贝叶斯更新

此动画显示在新数据到达时重新安装的后验估计更新。

垂直线表示绘制的分布应该收敛的理论值。

贝叶斯更新示例

  1. import math
  3. import numpy as np
  4. import matplotlib.pyplot as plt
  5. from matplotlib.animation import FuncAnimation
  8. def beta_pdf(x, a, b):
  9.     return (x**(a-1) * (1-x)**(b-1) * math.gamma(a + b)
  10.             / (math.gamma(a) * math.gamma(b)))
  13. class UpdateDist(object):
  14.     def __init__(self, ax, prob=0.5):
  15.         self.success = 0
  16.         self.prob = prob
  17.         self.line, = ax.plot([], [], 'k-')
  18.         self.x = np.linspace(0, 1, 200)
  19.         self.ax = ax
  21.         # Set up plot parameters
  22.         self.ax.set_xlim(0, 1)
  23.         self.ax.set_ylim(0, 15)
  24.         self.ax.grid(True)
  26.         # This vertical line represents the theoretical value, to
  27.         # which the plotted distribution should converge.
  28.         self.ax.axvline(prob, linestyle='--', color='black')
  30.     def init(self):
  31.         self.success = 0
  32.         self.line.set_data([], [])
  33.         return self.line,
  35.     def __call__(self, i):
  36.         # This way the plot can continuously run and we just keep
  37.         # watching new realizations of the process
  38.         if i == 0:
  39.             return self.init()
  41.         # Choose success based on exceed a threshold with a uniform pick
  42.         if np.random.rand(1,) < self.prob:
  43.             self.success += 1
  44.         y = beta_pdf(self.x, self.success + 1, (i - self.success) + 1)
  45.         self.line.set_data(self.x, y)
  46.         return self.line,
  48. # Fixing random state for reproducibility
  49. np.random.seed(19680801)
  52. fig, ax = plt.subplots()
  53. ud = UpdateDist(ax, prob=0.7)
  54. anim = FuncAnimation(fig, ud, frames=np.arange(100), init_func=ud.init,
  55.                      interval=100, blit=True)
  56. plt.show()

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