如何在 PyMC3 中正确定义 Beta 分布的混合

Question

我正在尝试使用来自 PyMC3 的 Mixture 混合使用两个 Beta 分布（我不知道每个分布的权重）来拟合数据。这是代码：

model=pm.Model()
with model:
    alpha1=pm.Uniform("alpha1",lower=0,upper=20)
    beta1=pm.Uniform("beta1",lower=0,upper=20)
    alpha2=pm.Uniform("alpha2",lower=0,upper=20)
    beta2=pm.Uniform("beta2",lower=0,upper=20)
    w=pm.Uniform("w",lower=0,upper=1)
    b1=pm.Beta("B1",alpha=alpha1,beta=beta1)
    b2=pm.Beta("B2",alpha=alpha2,beta=beta2)
    mix=pm.Mixture("mix",w=[1.0,w],comp_dists=[b1,b2])

在运行这段代码之后，我得到以下错误：AttributeError: 'list' object has no attribute 'mean'。有什么建议吗？

Answer 1

PyMC3 自带 pymc3.tests module which contains useful examples. By searching that directory for the word "mixture" I came upon this example:

Mixture('x_obs', w,
        [Normal.dist(mu[0], tau=tau[0]), Normal.dist(mu[1], tau=tau[1])],
        observed=self.norm_x)

请注意 classmethod dist is called. Googling "pymc3 dist classmethod" leads to this doc page 解释

... each Distribution has a dist class method that returns a stripped-down distribution object that can be used outside of a PyMC model.

除此之外，我不完全清楚为什么这里需要精简版，但它似乎有效：

import pymc3 as pm

model = pm.Model()
with model:
    alpha1 = pm.Uniform("alpha1", lower=0, upper=20)
    beta1 = pm.Uniform("beta1", lower=0, upper=20)
    alpha2 = pm.Uniform("alpha2", lower=0, upper=20)
    beta2 = pm.Uniform("beta2", lower=0, upper=20)
    w = pm.Uniform("w", lower=0, upper=1)
    b1 = pm.Beta.dist(alpha=alpha1, beta=beta1)
    b2 = pm.Beta.dist(alpha=alpha2, beta=beta2)
    mix = pm.Mixture("mix", w=[1.0, w], comp_dists=[b1, b2])

注意使用dist类方法时，名称字符串被省略。

如何在 PyMC3 中正确定义 Beta 分布的混合

How to correctly defined mixture of Beta distributions in PyMC3

python

pymc

pymc3

mcmc