如何使用Pymc3模拟偏置的6面骰子?

问题描述

如何使用Pymc3模拟6面骰子掷骰?另外，我知道骰子的不同面具有不同的分布吗?

How do I simulate a 6-side Dice roll using Pymc3? Also, what is I know that different sides of the dice have different distributions?

推荐答案

在PyMC3中模拟1000卷6面公平骰子的最简单方法是

The easiest way to simulate 1000 rolls of a fair 6-sided die in PyMC3 is

import pymc3 as pm

with pm.Model():
    rolls = pm.DiscreteUniform('rolls', lower=1, upper=6)
    trace = pm.sample(1000)
trace['rolls']  # shows you the result of 1000 rolls

请注意，这比调用np.random.randint(1, 7, size=1000)慢，但等效.

Note that this is slower, but equivalent, to just calling np.random.randint(1, 7, size=1000).

对于1000卷不公平的死亡

For 1000 rolls of an unfair die

probs = np.array([0.1, 0.2, 0.3, 0.2, 0.1, 0.1])

with pm.Model():
    rolls = pm.Multinomial('rolls', n=1000, p=probs, shape=6)
    trace = pm.sample(1)

与np.random.multinomial(1000, pval=probs)相同，但速度较慢.

想要 使用PyMC3的情况是，例如，如果您观察到50卷不公平的骰子，则有 prior 期望一个公平的死者，并且想要评估那个期望的后验.这是一个示例:

The situtation in which you would want to use PyMC3 is if you observe, say, 50 rolls of an unfair die, have some prior expectation that it is a fair die, and want to evaluate the posterior of that expectation. Here's an example of that:

observations = np.array([20, 6, 6, 6, 6, 6])
with pm.Model():
    probs = pm.Dirichlet('probs', a=np.ones(6))  # flat prior
    rolls = pm.Multinomial('rolls', n=50, p=probs, observed=observations)
    trace = pm.sample(1000)
trace['probs']  # posterior samples of how fair the die are

您可以使用内置的traceplot来查看示例的外观:

You can use the built-in traceplot to see how the samples look:

请注意，我们正确地计算出其中一方比另一方更经常出现！

Note that we correctly work out that one of the sides comes up more often than the others!

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