Markov Chain Monte-Carlo Methods for Missing Data Under Ignorability Assumptions

Missing observations are a common occurrence in public health, clinical studies and social science research. Consequences of discarding missing observations, sometimes called complete case analysis, are low statistical power and potentially biased estimates. Fully Bayesian methods using Markov Chain Monte-Carlo (MCMC) provide an alternative model-based solution to complete case analysis by treating missing values as unknown parameters. Fully Bayesian paradigms are naturally equipped to handle this situation by augmenting MCMC routines with additional layers and sampling from the full conditional distributions of the missing data, in the case of Gibbs sampling . Here we detail ideas behind the Bayesian treatment of missing data and conduct simulations to illustrate the methodology. We consider specifically Bayesian multivariate regression with missing responses and the missing covariate setting under an ignorability assumption. Applications to real datasets are provided.