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"""
================
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.
"""
# update a distribution based on new data.
import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as ss
from matplotlib.animation import FuncAnimation
class UpdateDist(object):
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, 15)
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 init(self):
self.success = 0
self.line.set_data([], [])
return self.line,
def __call__(self, i):
# This way the plot can continuously run and we just keep
# watching new realizations of the process
if i == 0:
return self.init()
# Choose success based on exceed a threshold with a uniform pick
if np.random.rand(1,) < self.prob:
self.success += 1
y = ss.beta.pdf(self.x, self.success + 1, (i - self.success) + 1)
self.line.set_data(self.x, y)
return self.line,
fig, ax = plt.subplots()
ud = UpdateDist(ax, prob=0.7)
anim = FuncAnimation(fig, ud, frames=np.arange(100), init_func=ud.init,
interval=100, blit=True)
plt.show()
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