tutorials/W2D1_BayesianStatistics/W2D1_Tutorial2.ipynb

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   "source": [
    "<a href=\"https://colab.research.google.com/github/NeuromatchAcademy/course-content/blob/mrk-W2D1/tutorials/W2D1_BayesianStatistics/W2D1_Tutorial2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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   "source": [
    "# Neuromatch Academy: Week 2, Day 1, Tutorial 2\n",
    "# Causal inference with mixture of Gaussians\n",
    "\n",
    "__Content creators:__ Vincent Valton, Konrad Kording, with help from Matt Krause\n",
    "\n",
    "__Content reviewers:__ Matt Krause, Jesse Livezey, Karolina Stosio, Saeed Salehi, Michael Waskom"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1kGSaKhXykZs"
   },
   "source": [
    "# Tutorial Objectives\n",
    "\n",
    "The previous notebook introduced Gaussians and Bayes' rule, allowing us to model very simple combinations of auditory and visual input. In this and the following notebook, we will use those building blocks to explore more complicated sensory integration and ventriloquism! \n",
    "\n",
    "In this notebook, you will:\n",
    "1. Learn more about the problem setting, which we wil also use in Tutorial 3,\n",
    "2. Implement a mixture-of-Gaussian prior, and\n",
    "3. Explore how that prior produces more complex posteriors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "cellView": "form",
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    },
    "colab_type": "code",
    "id": "fwHP4D3p3c2A",
    "outputId": "422497ee-b213-4f13-db03-85476ca822b7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Video available at https://youtube.com/watch?v=GdIwJWsW9-s\n"
     ]
    },
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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/GdIwJWsW9-s?fs=1\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f9265b9fb10>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# @title Video 1: Introduction\n",
    "from IPython.display import YouTubeVideo\n",
    "video = YouTubeVideo(id='GdIwJWsW9-s', width=854, height=480, fs=1)\n",
    "print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
    "video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "wcHSXKdUx8x9"
   },
   "source": [
    "---\n",
    "##Setup  \n",
    "Please execute the cells below to initialize the notebook environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "gTb-QAsTIm6L"
   },
   "outputs": [],
   "source": [
    "# imports\n",
    "import numpy as np                 \n",
    "import matplotlib.pyplot as plt "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "cellView": "form",
    "colab": {},
    "colab_type": "code",
    "id": "GVwNeV6MIta6"
   },
   "outputs": [],
   "source": [
    "#@title Figure Settings\n",
    "plt.style.use(\"https://raw.githubusercontent.com/NeuromatchAcademy/course-content/master/nma.mplstyle\")\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "cellView": "form",
    "colab": {},
    "colab_type": "code",
    "id": "mmp9WCoEzFOO"
   },
   "outputs": [],
   "source": [
    "#@title Helper functions\n",
    "    \n",
    "def my_gaussian(x_points, mu, sigma):\n",
    "    \"\"\"\n",
    "    DO NOT EDIT THIS FUNCTION !!!\n",
    "\n",
    "    Returns normalized Gaussian estimated at points `x_points`, with parameters `mu` and `sigma`\n",
    "    \n",
    "    Args: \n",
    "      x_points (numpy array of floats) - points at which the gaussian is evaluated\n",
    "      mu (scalar) - mean of the Gaussian\n",
    "      sigma (scalar) - standard deviation of the gaussian\n",
    "    Returns:\n",
    "      (numpy array of floats): normalized Gaussian (i.e. without constant) evaluated at `x`\n",
    "    \"\"\"\n",
    "    px = np.exp(- 1/2/sigma**2 * (mu - x_points) ** 2)\n",
    "\n",
    "    px = px / px.sum() # this is the normalization part with a very strong assumption, that\n",
    "                       # x_points cover the big portion of probability mass around the mean.\n",
    "                       # Please think/discuss when this would be a dangerous assumption.\n",
    "    \n",
    "    return px\n",
    "\n",
    "def plot_mixture_prior(x, gaussian1, gaussian2, combined):\n",
    "    \"\"\"\n",
    "    DO NOT EDIT THIS FUNCTION !!!\n",
    "\n",
    "    Plots a prior made of a mixture of gaussians\n",
    "    \n",
    "    Args: \n",
    "      x (numpy array of floats):         points at which the likelihood has been evaluated\n",
    "      gaussian1 (numpy array of floats): normalized probabilities for Gaussian 1 evaluated at each `x`\n",
    "      gaussian2 (numpy array of floats): normalized probabilities for Gaussian 2 evaluated at each `x`\n",
    "      posterior (numpy array of floats): normalized probabilities for the posterior evaluated at each `x`\n",
    "             \n",
    "    Returns:\n",
    "      Nothing\n",
    "    \"\"\"\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x, gaussian1, '--b', LineWidth=2, label='Gaussian 1')\n",
    "    ax.plot(x, gaussian2, '-.b', LineWidth=2, label='Gaussian 2')\n",
    "    ax.plot(x, combined, '-r', LineWidth=2, label='Gaussian Mixture')\n",
    "    ax.legend()\n",
    "    ax.set_ylabel('Probability')\n",
    "    ax.set_xlabel('Orientation (Degrees)')\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tF5caxVGYURh"
   },
   "source": [
    "# Section 1: Motivating example\n",
    "\n",
    "Ventriloquists produce the illusion that their puppets are talking because:\n",
    "1. We observe the visual input of the puppet moving its mouth, as if speaking.\n",
    "2. The speech that the puppeteer generates originates near the puppet's mouth. \n",
    "\n",
    "Since we are accustomed to voices coming from moving mouths, we tend to interpret the voice as coming directly from the puppet itself rather than from the puppeteer (who is also hiding his/her own mouth movements). In the remaining tutorials, we will study how this illusion breaks down as the distance between the visual stimulus (the puppet's mouth) and the auditory stimulus (the puppeter's concealed speech) changes. \n",
    "\n",
    "Imagine an experiment where participants are shown a puppet moving its mouth at a location directly in front of them (at position 0˚). The subjects are told that 75% of the time, the voice they hear originates from the puppet. On the remaining 25% of trials, sounds come from elsewhere. Participants learn this over multiple trials, after which a curtain is dropped in front of the puppeteer and the puppet. \n",
    "\n",
    "Next, we present only the auditory stimulus at varying locations and we ask participants to report where the source of the sound is located. The participants have access to two pieces of information:\n",
    "\n",
    "*   The prior information about sound localization, learned during the trials before the curtain fell.\n",
    "*   Their noisy sensory estimates about where a particular sound originates. \n",
    "\n",
    "Our eventual goal, which we achieve in Tutorial 3, is to predict the subjects' responses: when do subjects ascribe a sound to the puppet, and when do they believe it originated elsewhere? Doing so requires building a prior that captures the participant's knowledge and expectations, which we wil do in the exercises that follow here. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "M6II_9AmykZt"
   },
   "source": [
    "# Section 2: Mixture-of-Gaussians Prior\n",
    "\n",
    "In the previous tutorial, you learned how to create a single Gaussian prior that could represent one of these possibilties. A broad Gaussian with a large $\\sigma$ could represent sounds originating from nearly anywhere, while a narrow Gaussian with $\\mu$ near zero could represent sounds orginating from the puppet. \n",
    "\n",
    "Here, we will combine those into a mixure-of-Gaussians probability density function (PDF) that captures both possibilties. We will control how the Gaussians are mixed by summing them together with a 'mixing' or weight parameter $p_{common}$, set to a value between 0 and 1, like so:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "    \\text{Mixture} = \\bigl[\\; p_{common} \\times \\mathcal{N}(\\mu_{common},\\sigma_{common}) \\; \\bigr] + \\bigl[ \\;\\underbrace{(1-p_{common})}_{p_{independent}} \\times \\mathcal{N}(\\mu_{independent},\\sigma_{independent}) \\; \\bigr]\n",
    "\\end{eqnarray}\n",
    "\n",
    "$p_{common}$ denotes the probability that auditory stimulus shares a \"common\" source with the learnt visual input; in other words, the probability that the \"puppet\" is speaking. You might think that we need to include a separate weight for the possibility that sound is \"independent\" from the puppet. nHowever, since there are only two, mutually-exclusive possibilties, we can replace $p_{independent}$ with $(1 - p_{common})$ since, by the law of total probability, $p_{common} + p_{independent}$ must equal one. \n",
    "\n",
    "Using the formula above, complete the code to build this mixture-of-Gaussians PDF: \n",
    "* Generate a Gaussian with mean 0 and standard deviation 0.5 to be the 'common' part of the Gaussian mixture prior. (This is already done for you below).\n",
    "* Generate another Gaussian with mean 0 and standard deviation 3 to serve as the 'independent' part. \n",
    "* Combine the two Gaussians to make a new prior by mixing the two Gaussians with mixing parameter $p_{common}$ = 0.75 so that the peakier \"common-cause\" Gaussian has 75% of the weight. Don't forget to normalize afterwards! \n",
    "\n",
    "Hints:\n",
    "* Code for the `my_gaussian` function from Tutorial 1 is available for you to use. Its documentation is below. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BqnE69bSyorO"
   },
   "source": [
    "**Helper function(s)**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 247
    },
    "colab_type": "code",
    "id": "owJc8QeMzAAg",
    "outputId": "5e888a13-7abb-4cbc-a623-ae600d677ead"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function my_gaussian in module __main__:\n",
      "\n",
      "my_gaussian(x_points, mu, sigma)\n",
      "    DO NOT EDIT THIS FUNCTION !!!\n",
      "    \n",
      "    Returns normalized Gaussian estimated at points `x_points`, with parameters `mu` and `sigma`\n",
      "    \n",
      "    Args: \n",
      "      x_points (numpy array of floats) - points at which the gaussian is evaluated\n",
      "      mu (scalar) - mean of the Gaussian\n",
      "      sigma (scalar) - standard deviation of the gaussian\n",
      "    Returns:\n",
      "      (numpy array of floats): normalized Gaussian (i.e. without constant) evaluated at `x`\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(my_gaussian)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "dqKKm5dpQ07Y"
   },
   "source": [
    "## Exercise 1: Implement the prior "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "cellView": "code",
    "colab": {},
    "colab_type": "code",
    "id": "y34EhXtnykZu"
   },
   "outputs": [],
   "source": [
    "def mixture_prior(x, mean=0, sigma_common=0.5, sigma_independent=3, p_common=0.75):\n",
    "\n",
    "  ###############################################################################\n",
    "  ## Insert your code here to:\n",
    "  #   * Create a second gaussian representing the independent-cause component\n",
    "  #   * Combine the two priors, using the mixing weight p_common. Don't forget\n",
    "  #      to normalize the result so it remains a proper probability density function\n",
    "  #\n",
    "  #   * Comment the line below to test out your function   \n",
    "  raise NotImplementedError(\"Please complete Exercise 1\")\n",
    "  ###############################################################################\n",
    "  \n",
    "  gaussian_common = my_gaussian(x, mean, sigma_common) \n",
    "  gaussian_independent = ...\n",
    "  mixture = ...\n",
    "\n",
    "  return gaussian_common, gaussian_independent, mixture\n",
    "\n",
    "\n",
    "x = np.arange(-10, 11, 0.1)\n",
    "\n",
    "# Uncomment the lines below to visualize out your solution\n",
    "# common, independent, mixture = mixture_prior(x)\n",
    "# plot_mixture_prior(x, common, independent, mixture)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 329
    },
    "colab_type": "code",
    "id": "TbTSz-TtykZy",
    "outputId": "371c906d-ddd0-42f4-bd7d-6170c8818f94"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/hostedtoolcache/Python/3.7.8/x64/lib/python3.7/site-packages/ipykernel_launcher.py:40: MatplotlibDeprecationWarning: Case-insensitive properties were deprecated in 3.3 and support will be removed two minor releases later\n",
      "/opt/hostedtoolcache/Python/3.7.8/x64/lib/python3.7/site-packages/ipykernel_launcher.py:41: MatplotlibDeprecationWarning: Case-insensitive properties were deprecated in 3.3 and support will be removed two minor releases later\n",
      "/opt/hostedtoolcache/Python/3.7.8/x64/lib/python3.7/site-packages/ipykernel_launcher.py:42: MatplotlibDeprecationWarning: Case-insensitive properties were deprecated in 3.3 and support will be removed two minor releases later\n",
      "findfont: Font family ['xkcd', 'xkcd Script', 'Humor Sans', 'Comic Neue', 'Comic Sans MS'] not found. Falling back to DejaVu Sans.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "findfont: Font family ['xkcd', 'xkcd Script', 'Humor Sans', 'Comic Neue', 'Comic Sans MS'] not found. Falling back to DejaVu Sans.\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 280,
       "width": 424
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# to_remove solution\n",
    "def mixture_prior(x, mean=0, sigma_common=0.5, sigma_independent=3, p_common=0.75):\n",
    "\n",
    "  gaussian_common = my_gaussian(x, mean, sigma_common) \n",
    "  ###############################################################################\n",
    "  ## Insert your code here to:\n",
    "  ##   * Create a second gaussian representing the independent-cause component\n",
    "  ##   * Combine the two priors, using the mixing weight p_common. Don't forget\n",
    "  #      to normalize the result so it remains a proper probability density function\n",
    "  #\n",
    "  #    * Comment the line below to test out your function   \n",
    "  #raise NotImplementedError(\"Please complete Exercise 1\")\n",
    "  ###############################################################################\n",
    "  gaussian_independent = my_gaussian(x, mean, sigma_independent)\n",
    "  \n",
    "  mixture = p_common * gaussian_common + ((1-p_common) * gaussian_independent) \n",
    "  mixture = mixture / np.sum(mixture)\n",
    "  \n",
    "  return gaussian_common, gaussian_independent, mixture\n",
    "\n",
    "\n",
    "x = np.arange(-10, 11, 0.1)\n",
    "\n",
    "# Uncomment the lines below to visualize out your solution\n",
    "common, independent, mixture = mixture_prior(x)\n",
    "with plt.xkcd():\n",
    "  plot_mixture_prior(x, common, independent, mixture)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "3cd1_HLZ0CCX"
   },
   "source": [
    "\n",
    "# Section 3: Bayes Theorem with Complex Posteriors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 516
    },
    "colab_type": "code",
    "id": "fWRT63esyZiD",
    "outputId": "79136cf7-30de-475f-83ba-29887aef24fb"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Video available at https://youtube.com/watch?v=LWKM35te0WI\n"
     ]
    },
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/LWKM35te0WI?fs=1\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f9240f68a10>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Video 2: Mixture-of-Gaussians and Bayes' Theorem\n",
    "video = YouTubeVideo(id='LWKM35te0WI', width=854, height=480, fs=1)\n",
    "print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
    "video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6Im6Qo6_ykZ2"
   },
   "source": [
    "Now that we have created a mixture of Gaussians prior that embodies the participants' expectations about sound location, we want to compute the posterior probability, which represents the subjects' beliefs about a specific sound's origin. \n",
    "\n",
    "To do so we will compute the posterior by using *Bayes Theorem* to combine the mixture-of-gaussians prior and varying auditory Gaussian likelihood. This works exactly the same as in Tutorial 1: we simply multiply the prior and likelihood pointwise, then normalize the resulting distribution so it sums to 1. (The closed-form solution from Exercise 2B, however, no longer applies to this more complicated prior). \n",
    "\n",
    "Here, we provide you with the code mentioned in the video (lucky!). Instead, use the interactive demo to explore how a mixture-of-Gaussians prior and Gaussian likelihood interact. For simplicity, we have fixed the prior mean to be zero. We also recommend starting with same other prior parameters used in Exercise 1: $\\sigma_{common} = 0.5, \\sigma_{independent} = 3, p_{common}=0.75$; vary the likelihood instead. \n",
    "\n",
    "Unlike the demo in Tutorial 1, you should see several qualitatively different effects on the posterior, depending on the relative position and width of likelihood. Pay special attention to both the overall shape of the posterior and the location of the peak. What do you see?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "e4Jq2rczSm1M"
   },
   "source": [
    "## Interactive Demo 1: Mixture-of-Gaussian prior and the posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 456,
     "referenced_widgets": [
      "2ae86f7825fa42089f00b630d0408324",
      "6f60bf5e489b432fb238f743a1092427",
      "3e2a788493a34bb3b5343a621de06716",
      "b1d6aa7aa27143b7bed7d2131f93315c",
      "ce3f0d132c0348cb9a4cdbe1a1a55617",
      "33aceea223704d10a3f953895c208fef",
      "818c70bbc9f04aac8e319e0b74d7a402",
      "8e60f63452ac4122aa23a52ed6c7a31e",
      "54528ae871ba42f0aafb59a6d4a743cd",
      "e7aab8621eaf473fb04c9048ffc70158",
      "cc50a31c3bb644b48d2a68140b7a92ff",
      "6b62f20ee2204461b4fc2e6058ee8100",
      "abac0add4423425c8892ef4f985c7e06",
      "c7628a32462b47f8bd8a3d7c4f2b5cfe",
      "b74e7dd69dfc4dd882d38e020b51898f",
      "8e96eb6720c9422f9ba320457afe1df0",
      "39b28819bf8a4c0bb051c91b718200e5",
      "9dedcc20a79845779a6447ceb77051e9",
      "e22f2c8ff4ec4e37a6a856d5ccbed3c9"
     ]
    },
    "colab_type": "code",
    "id": "ZlIOO-3SRD-0",
    "outputId": "12577f11-30f0-484f-c043-d409104ab8d5"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 280,
       "width": 424
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#@title\n",
    "#@markdown Make sure you execute this cell to enable the widget!\n",
    "\n",
    "fig_domain = np.arange(-10, 11, 0.1)\n",
    "import ipywidgets as widgets\n",
    "\n",
    "def refresh(sigma_common=0.5, sigma_independent=3, p_common=0.75, mu_auditory=3, sigma_auditory=1.5):\n",
    "    _, _, prior = mixture_prior(fig_domain, 0, sigma_common, sigma_independent, p_common)\n",
    "    likelihood = my_gaussian(fig_domain, mu_auditory, sigma_auditory)\n",
    "\n",
    "    posterior = prior * likelihood\n",
    "    posterior /= posterior.sum()\n",
    "\n",
    "    plt.plot(fig_domain, prior, label=\"Mixture Prior\")\n",
    "    plt.plot(fig_domain, likelihood, label=\"Likelihood\")\n",
    "    plt.plot(fig_domain, posterior, label=\"Posterior\")\n",
    "\n",
    "    plt.legend()\n",
    "\n",
    "    plt.show()\n",
    "\n",
    "style = {'description_width': 'initial'}\n",
    "\n",
    "_ = widgets.interact(refresh, \n",
    "    sigma_common=widgets.FloatSlider(value=0.5, min=0.01, max=10, step=0.5, description=\"sigma_common\", style=style),\n",
    "    sigma_independent=widgets.FloatSlider(value=3, min=0.01, max=10, step=0.5, description=\"sigma_independent:\", style=style),\n",
    "    p_common=widgets.FloatSlider(value=0.75, min=0, max=1, steps=0.01, description=\"p_common\"),\n",
    "    mu_auditory=widgets.FloatSlider(value=2, min=-10, max=10, step=0.1, description=\"mu_auditory:\", style=style),\n",
    "    sigma_auditory=widgets.FloatSlider(value=0.5, min=0.01, max=10, step=0.5, description=\"sigma_auditory:\", style=style),\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 100
    },
    "colab_type": "code",
    "id": "GXrEe4ctakqR",
    "outputId": "17a71ae3-6fd7-47ba-ce59-34e72ad104b2"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"\\nThe mixture of Gaussian prior creates some interesting behaviour: \\n  1. We observe multiple modes (i.e. peaks) in our posterior\\n  (the common and independent causes). \\n  2. The mode of the posterior jumps between stimulus locations. These \\n  correspond to the participant switching from the independent to the common \\n  parts (i.e. causes) of the prior. \\n\\nA similar discontinuity (ie. 'jump') in the posterior mode would happen in the \\ncase of cue combination illusion with the puppet and puppeteer voice. \\nThe illusion that the puppet is generating the speech would break-down when the\\nvoice stimulus is presented too far away from the visual input (the puppet's \\nlocation).\\n\""
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#to_remove explanation\n",
    "\"\"\"\n",
    "The mixture of Gaussian prior creates some interesting behaviour: \n",
    "  1. We observe multiple modes (i.e. peaks) in our posterior\n",
    "  (the common and independent causes). \n",
    "  2. The mode of the posterior jumps between stimulus locations. These \n",
    "  correspond to the participant switching from the independent to the common \n",
    "  parts (i.e. causes) of the prior. \n",
    "\n",
    "A similar discontinuity (ie. 'jump') in the posterior mode would happen in the \n",
    "case of cue combination illusion with the puppet and puppeteer voice. \n",
    "The illusion that the puppet is generating the speech would break-down when the\n",
    "voice stimulus is presented too far away from the visual input (the puppet's \n",
    "location).\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ujxQsL_vMSFW"
   },
   "source": [
    "# Section 3: Conclusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "cellView": "form",
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 516
    },
    "colab_type": "code",
    "id": "B8itfnz_4VV_",
    "outputId": "f4d716db-7d2b-44d8-ee9e-1191a3b4b5e6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Video available at https://youtube.com/watch?v=UgeAtE8xZT8\n"
     ]
    },
    {
     "data": {
      "image/jpeg": 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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"854\"\n",
       "            height=\"480\"\n",
       "            src=\"https://www.youtube.com/embed/UgeAtE8xZT8?fs=1\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7f9240f71750>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#@title Video 3: Outro\n",
    "video = YouTubeVideo(id='UgeAtE8xZT8', width=854, height=480, fs=1)\n",
    "print(\"Video available at https://youtube.com/watch?v=\" + video.id)\n",
    "video"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "b7wWZWA2hQkP"
   },
   "source": [
    "In this tutorial, we introduced the ventriloquism setting that will form the basis of Tutorials 3 and 4 as well. We built a mixture-of-Gaussians prior that captures the participants' subjective experiences. In the next tutorials, we will use these to perform causal inference and predict the subject's responses to indvidual stimuli. "
   ]
  }
 ],
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