贝叶斯估计和推理

M. Edge
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引用次数: 0

摘要

贝叶斯方法允许研究人员以一种有原则的方式将先前信念的精确描述与新数据结合起来。贝叶斯统计的主要研究对象是后验分布,它描述了与参数相关的不确定性,给出了对参数和观测数据的先验信念。后验很难用数学方法计算,但在大多数情况下,计算方法可以给出任意好的近似值。贝叶斯点和区间估计是后验的特征,例如对其集中趋势或参数以指定概率落在其中的区间的度量。贝叶斯假设检验是复杂而有争议的,但一个相关的工具是贝叶斯因子,它比较在一对不同的假设下观察数据的概率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bayesian estimation and inference
Bayesian methods allow researchers to combine precise descriptions of prior beliefs with new data in a principled way. The main object of interest in Bayesian statistics is the posterior distribution, which describes the uncertainty associated with parameters given prior beliefs about them and the observed data. The posterior can be difficult to compute mathematically, but computational methods can give arbitrarily good approximations in most cases. Bayesian point and interval estimates are features of the posterior, such as measures of its central tendency or intervals into which the parameter falls with specified probability. Bayesian hypothesis testing is complicated and controversial, but one relevant tool is the Bayes factor, which compares the probability of observing the data under a pair of distinct hypotheses.
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