Application of Likelihood Methods to Models Involving Large Numbers of Parameters
Application of Likelihood Methods to Models Involving Large Numbers of Parameters
复制标题
似然法在涉及大量参数的模型中的应用
DOI：
10.1111/j.2517-6161.1970.tb00830.x
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发表时间：
1970
期刊：
影响因子：
--
通讯作者：
D. A. Sprott
中科院分区：
文献类型：
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作者：
J. Kalbfleisch;D. A. Sprott
[1970年3月11日，星期三，研究部在皇家统计学会组织的一次会议上宣读，主持会议的J. DURBIN教授]摘要：介绍并举例说明了处理一些多参数问题的似然方法。具体地说，考虑了从似然函数中消除干扰参数的方法，以便可以对感兴趣的参数进行推断。在这方面，介绍了综合似然、最大相对似然、条件似然、边际似然和二阶似然，并举例说明了它们的用法。边际似然和条件似然取决于似然函数的因式。它们被应用于线性函数关系和相关模型，并被发现给出直观的吸引人的结果。这些方法表明，在许多常见的情况下，可以采用客观的方法从似然函数中消除不需要的参数。这提供了一种解释贝叶斯方法提供的多参数可能性的替代方法。
[Read before the ROYAL STATISTICAL SOCIETY at a meeting organized by the RESEARCH SECTION on Wednesday, March 11th, 1970, Professor J. DURBIN in the Chair] SUMMARY Likelihood methods of dealing with some multiparameter problems are introduced and exemplified. Specifically, methods of eliminating nuisance parameters from the likelihood function so that inferences can be made about the parameters of interest are considered. In this regard integrated likelihoods, maximum relative likelihoods, conditional likelihoods, marginal likelihoods and second-order likelihoods are introduced and their uses illustrated in examples. Marginal and conditional likelihoods are dependent upon factorings of the likelihood function. They are applied to the linear functional relationship and to related models and are found to give intuitively appealing results. These methods indicate that in many situations commonly encountered objective methods of eliminating unwanted parameters from the likelihood function can be adopted. This gives an alternative method of interpreting multiparameter likelihoods to that offered by the Bayesian approach.