Comparing spatial models in the presence of spatial smoothing
Earl Duncan (Queensland University of Technology)
Friday 30th August 15:00-16:00 Maths 311B
Spatial models are characterised by how spatial dependencies are modelled. In Bayesian spatial models, this is achieved by purposefully designed prior(s) or smoothing functions which smooth estimates towards a local or global mean. Smoothing is important for several reasons, not least of all because it increases confidence in the estimates of area-specific parameters. The uncertainty associated with the observed data can be very large, especially in epidemiology, where quantities like the standardised incidence ratio can be sensitive to small changes either in the incidence rates, or in the population data. With advances in software and methodology, implementing Bayesian spatial models has become relatively easy. However, comparing them is less straightforward. Traditional goodness-of-fit or predictive metrics such as DIC, WAIC, CPO, etc. are not necessarily good indicators of the performance a spatial model because smoothing and model fit are opposing goals – an interaction that is all but ignored in the literature. While some level of smoothing is usually desirable, over- and under-smoothing are very real concerns. This poses several research questions. How can we quantify the degree of smoothing performed by a given model? How can we use such metrics to detect under- and over-smoothing, and compare models in the face of opposing objective functions? In this talk, I propose several methods for quantifying the degree of smoothing in the context of disease mapping.