Investigation of bimodality in likelihoods and posterior densities

Firat M. Z., Thompson R.

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, vol.54, no.4, pp.379-386, 1996 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 54 Issue: 4
  • Publication Date: 1996
  • Doi Number: 10.1080/00949659608811741
  • Journal Name: JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.379-386
  • Keywords: variance components, Bayesian methods, maximum likelihood, bimodality, RESTRICTED MAXIMUM-LIKELIHOOD, COMPONENT ESTIMATION, VARIANCE
  • Akdeniz University Affiliated: No

Abstract

A univariate balanced one-way sire model with two variance components is used to investigate whether likelihood and Bayesian methods can encounter the problem of multiple solutions within the permissible parameter space. Analytical results suggest that the posterior density function is sometimes bimodal when an improper density function is used. Visualization of the log-likelihood density however, did not reveal bimodality.

A univariate balanced one-way sire model with two variance components is used to investigate whether likelihood and Bayesian methods can encounter the problem of multiple solutions within the permissible parameter space. Analytical results suggest that the posterior density function is sometimes bimodal when an improper density function is used. Visualization of the log-likelihood density however, did not reveal bimodality.