python - 通过移植到 PyMC3 的蒙特卡洛马尔可夫链的简单贝叶斯网络

Question

我正在移植 Simple Bayesian Network via Monte Carlo Markov Chain 的示例从 PyMC2 到 PyMC3 并且它有效。
结果见下gist在 GitHub 上的文件 pymc3_rain_sprinkler_grass_simple_bayesian_network.py.

我想通过提供证据来扩展原始示例，例如草是湿的，然后让 PyMC3 给我诸如“给定草是湿的，下雨的概率是多少？”之类的问题的答案。

结果轨迹似乎是“恒定的”，例如它不再有随机性的元素。查看要点中的 pymc3_rain_sprinkler_grass_simple_bayesian_network_with_evidence.py 并执行 df.drop_duplicates() 以了解我的意思。

我做错了什么？

Answer 1

我设法解决了我的问题。要点是将 testval 设置为“true”而不是“false”。将步长方法从 Metropolis 更改为 BinaryGibbsMetropolis 改善了这种情况。

完整的解决方案供引用。我还更新了要点。

import numpy as np
import pandas as pd
import pymc3 as pm

niter = 10000  # 10000
tune = 5000  # 5000

model = pm.Model()

with model:
    tv = [1]
    rain = pm.Bernoulli('rain', 0.2, shape=1, testval=tv)
    sprinkler_p = pm.Deterministic('sprinkler_p', pm.math.switch(rain, 0.01, 0.40))
    sprinkler = pm.Bernoulli('sprinkler', sprinkler_p, shape=1, testval=tv)
    grass_wet_p = pm.Deterministic('grass_wet_p', pm.math.switch(rain, pm.math.switch(sprinkler, 0.99, 0.80), pm.math.switch(sprinkler, 0.90, 0.0)))
    grass_wet = pm.Bernoulli('grass_wet', grass_wet_p, observed=np.array([1]), shape=1)

    trace = pm.sample(20000, step=[pm.BinaryGibbsMetropolis([rain, sprinkler])], tune=tune, random_seed=124)

# pm.traceplot(trace)

dictionary = {
              'Rain': [1 if ii[0] else 0 for ii in trace['rain'].tolist() ],
              'Sprinkler': [1 if ii[0] else 0 for ii in trace['sprinkler'].tolist() ],
              'Sprinkler Probability': [ii[0] for ii in trace['sprinkler_p'].tolist()],
              'Grass Wet Probability': [ii[0] for ii in trace['grass_wet_p'].tolist()],
              }
df = pd.DataFrame(dictionary)

p_rain = df[(df['Rain'] == 1)].shape[0] / df.shape[0]
print(p_rain)

p_sprinkler = df[(df['Sprinkler'] == 1)].shape[0] / df.shape[0]
print(p_sprinkler)