A Mixture Approach to Bayesian Goodness of Fit
A Mixture Approach to Bayesian Goodness of Fit
复制标题
贝叶斯拟合优度的混合方法
DOI：
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复制
发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Rousseau
中科院分区：
文献类型：
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作者：
C. Robert;J. Rousseau
我们认为贝叶斯方法的拟合优度，也就是说，测试是否给定的参数模型是兼容的数据在手的问题。因此，我们考虑一个参数族！#"%$其中表示带参数的累积分布函数。零假设是& '）（+*-，.对于一个未知数，也就是说，存在这样的/0*#12，435/768：9 1。如果“&）”不成立，则/0*#1是/768：9 1上的随机变量，其不分布为35/768 ;9 1。因此，替代非参数假设可以解释为从一般cdf分布的/0*#1是无限维的。与Verdinelli和Wasserman（1998）中使用的函数基不同，我们将<%=表示为Beta分布的（无限）混合，？'@35/768：9 1BAC/D9FEG？'：1 HJI K L？参数和非参数结构内的估计都是使用估计混合物中分量数量的MCMC算法来实现的。由于我们关心的是拟合优度问题，因此更感兴趣的是考虑到被测模型T /7 2 D 1的函数距离作为我们测试的基础，而不是相应的贝叶斯因子，因为后者更强调参数。因此，我们提出了一个新的测试程序的基础上U%V W T /YX D 1;Z *\[^]，与渐近的理由和有限采样器的实现。
We consider a Bayesian approach to goodness of fit, that is, to the problem of testing whether or not a given parametric model is compatible with the data at hand. We thus consider a parametric family ! #"%$ where denotes a cumulative distribution function with parameter . The null hypothesis is & ')(+*-,. for an unknown , that is, there exists such that /0*#12,435/768 :9 1 . If &)' does not hold, /0*#1 is a random variable on /768 :9 1 which is not distributed as 35/768 ;9 1 . The alternative nonparametric hypothesis can thus be interpreted as /0*#1 being distributed from a general cdf is infinite dimensional. Instead of using a functional basis as in Verdinelli and Wasserman (1998), we represent <%= as the (infinite) mixture of Beta distributions, ? '@35/768 :9 1BAC/D9FEG? ':1 HJI K L ? I MON /0P I DQ I 1SR Estimation within both parametric and nonparametric structures are implemented using MCMC algorithms that estimate the number of components in the mixture. Since we are concerned with a goodness of fit problem, it is more of interest to consider a functional distance to the tested model T /7 2 D 1 as the basis of our test, rather than the corresponding Bayes factor, since the later puts more emphasis on the parameters. We therefore propose a new test procedure based on U%V W T /YX D 1;Z *\[^] , with both an asymptotic justification and a finite sampler implementation.
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