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Title of Journal: Comput Stat

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Abbravation: Computational Statistics

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Springer Berlin Heidelberg

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DOI

10.1007/bf02054320

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1613-9658

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Integrated likelihood computation methods

Authors: Zhenyu Zhao Thomas A Severini
Publish Date: 2016/09/01
Volume: 32, Issue: 1, Pages: 281-313
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Abstract

Suppose a model has parameter theta =psi lambda where psi is the parameter of interest and lambda is a nuisance parameter The integrated likelihood method eliminates lambda from the likelihood function Lpsi lambda by integrating with respect to a weight function pi lambda psi The resulting integrated likelihood function barLpsi can be used for inference for psi However the analytical form for the integrated likelihood is not always available This paper discusses 12 different approaches to computing the integrated likelihood Some methods were originally developed for other computation purposes and they are modified to fit in the integrated likelihood framework Methods considered include direct numerical integration methods such as Monte Carlo integration method importance sampling Laplace method marginal likelihood computation methods and methods for computing the marginal posterior density Simulation studies and real data example are presented to evaluate and compare these methods empiricallyThe work of T A Severini was supported by NSF Grant DMS1308009 This research was supported in part through the computational resources and staff contributions provided for the Social Sciences Computing cluster SSCC at Northwestern University Recurring funding for the SSCC is provided by Office of the President Weinberg College of Arts and Sciences Kellogg School of Management the School of Professional Studies and Northwestern University Information Technology

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