UCSC-SOE-17-13: Bayesian Nonparametric Areal Wombling for Small Scale Maps with an Application to Urinary Bladder Cancer Data from Connecticut

Rajarshi Guhaniyogi
06/23/2017 01:06 PM
Applied Mathematics & Statistics
With increasingly abundant spatial data in the form of case counts or rates com-
bined over areal regions (e.g ZIP codes, census-tracts or counties), interest turns to
formal identifi cation of difference "boundaries", or barriers on the map, in addition
to the estimated statistical map itself. "Boundary" refers to a border that describes
vastly disparate outcomes in the adjacent areal units, perhaps caused due to latent
risk factors. This article focuses on developing a model based statistical tool, equipped
to identify difference boundaries in maps with a small number of areal units, also re-
ferred to as small scale maps. This article proposes a novel and robust nonparametric
boundary detection rule based on nonparametric Dirichlet Processes, later referred to
as DPW rule, by employing Dirichlet Process based mixture models for small scale
maps. Unlike the recently proposed nonparametric boundary detection rules based
on false discovery rates, DPW rule is free of ad-hoc parameters, computation-
ally simple and readily implementable in freely available software for public health
practitioners such as JAGS and OpenBUGS and yet provides statistically interpretable
boundary detection in small scale wombling. We offer a detailed simulation study and
an application of our proposed approach to a urinary bladder cancer incidence rates
dataset between 1990-2012 in the eight counties in Connecticut.