最高后密度区和中央可信区 [英] Highest Posterior Density Region and Central Credible Region

问题描述

给定一些参数 Θ 的后验 p(Θ|D)，可以 ?

对于常见的参数分布(例如 Beta、Gaussian 等)，是否有任何内置程序或库可以使用 SciPy 或 statsmodels?

解决方案

你可以利用 pymc3 来计算 HPD，这是一个例子

导入pymc3从 scipy.stats 导入规范a = norm.rvs(大小=10000)pymc3.stats.hpd(a)

Given a posterior p(Θ|D) over some parameters Θ, one can define the following:

Highest Posterior Density Region:

The Highest Posterior Density Region is the set of most probable values of Θ that, in total, constitute 100(1-α) % of the posterior mass.

In other words, for a given α, we look for a p* that satisfies:

and then obtain the Highest Posterior Density Region as the set:

Central Credible Region:

Using the same notation as above, a Credible Region (or interval) is defined as:

Depending on the distribution, there could be many such intervals. The central credible interval is defined as a credible interval where there is (1-α)/2 mass on each tail.

Computation:

• For general distributions, given samples from the distribution, are there any built-ins in to obtain the two quantities above in Python or PyMC?

• For common parametric distributions (e.g. Beta, Gaussian, etc.) are there any built-ins or libraries to compute this using SciPy or statsmodels?

解决方案

To calculate HPD you can leverage pymc3, Here is an example

import pymc3
from scipy.stats import norm
a = norm.rvs(size=10000)
pymc3.stats.hpd(a)

这篇关于最高后密度区和中央可信区的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！