PJG Home | Research

Identifying influential model choices in Bayesian hierarchical models

by Ida Scheel, Department of Mathematics, University of Oslo, P.O.Box 1053 Blindern, 0316 Oslo, Norway,
and Peter J. Green and Jonty Rougier, School of Mathematics, University of Bristol, Bristol BS8 1TW, UK.

Real-world phenomena are frequently modelled by Bayesian hierarchical models. The building blocks in such models are the distributions of each variable conditional on parent and/or neighbour variables in the graph. The specifications of centre and spread of these conditional distributions may be well-motivated, while the tail specifications are often left to convenience. However, the posterior distribution of a parameter may depend strongly on such arbitrary tail specifications. This is not easily detected in complex models.

In this paper we propose a graphical diagnostic which identifies such influential statistical modelling choices at the node level in any chain graph model. Our diagnostic, the local critique plot, examines local conflict between the information coming from the parents and neighbours (local prior) and from the children and co-parents (lifted likelihood). It identifies properties of the local prior and the lifted likelihood that are influential on the posterior density. We illustrate the use of the local critique plot with applications involving models of different levels of complexity. The local critique plot can be derived for all parameters in a chain graph model, and is easy to implement using the output of posterior sampling.

The paper (pdf) which appears, after final revision, in Scandinavian Journal of Statistics. Online version. DOI: 10.1111/j.1467-9469.2010.00717.x

This page is incomplete; please email Peter Green via Email link to request any supplementary information on this work that does not yet appear below:

  • Algorithm for finding the integration interval (pdf)
  • Two further examples, SAVIAH 2&3 (pdf)