Determining the effective sample size of a parametric prior
Determining the effective sample size of a parametric prior
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DOI：
10.1111/j.1541-0420.2007.00888.x
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发表时间：
2008-06-01
期刊：
影响因子：
1.9
通讯作者：
Mueller, Peter
中科院分区：
文献类型：
--
作者：
Morita, Satoshi;Thall, Peter F.;Mueller, Peter
我们提出了一个定义的有效样本量的参数先验分布在贝叶斯模型，并提出了计算方法的有效样本量在各种设置。我们的方法首先构造一个先验选择是模糊的，在适当的意义上，并更新此之前获得一系列的后验对应的样本量的范围。然后，我们计算每个后验和参数先验之间的距离，根据每个分布的对数的曲率定义，最小化距离的后验定义了先验的有效样本量。对于无法解析计算距离的情况，我们提供了基于Monte Carlo模拟的数值近似。我们提供了一般的应用指南，说明了在几个标准的情况下，答案似乎是显而易见的方法，然后将其应用到一些非标准的设置。
We present a definition for the effective sample size of a parametric prior distribution in a Bayesian model, and propose methods for computing the effective sample size in a variety of settings. Our approach first constructs a prior chosen to be vague in a suitable sense, and updates this prior to obtain a sequence of posteriors corresponding to each of a range of sample sizes. We then compute a distance between each posterior and the parametric prior, defined in terms of the curvature of the logarithm of each distribution, and the posterior minimizing the distance defines the effective sample size of the prior. For cases where the distance cannot be computed analytically, we provide a numerical approximation based on Monte Carlo simulation. We provide general guidelines for application, illustrate the method in several standard cases where the answer seems obvious, and then apply it to some nonstandard settings.