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这是我为了更好地理解 pymc3 而进行的一个实验。我有三个有偏见的硬币，我进行了以下实验：

1. Toss Coin1. If head choose Coin2 else choose Coin3
2. Randomly choose a number n (between 1 and 10) that implies coin tosses to perform
3. Toss Coin2/3 (as per 1. above) n times and observe number of heads.
4. Perform 1,2,3 above multiple times

问题是从上面的实验中给出的数据，我们可以对这三个硬币进行建模吗？

代码：数据生成器：

coin1 = 0.4
coin2 = 0.9
coin3 = 0.1
numberOfDataPoints = 20000
maxTosses = 10
percentOfmaxTosses = 0.65

headTosses = []
totalTosses = []
for i in range(numberOfDataPoints):
    heads = 0
    total = 0
    isCoint2 = random() < coin1
    for rater in range(maxTosses):
        if random() <= percentOfmaxTosses:
            total = total + 1
            if isCoint2:
                if random() < coin2:
                    heads += 1
            else:
                if random() < coin3:
                    heads += 1
    if total > 5:
        headTosses.append(heads)
        totalTosses.append(total)

型号代码：

with pm.Model() as coins:
    coin1 = pm.Beta('coin1',2,2)
    coin2 = pm.Beta('coin2',5,2)
    coin3 = pm.Beta('coin3',2,5)
    first_toss = pm.Bernoulli('first_toss', coin1)
    p = pm.math.switch(first_toss > 0.5, coin2, coin3)
    output = pm.Binomial('output', n=totalTosses, p=p,observed=headTosses)
    exp = pm.sample(10000, tune = 5000)

结果：

  • 发现coin1的模型很好
  • coin2 似乎接近原始值
  • coin3 很遥远

疑点：

  • 上面的实验有什么问题吗？
  • 有没有更好的方法来模拟这个实验？
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