Daniel Nordman - Colloquium Speaker

Professor, Department of Statistics, Iowa State University
Date: 
Thursday, March 31, 2016 - 3:30pm
Colloquium Title: 
Goodness of fit tests for spatial Markov random fields
Location: 
Reception at 3:00 p.m. in 241 SH / Talk at 3:30 in 61 SH

 

Abstract:

For spatial data, conditionally specified models formulated on the basis of an underlying Markov random field are an attractive alternative to direct specification of a full joint data distribution. That is, the model is defined by prescribing a conditional distribution for each spatial location which depends on a set of neighboring observations. This talk aims to describe goodness-of-fit statistics that can be used to test and diagnose Markov random field models for spatial data. Test statistics are formed by spatial residuals which are collected over groups of non-neighboring spatial observations, called concliques. Under a hypothesized Markov model structure, spatial residuals within each conclique turn out to be independent and identically distributed as uniform variables, and the information from a series of concliques is pooled into goodness-of-fit statistics. Distributions for these test statistics typically require numerical approximation via parametric bootstrap. This step requires simulating spatial data sets through a Gibbs sampler (as distributions for each spatial observation are conditionally specified), and we describe a Markov Chain Monte Carlo (MCMC) method that exploits the conclique structure. Apart from the bootstrap, this approach also provides a new and fast way to simulate spatial data from Markov random fields, with provable MCMC properties such geometric ergodicity. Several examples are used to illustrate the proposed spatial testing method.