|
Abstract:
|
The Bayesian approach gives great flexibility for complex modeling of interesting phenomena. However, any assumed model may be unreasonable in light of the observed data, and different sources of evidence may be in conflict with each other. Therefore, there is an increasing need for flexible, general, and computationally efficient methods for model criticism and conflict detection. Usually, a Bayesian hierarchical model incorporates a grouping of the individual data points. For example, in clinical trials, repeated measurements are grouped by patient; in disease mapping, cancer counts may be grouped by year or by geographical area. In such cases, the following question arises: Are any of the groups "outliers", or in conflict with the remaining groups? Existing general approaches aiming to answer such questions tend to be extremely computationally demanding when model fitting is based on MCMC. We show how group-level model criticism and conflict detection can be done quickly and accurately through integrated nested Laplace approximations (INLA). The new method will be implemented as a part of the open source R-INLA package for Bayesian computing (www.r-inla.org).
|
