cdn')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The prior\n",
    "fig.add_shape(\n",
    "        name=\"Prior\",\n",
    "        type=\"rect\",\n",
    "        xref=\"x\",\n",
    "        yref=\"y\",\n",
    "        x0=0,\n",
    "        y0=0,\n",
    "        x1=0.72,\n",
    "        y1=1,\n",
    "        line=dict(color=\"Green\"),\n",
    "        fillcolor=\"LightGreen\")\n",
    "\n",
    "fig.data = []\n",
    "fig.add_trace(go.Scatter(x=[0.8],\n",
    "                         y=[0.5],\n",
    "                         showlegend=False,\n",
    "                         marker=dict(color='LightSkyBlue', size=50),\n",
    "                         mode='markers',\n",
    "                         hovertext=\"Probability\",\n",
    "                         hoverinfo=\"text\",\n",
    "                         hoverlabel=dict(font_size=20, align='left'),\n",
    "                         opacity=1))\n",
    "fig.add_trace(go.Scatter(x=[0.25],\n",
    "                         y=[0.5],\n",
    "                         showlegend=False,\n",
    "                         marker=dict(color='LightGreen', size=100),\n",
    "                         mode='markers',\n",
    "                         hovertext=\"Prior\",\n",
    "                         hoverinfo=\"text\",\n",
    "                         hoverlabel=dict(font_size=20, align='left'),\n",
    "                         opacity=1))\n",
    "\n",
    "annotations = []\n",
    "prior = [dict(showarrow=False,\n",
    "             x=0.36,\n",
    "             y=-0.1,\n",
    "             text=\"p(middle)\",\n",
    "             font_size=18),\n",
    "        dict(showarrow=False,\n",
    "            x=0.36,\n",
    "            y=-0.035,\n",
    "            text=\"}\",\n",
    "            font_size=40,\n",
    "            font_family='Helvetica Neue UltraLight',\n",
    "            textangle=90)]\n",
    "annotations.extend(prior)\n",
    "fig.layout.annotations = annotations\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save figure\n",
    "pio.write_html(fig,\n",
    "               file='../_includes/figures/prior.html',\n",
    "               full_html=False,\n",
    "               include_plotlyjs='cdn')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The likelihood\n",
    "fig.add_shape(\n",
    "        name=\"Likelihood\",\n",
    "        type=\"rect\",\n",
    "        xref=\"x\",\n",
    "        yref=\"y\",\n",
    "        x0=0,\n",
    "        y0=0,\n",
    "        x1=0.72,\n",
    "        y1=0.1,\n",
    "        line=dict(color=\"Yellow\"),\n",
    "        fillcolor=\"LightYellow\")\n",
    "\n",
    "fig.add_trace(go.Scatter(x=[0.3],\n",
    "                         y=[0.05],\n",
    "                         showlegend=False,\n",
    "                         marker=dict(color='LightYellow', size=20),\n",
    "                         mode='markers',\n",
    "                         hovertext=\"Likelihood\",\n",
    "                         hoverinfo=\"text\",\n",
    "                         hoverlabel=dict(font_size=20, align='left'),\n",
    "                         opacity=1))\n",
    "\n",
    "likelihood = [dict(showarrow=False,\n",
    "             x=-0.3,\n",
    "             y=0.055,\n",
    "             text=\"p(I|middle)\",\n",
    "             font_size=18),\n",
    "        dict(showarrow=False,\n",
    "            x=-0.05,\n",
    "            y=0.055,\n",
    "            text=\"{\",\n",
    "            font_size=35,\n",
    "            font_family='Helvetica Neue UltraLight')]\n",
    "annotations.extend(likelihood)\n",
    "fig.layout.annotations = annotations\n",
    "fig.layout.xaxis.range = [-0.55, 1.1]\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save figure\n",
    "pio.write_html(fig,\n",
    "               file='../_includes/figures/likelihood.html',\n",
    "               full_html=False,\n",
    "               include_plotlyjs='cdn')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The \"not\" likelihood\n",
    "fig.add_shape(\n",
    "        name=\"Likelihood\",\n",
    "        type=\"rect\",\n",
    "        xref=\"x\",\n",
    "        yref=\"y\",\n",
    "        x0=0.72,\n",
    "        y0=0,\n",
    "        x1=1,\n",
    "        y1=0.225,\n",
    "        line=dict(color=\"Coral\"),\n",
    "        fillcolor=\"LightCoral\")\n",
    "\n",
    "likelihood = [dict(showarrow=False,\n",
    "             x=1.33,\n",
    "             y=0.115,\n",
    "             text=\"p(I|!middle)\",\n",
    "             font_size=18),\n",
    "        dict(showarrow=False,\n",
    "            x=1.05,\n",
    "            y=0.12,\n",
    "            text=\"}\",\n",
    "            font_size=50,\n",
    "            font_family='Helvetica Neue UltraLight')]\n",
    "annotations.extend(likelihood)\n",
    "fig.layout.annotations = annotations\n",
    "fig.layout.xaxis.range = [-0.55, 1.33]\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save figure\n",
    "pio.write_html(fig,\n",
    "               file='../_includes/figures/not_likelihood.html',\n",
    "               full_html=False,\n",
    "               include_plotlyjs='cdn')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig.data = []\n",
    "fig.layout.annotations = []\n",
    "for shape in fig.layout.shapes[:-2]:\n",
    "    shape.opacity = 0.1\n",
    "fig.layout.shapes[-1].line.width = 4\n",
    "fig.layout.shapes[-2].line.width = 4\n",
    "fig.layout.xaxis.range = [-0.1, 1.1]\n",
    "fig.layout.yaxis.range = [-0.1, 1.1]\n",
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save figure\n",
    "pio.write_html(fig,\n",
    "               file='../_includes/figures/total_prob.html',\n",
    "               full_html=False,\n",
    "               include_plotlyjs='cdn')"
   ]
  }
 ],
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