Simulation Pseudo-Bias Correction to the Harmonic Mean Estimator of Integrated Likelihoods

• Activity Number: 77
• Type: Contributed
• Date/Time: Sunday, August 2, 2009 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Peter Lenk*+
• Companies: University of Michigan
• Keywords: Model Selection ; Bayesian Inference ; Integrated Likelihooh ; Harmoni Mean ; Simulation Bias

Abstract

Newton and Raftrey's (1994) harmonic mean estimator (HME) of the integrated likelihood is theoretically consistent but can have an infinite variance. In practice, the computed HME often is simulation pseudo-biased and over estimates. This paper identifies the source of the pseudo-bias and recommends several algorithms for adjusting the HME to remove it. The pseudo-bias can be substantial and can negatively affect HME's ability to select the correct model in Bayesian model selection. When the computed HME errs, it tends to select models that are too complex. Simulation studies of linear and logistic regression models demonstrate that the adjusted HME effectively removes the pseudo-bias, is more accurate, and indicates more reliably the best model.