ABSTRACT
Bayesian statistical modeling represents a fundamental shift from the frequentist methods of model parameter estimation that we used earlier. This paradigm shift is evident in part through the methodology used to obtain the estimates: Markov chain Monte Carlo (MCMC) most commonly for the Bayesian approach, and maximum likelihood (ML) and restricted maximum likelihood (REML) in the frequentist case. In addition, Bayesian estimation involves the use of prior distributional information that is not present in frequentist-based approaches. Perhaps even more than the obvious methodological differences, however, the Bayesian analytic framework involves a very different view from that traditionally espoused in the likelihood-based literature as to the nature of population parameters. In particular, frequentist-based methods estimate the population parameter using a single value obtained using sample data only.
