V2EX hpd interval

HPD Interval

释义 Definition

HPD interval“最高后验密度区间”(Highest Posterior Density interval):在贝叶斯统计中,用来表示参数在给定数据后最可能落入的区间。它通常满足两个特点:

  1. 区间内包含给定比例(如 95%)的后验概率质量;
  2. 区间内任一点的后验密度都不低于区间外任一点(因此更“贴着”概率密度最高的区域)。
    (也常被视为一种“贝叶斯可信区间”,但与等尾 credible interval 不同。)

发音 Pronunciation (IPA)

/et pi di ntrvl/

例句 Examples

The 95% HPD interval for the parameter is [1.2, 2.8].
该参数的 95% 最高后验密度区间为 [1.2, 2.8]。

Because the posterior is skewed, the HPD interval is shorter than the equal-tailed credible interval and better captures the most plausible values.
由于后验分布是偏斜的,HPD 区间比等尾可信区间更短,更能抓住最可能的取值范围。

词源 Etymology

HPD 是统计学术语的缩写,来自 Highest Posterior Density(最高的后验密度);interval 来自拉丁语 intervallum

相关词 Related Words

文学与名著用例 Literary Works

  • Bayesian Data Analysis(Gelman, Carlin, Stern, Dunson, Vehtari, Rubin):讨论后验分布摘要与区间估计时常涉及 HPD/credible interval 的概念。
  • Doing Bayesian Data Analysis(John K. Kruschke):在介绍后验总结与区间估计时使用并解释 HPD 区间。
  • Statistical Rethinking(Richard McElreath):讲解贝叶斯推断实践中常对比不同的后验区间(包括与 HPD 思路相近的区间表述)。
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