
.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/animation/bayes_update.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_gallery_animation_bayes_update.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_gallery_animation_bayes_update.py:


================
The Bayes update
================

This animation displays the posterior estimate updates as it is refitted when
new data arrives.
The vertical line represents the theoretical value to which the plotted
distribution should converge.

.. GENERATED FROM PYTHON SOURCE LINES 11-64



.. container:: sphx-glr-animation

    .. raw:: html

        
     <link rel="stylesheet"
     href="https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css">
     <script language="javascript">
       function isInternetExplorer() {
         ua = navigator.userAgent;
         /* MSIE used to detect old browsers and Trident used to newer ones*/
         return ua.indexOf("MSIE ") > -1 || ua.indexOf("Trident/") > -1;
       }

       /* Define the Animation class */
       function Animation(frames, img_id, slider_id, interval, loop_select_id){
         this.img_id = img_id;
         this.slider_id = slider_id;
         this.loop_select_id = loop_select_id;
         this.interval = interval;
         this.current_frame = 0;
         this.direction = 0;
         this.timer = null;
         this.frames = new Array(frames.length);

         for (var i=0; i<frames.length; i++)
         {
          this.frames[i] = new Image();
          this.frames[i].src = frames[i];
         }
         var slider = document.getElementById(this.slider_id);
         slider.max = this.frames.length - 1;
         if (isInternetExplorer()) {
             // switch from oninput to onchange because IE <= 11 does not conform
             // with W3C specification. It ignores oninput and onchange behaves
             // like oninput. In contrast, Microsoft Edge behaves correctly.
             slider.setAttribute('onchange', slider.getAttribute('oninput'));
             slider.setAttribute('oninput', null);
         }
         this.set_frame(this.current_frame);
       }

       Animation.prototype.get_loop_state = function(){
         var button_group = document[this.loop_select_id].state;
         for (var i = 0; i < button_group.length; i++) {
             var button = button_group[i];
             if (button.checked) {
                 return button.value;
             }
         }
         return undefined;
       }

       Animation.prototype.set_frame = function(frame){
         this.current_frame = frame;
         document.getElementById(this.img_id).src =
                 this.frames[this.current_frame].src;
         document.getElementById(this.slider_id).value = this.current_frame;
       }

       Animation.prototype.next_frame = function()
       {
         this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));
       }

       Animation.prototype.previous_frame = function()
       {
         this.set_frame(Math.max(0, this.current_frame - 1));
       }

       Animation.prototype.first_frame = function()
       {
         this.set_frame(0);
       }

       Animation.prototype.last_frame = function()
       {
         this.set_frame(this.frames.length - 1);
       }

       Animation.prototype.slower = function()
       {
         this.interval /= 0.7;
         if(this.direction > 0){this.play_animation();}
         else if(this.direction < 0){this.reverse_animation();}
       }

       Animation.prototype.faster = function()
       {
         this.interval *= 0.7;
         if(this.direction > 0){this.play_animation();}
         else if(this.direction < 0){this.reverse_animation();}
       }

       Animation.prototype.anim_step_forward = function()
       {
         this.current_frame += 1;
         if(this.current_frame < this.frames.length){
           this.set_frame(this.current_frame);
         }else{
           var loop_state = this.get_loop_state();
           if(loop_state == "loop"){
             this.first_frame();
           }else if(loop_state == "reflect"){
             this.last_frame();
             this.reverse_animation();
           }else{
             this.pause_animation();
             this.last_frame();
           }
         }
       }

       Animation.prototype.anim_step_reverse = function()
       {
         this.current_frame -= 1;
         if(this.current_frame >= 0){
           this.set_frame(this.current_frame);
         }else{
           var loop_state = this.get_loop_state();
           if(loop_state == "loop"){
             this.last_frame();
           }else if(loop_state == "reflect"){
             this.first_frame();
             this.play_animation();
           }else{
             this.pause_animation();
             this.first_frame();
           }
         }
       }

       Animation.prototype.pause_animation = function()
       {
         this.direction = 0;
         if (this.timer){
           clearInterval(this.timer);
           this.timer = null;
         }
       }

       Animation.prototype.play_animation = function()
       {
         this.pause_animation();
         this.direction = 1;
         var t = this;
         if (!this.timer) this.timer = setInterval(function() {
             t.anim_step_forward();
         }, this.interval);
       }

       Animation.prototype.reverse_animation = function()
       {
         this.pause_animation();
         this.direction = -1;
         var t = this;
         if (!this.timer) this.timer = setInterval(function() {
             t.anim_step_reverse();
         }, this.interval);
       }
     </script>

     <style>
     .animation {
         display: inline-block;
         text-align: center;
     }
     input[type=range].anim-slider {
         width: 374px;
         margin-left: auto;
         margin-right: auto;
     }
     .anim-buttons {
         margin: 8px 0px;
     }
     .anim-buttons button {
         padding: 0;
         width: 36px;
     }
     .anim-state label {
         margin-right: 8px;
     }
     .anim-state input {
         margin: 0;
         vertical-align: middle;
     }
     </style>

     <div class="animation">
       <img id="_anim_img2e2a8be6bb204775b2b0747b7dffac4f">
       <div class="anim-controls">
         <input id="_anim_slider2e2a8be6bb204775b2b0747b7dffac4f" type="range" class="anim-slider"
                name="points" min="0" max="1" step="1" value="0"
                oninput="anim2e2a8be6bb204775b2b0747b7dffac4f.set_frame(parseInt(this.value));"></input>
         <div class="anim-buttons">
           <button title="Decrease speed" aria-label="Decrease speed" onclick="anim2e2a8be6bb204775b2b0747b7dffac4f.slower()">
               <i class="fa fa-minus"></i></button>
           <button title="First frame" aria-label="First frame" onclick="anim2e2a8be6bb204775b2b0747b7dffac4f.first_frame()">
             <i class="fa fa-fast-backward"></i></button>
           <button title="Previous frame" aria-label="Previous frame" onclick="anim2e2a8be6bb204775b2b0747b7dffac4f.previous_frame()">
               <i class="fa fa-step-backward"></i></button>
           <button title="Play backwards" aria-label="Play backwards" onclick="anim2e2a8be6bb204775b2b0747b7dffac4f.reverse_animation()">
               <i class="fa fa-play fa-flip-horizontal"></i></button>
           <button title="Pause" aria-label="Pause" onclick="anim2e2a8be6bb204775b2b0747b7dffac4f.pause_animation()">
               <i class="fa fa-pause"></i></button>
           <button title="Play" aria-label="Play" onclick="anim2e2a8be6bb204775b2b0747b7dffac4f.play_animation()">
               <i class="fa fa-play"></i></button>
           <button title="Next frame" aria-label="Next frame" onclick="anim2e2a8be6bb204775b2b0747b7dffac4f.next_frame()">
               <i class="fa fa-step-forward"></i></button>
           <button title="Last frame" aria-label="Last frame" onclick="anim2e2a8be6bb204775b2b0747b7dffac4f.last_frame()">
               <i class="fa fa-fast-forward"></i></button>
           <button title="Increase speed" aria-label="Increase speed" onclick="anim2e2a8be6bb204775b2b0747b7dffac4f.faster()">
               <i class="fa fa-plus"></i></button>
         </div>
         <form title="Repetition mode" aria-label="Repetition mode" action="#n" name="_anim_loop_select2e2a8be6bb204775b2b0747b7dffac4f"
               class="anim-state">
           <input type="radio" name="state" value="once" id="_anim_radio1_2e2a8be6bb204775b2b0747b7dffac4f"
                  >
           <label for="_anim_radio1_2e2a8be6bb204775b2b0747b7dffac4f">Once</label>
           <input type="radio" name="state" value="loop" id="_anim_radio2_2e2a8be6bb204775b2b0747b7dffac4f"
                  checked>
           <label for="_anim_radio2_2e2a8be6bb204775b2b0747b7dffac4f">Loop</label>
           <input type="radio" name="state" value="reflect" id="_anim_radio3_2e2a8be6bb204775b2b0747b7dffac4f"
                  >
           <label for="_anim_radio3_2e2a8be6bb204775b2b0747b7dffac4f">Reflect</label>
         </form>
       </div>
     </div>


     <script language="javascript">
       /* Instantiate the Animation class. */
       /* The IDs given should match those used in the template above. */
       (function() {
         var img_id = "_anim_img2e2a8be6bb204775b2b0747b7dffac4f";
         var slider_id = "_anim_slider2e2a8be6bb204775b2b0747b7dffac4f";
         var loop_select_id = "_anim_loop_select2e2a8be6bb204775b2b0747b7dffac4f";
         var frames = new Array(100);
    
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         /* set a timeout to make sure all the above elements are created before
            the object is initialized. */
         setTimeout(function() {
             anim2e2a8be6bb204775b2b0747b7dffac4f = new Animation(frames, img_id, slider_id, 100.0,
                                      loop_select_id);
         }, 0);
       })()
     </script>






.. code-block:: default


    import math

    import numpy as np
    import matplotlib.pyplot as plt
    from matplotlib.animation import FuncAnimation


    def beta_pdf(x, a, b):
        return (x**(a-1) * (1-x)**(b-1) * math.gamma(a + b)
                / (math.gamma(a) * math.gamma(b)))


    class UpdateDist:
        def __init__(self, ax, prob=0.5):
            self.success = 0
            self.prob = prob
            self.line, = ax.plot([], [], 'k-')
            self.x = np.linspace(0, 1, 200)
            self.ax = ax

            # Set up plot parameters
            self.ax.set_xlim(0, 1)
            self.ax.set_ylim(0, 10)
            self.ax.grid(True)

            # This vertical line represents the theoretical value, to
            # which the plotted distribution should converge.
            self.ax.axvline(prob, linestyle='--', color='black')

        def __call__(self, i):
            # This way the plot can continuously run and we just keep
            # watching new realizations of the process
            if i == 0:
                self.success = 0
                self.line.set_data([], [])
                return self.line,

            # Choose success based on exceed a threshold with a uniform pick
            if np.random.rand(1,) < self.prob:
                self.success += 1
            y = beta_pdf(self.x, self.success + 1, (i - self.success) + 1)
            self.line.set_data(self.x, y)
            return self.line,

    # Fixing random state for reproducibility
    np.random.seed(19680801)


    fig, ax = plt.subplots()
    ud = UpdateDist(ax, prob=0.7)
    anim = FuncAnimation(fig, ud, frames=100, interval=100, blit=True)
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  6.464 seconds)


.. _sphx_glr_download_gallery_animation_bayes_update.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download sphx-glr-download-python

     :download:`Download Python source code: bayes_update.py <bayes_update.py>`



  .. container:: sphx-glr-download sphx-glr-download-jupyter

     :download:`Download Jupyter notebook: bayes_update.ipynb <bayes_update.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    Keywords: matplotlib code example, codex, python plot, pyplot
    `Gallery generated by Sphinx-Gallery
    <https://sphinx-gallery.readthedocs.io>`_
