The Bayes factor for model evaluation in a hierarchical Poisson model for area counts

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1992

OSTI ID:5146682

Rosenkranz, S L

When confronted with the rates of health event for a collection of geographic areas, health services researchers and planners often want to judge whether the rate in a particular area is too high. They may ask, for example, if the lung cancer mortality rate in a particular community is systematically higher than the rates in the surrounding communities. Before seeking to detect outliers, we may first want to include in our model those area-level covariates (eg, demographic characteristics and availability of health resources) which account for some of the between-area variation. Both the selection of covariates and the identification of outliers may be phased in terms of model evaluation. The Bayes factor is one model evaluation criterion. In the context of a hierarchical model for area counts (the Poisson-Gamma, or PG, model), the use of the approximate Bayes factor to select a covariate set and to identify outliers is investigated. Unlike the usual model selection criteria (eg, the deviance test), the Bayes factor can be used to compare; nonnested sets of covariates, to evaluate aspects of the model other than the covariate set, and to assess the relative likelihood of each of a group of models. The Bayses factor also lends itself naturally to sensitivity analysis. The Bayes factor is the ratio of the probabilities of the observed data under two different models. These probabilities are represented by integrals, which are intractable for the PG model. We approximate the marginal probabilities (and the Bayes factors) using Monte Carlo integration. We also examine the Laplace approximation. The Laplace approximation to the Bayes factor is very accurate and is quick to obtain, provided the model dimension is small enough. We also consider a family importance sampling approximations to the marginal likelihood, employing Markov chain Monte Carlo methods to generate parameter samples from the posterior distribution.

• Research Organization: Washington Univ., Seattle, WA (United States)
• OSTI ID: 5146682
• Country of Publication: United States
• Language: English

Related Subjects

550100 -- Behavioral Biology
552000* -- Public Health
59 BASIC BIOLOGICAL SCIENCES
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
CALCULATION METHODS
COMMUNITIES
DEMOGRAPHY
DIFFERENTIAL EQUATIONS
DISEASE INCIDENCE
EPIDEMIOLOGY
EQUATIONS
LAPLACE EQUATION
MATHEMATICAL MODELS
MONTE CARLO METHOD
PARTIAL DIFFERENTIAL EQUATIONS
POISSON EQUATION
REGIONAL ANALYSIS