Bayesian Statistics: Markov Chain Monte Carlo Sampling

Abstract

Markov chain Monte Carlo (MCMC) procedures can be laid out as Bayesian tests. The Bayesian prior likelihood distribution of MCMC procedures could, for example, be a data file with missing data. The posterior likelihood distribution is based on the prior plus the MCMC computed imputation values. In a 500 patient multiple variables model with missing data five MCMC imputated models were produced with the help of the multiple imputations module in SPSS statistical software. The correlation coefficients of the predictor versus outcome values in the original data and those of five MCMC imputated models were respectively

• 0.533

• 0.596

• 0.567

• 0.594

• 0.586

• 0.580.

The Bayes factors of the Bayesian analyses of the above imputated models were respectively

• 1.187963

• 2.671638

• 1.518048

• 2.537739

• 2.142738

• 1.90718.

We conclude that both the traditional correlation coefficients of the imputated models and their Bayes factors were consistently robuster. However, the magnitudes of the Bayes factors increased over 100%, while the magnitudes of the traditional correlation coefficients increased by 8% at best.