Estimation, model checking and diagnostics in finite mixture models for point mass data: Methods in a Bayesian framework

In this work, we are interested in examining how estimation methods in a Bayesian framework which make use of data augmentation can be applied to data subject to missingness and zero inflation. We are examining these estimation methods in the point mass mixture model, and applying it in the context of assay measurements in which some measurements are censored due to falling below limits of detection, and some measurements represent 'true zero' values which are indistinguishable from the censored measurements. The assay measurements thus are modeled as a partially latent mixture of a degenerate point mass and a censored continuous distribution. Estimation and testing in this data setting is very challenging, and one propose methods to characterize the parameters of the continuous distribution as well as the mixing proportion in the univariate setting. We extend the methods to include modeling of covariate effects in the point mass mixture setting subject to nonignorable missingness and zero-inflation issues. We are examining model identifiability and estimability in the point mass mixture model, and the manner in which weak identifiability affects sampling procedures used in Bayesian inference. We are also developing model checking procedures for this unique model setting to enable checks on parametric assumptions and assessment of quality of fit of the model.