Abstract not found

Spatial heterogeneity of count data on a rare phenomenon occurs commonly in many domains of application, in particularly in disease mapping. We present new methodology to analyse such data, based on a hierarchical allocation model. We assume that the counts follow a Poisson model at the lowest level of the hierarchy, and introduce a finite mixture model for the Poisson rates at the next level. The novelty lies in the allocation model to the mixture components, which follows a spatially correlated process, the Potts model, and in treating the number of components of the spatial mixture as unknown. Inference is performed in a Bayesian framework using reversible jump MCMC. The model introduced can be viewed as a Bayesian semiparametric approach to specifying flexible spatial distribution in hierarchical models. It could also be used in contexts where the spatial mixture subgroups are themselves of interest, as in health care monitoring. Performance of the model and comparison wi...

this paper, we accomplish this comparison using the Deviance Information Criterion (DIC), a recently proposed generalization of the Akaike Information Criterion (AIC) designed for complex hierarchical model settings like ours. We investigate the use of the delta method for obtaining an approximate variance estimate for DIC, in order to attach significance to apparent differences between models. We illustrate our approach using a spatially misaligned dataset relating a measure of traffic density to pediatric asthma hospitalizations in San Diego County, California.

In this paper we consider inference using multivariate data that are spatially misaligned, i.e., involving variables (typically counts or rates) which are aggregated over differing sets of regional boundaries. Geographic information systems (GISs) enable the simultaneous display of such data sets, but their current capabilities are essentially only descriptive, not inferential. We describe a hierarchical modeling approach which provides a natural solution to this problem through its ability to sensibly combine information from several sources of data and available prior information. Illustrating in the context of counts, allocation under non-nested regional grids is handled using conditionally independent Poisson-multinomial models. Explanatory covariates and multilevel responses are also easily accommodated, with spatial correlation modeled using a conditionally autoregressive (CAR) prior structure. Methods for dealing with missing values in spatial "edge zones" are also discussed. Li...

We consider the problem of input variable selection of a Bayesian model. With suitable priors it is possible to have a large number of input variables in Bayesian models, as less relevant inputs can have a smaller effect in the model. To make the model more explainable and easier to analyse, or to reduce the cost of making measurements or the cost of computation, it may be useful to select a smaller set of input variables. Our goal is to find a model with the smallest number of input variables having statistically or practically the same expected utility as the full model. A good estimate for the expected utility, with any desired utility, can be computed using cross-validation predictive densities (Vehtari and Lampinen, 2001). In the case of input selection, there are 2 K input combinations and computing the cross-validation predictive densities for each model easily becomes computationally prohibitive. We propose to use the reversible jump Markov chain Monte Carlo (RJMCMC) method to find out potentially useful input combinations, for which the final model choice and assessment is done using the cross-validation predictive densities. The RJMCMC visits the models according to their posterior probabilities. As models with negligible probability are probably not visited in finite time, the computational savings can be considerable compared to going through all possible models. The posterior probabilities of the models, given by the RJMCMC, are proportional to the product of the prior probabilities of the models and the prior predictive likelihoods of the models. The prior predictive likelihood measures the goodness of the model if no training data were used, and thus can be used to estimate the lower limit of the expected predictive likelihood. These estimates indicate ...

this paper, Bayesian inferences for prevalence are developed using four different probit models for the diagnostic probabilities. The required computations are performed using Gibbs sampling (Gelfand and Smith, 1990). These models are then compared via the Deviance Information Criterion (DIC) recently introduced by Spiegalhalter et al. (1998).

The deviance information criterion (DIC) is widely used for Bayesian model comparison, despite the lack of a clear theoretical foundation. DIC is shown to be an approximation to a penalized loss function based on the deviance, with a penalty derived from a cross-validation argument. This approximation is valid only when the effective number of parameters in the model is much smaller than the number of independent observations. In disease mapping, a typical application of DIC, this assumption does not hold and DIC under-penalizes more complex models. Another deviance-based loss function, derived from the same decision-theoretic framework, is applied to mixture models, which have previously been considered an unsuitable application for DIC.

Advances in computation mean it is now possible to fit a wide range of complex models, but selecting a model on which to base reported inferences is a difficult problem. Following an early suggestion of Box and Tiao, it seems reasonable to seek `inference robustness' in reported models, so that alternative assumptions that are reasonably well supported would not lead to substantially different conclusions. We propose a four-stage modelling strategy in which we: iteratively assess and elaborate an initial model, measure the support for each of the resulting family of models, assess the influence of adopting alternative models on the conclusions of primary interest, and identify whether an approximate model can be reported. These stages are semi-formal, in that they are embedded in a decision-theoretic framework but require substantive input for any specific application. The ideas are illustrated on a dataset comprising the success rates of 46 in-vitro fertilisation clinics over three years. The analysis supports a model that assumes 43 of the 46 clinics have odds on success that are evolving at a constant proportional rate (i.e. linear on a logit scale), while three clinics are outliers in the sense of showing non-linear trends. For the 43 `linear' clinics, the intercepts and gradients can be assumed to follow a bivariate normal distribution except for one outlying intercept: the odds on success are significantly increasing for four clinics and significantly decreasing for three. This model displays considerable inference robustness and, although its conclusions could be approximated by other less-supported models, these would not be any more parsimonious. Technical issues include fitting mixture models of alternative hierarchical longitudinal models, t...

this paper we extend this hierarchical modeling approach to the spatio-temporal case, so that misalignment can arise either within a given timepoint, or across timepoints (as when the regional boundaries themselves evolve over time). Implemented using Markov chain Monte Carlo computing methods, our approach sensibly combines the relevant data sources and imposes the necessary constraints over the misaligned regional grids. We illustrate the method through an analysis of the dataset that motivated the method, which relates traffic density to pediatric asthma hospitalizations in San Diego County, California. We compare two different measures of the traffic covariate (neither of which is aligned with the zip code-level asthma data), mapping the resulting fitted risk estimates in the Geographic Information System (GIS) ARC/INFO. Results in both cases are consistent with those of several previous authors who have investigated the traffic-asthma link.