| One conclusion of a Bayesian analysis is the posterior of the parameters conditional on the full data and the model. The influence of a particular observation on this conclusion may be assessed by deleting the observation from the analysis, computing the reduced data posterior and comparing the reduced data posterior to the full data posterior. Typically the comparison is performed by reducing the two densities down to a single statistic using a utility function, but this can hide relevant information. Ideally, we would like to plot the full data density and the reduced data density and compare them visually, although this is difficult when the parameter vector is more than two dimensions.;In this thesis I develop a marginal function of the parameters whose full and reduced data posteriors can be plotted. The full and reduced data marginal are related to each other in much the same way that the complete parameter posteriors are related. The plot of the marginal densities is easy to interpret, is available for a range of standard models, and does not require the specification of a utility function. An optimality result is proven and interpreted. I describe how characteristics of the observation affect the configurations of the densities and what they mean. Alternative plots are developed to aid in assessment when the marginals are two dimensional or when the influence of multiple observations must be assessed. |
