Estimating the Marginal Likelihood Using the Arithmetic Mean Identity
Estimating the Marginal Likelihood Using the Arithmetic Mean Identity
复制标题
使用算术平均恒等式估计边际似然
DOI：
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Anna Pajor
中科院分区：
文献类型：
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作者：
Anna Pajor
在本文中，我们提出了一种概念上简单的方法来估计边际数据密度值(也称为边际似然)。我们证明了边际似然等于给定参数空间某一子集的参数向量A的数据条件密度的先验均值乘以子集A的后验概率的倒数。这一恒等式促使人们使用基于先验分布的算术平均估计器，该估计器来自受限于参数空间的任何(但合理的)子集的先验分布。通过修剪该空间，去除了相对低似然的区域，从而提高了算术平均估计器的效率。我们证明了调整后的算术平均估计是无偏的和相容的。
In this paper we propose a conceptually straightforward method to estimate the marginal data density value (also called the marginal likelihood). We show that the marginal likelihood is equal to the prior mean of the conditional density of the data given the vector of parameters restricted to a certain subset of the parameter space, A, times the reciprocal of the posterior probability of the subset A. This identity motivates one to use Arithmetic Mean estimator based on simulation from the prior distribution restricted to any (but reasonable) subset of the space of parameters. By trimming this space, regions of relatively low likelihood are removed, and thereby the efficiency of the Arithmetic Mean estimator is improved. We show that the adjusted Arithmetic Mean estimator is unbiased and consistent.
DOI：
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发表时间：
1997
期刊：
Journal of the royal statistical society series b-methodological
影响因子：
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作者：
S. Richardson;P. Green;Christian P. Robert;M. Aitkin;David R. Cox;Matthew Stephens;A. Polymenis;W. Gilks;A. Nobile;M. Hodgson;Anthony O'Hagan;N. Longford;A. Dawid;Anthony C. Atkinson;J. Bernardo;J. Besag;Stephen Brooks;S. Byers;A. Raftery;G. Celeux;R. Cheng;W. B. Liu;Yung-Hsin Chien;Edward I. George;N. Cressie;H.-C. Huang;M. Gruet;S. C. Heath;C. Jennison;Andrew B. Lawson;Allan Clark;Geoffrey J. McLachlan;D. Peel;K. Mengersen;A. George;Anne Philippe;Kathryn Roeder;Larry Wasserman;Peter Schlattmann;D. Böhning;D. M. Titterington;H. Tong;M. West
通讯作者：
S. Richardson;P. Green;Christian P. Robert;M. Aitkin;David R. Cox;Matthew Stephens;A. Polymenis;W. Gilks;A. Nobile;M. Hodgson;Anthony O'Hagan;N. Longford;A. Dawid;Anthony C. Atkinson;J. Bernardo;J. Besag;Stephen Brooks;S. Byers;A. Raftery;G. Celeux;R. Cheng;W. B. Liu;Yung-Hsin Chien;Edward I. George;N. Cressie;H.-C. Huang;M. Gruet;S. C. Heath;C. Jennison;Andrew B. Lawson;Allan Clark;Geoffrey J. McLachlan;D. Peel;K. Mengersen;A. George;Anne Philippe;Kathryn Roeder;Larry Wasserman;Peter Schlattmann;D. Böhning;D. M. Titterington;H. Tong;M. West
影响因子：
6.5
作者：
Xie, Wangang;Lewis, Paul O.;Chen, Ming-Hui
通讯作者：
Chen, Ming-Hui