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SM Journal of Biometrics & Biostatistics

On the Choice of the Weight Function for the Integrated Likelihood

[ ISSN : 2573-5470 ]

Abstract
Details

Received: 27-Jul-2018

Accepted: 06-Aug-2018

Published: 16-Aug-2018

Review Article | Volume 3 - Issue 3 | Article DOI :

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Alessandro Casa*

Department of Statistical Sciences, University of Padova, Italy

Corresponding Author:

Alessandro Casa, Department of Statistical Sciences, University of Padova, Italy, Tel: (0039) 049 8274111

Keywords

Bayesian Inference; Likelihood Inference; Nuisance Parameter; Profile Likelihood; Pseudo Likelihood; Reference Prior

Abstract

In the field of biostatistics it is often required to develop inferential tools dealing with the presence of nuisance parameters. The most adopted solution is to resort to pseudo-likelihood functions, having properties similar to the ones of a genuine likelihood. A possible choice is to use the integrated likelihood where the nuisance parameters are eliminated by means of integration with respect to a weight function. The selection of the weight function turns out to be crucial since it could have a strong impact on the properties of the resulting integrated likelihood. After having introduced the concept of pseudo-likelihood, the definition and the properties of the integrated likelihood, the focus will be on reviewing the main alternatives to choose the weight function according to different inference paradigms.

Citation

Casa A. On the Choice of the Weight Function for the Integrated Likelihood. SM J Biometrics Biostat. 2018; 3(3): 1033.