Matthew J. Heaton
Ph.D. Student
Department of Statistical Science, Duke University

Research Interests

MY CURRICULUM VITAE

Spatial Modeling

In many fields, data are often collected at specific spatial locations within some region of interest. For example, pollution concentrations are typically measured at several receptor sites within a region. Data collected in this manner often exhibit spatial dependence; i.e. observations measured at neighboring locations are postively correlated. Spatial modeling is the field of statistics which deals with spatially correlated data. My work in spatial modeling has to do with prediction of events using spatially correlated predictors. Specifically, I try to model neighboring predictors using stochastic processes then use interpolated values to explain the behavior of a response variable. My work is, mainly, done as a research assistant to Alan Gelfand but I also work with David Banks on problems in spatial disease surveillance.

Spatial Publications

Monte Carlo Methodology

Monte Carlo methodology is widely used in statistical analysis to obtain samples from complex distributions. However, Monte Carlo methods are difficult to implement effectively. For example, it is very hard to verify that a particular Markov chain has adequately explored the space of the target distribution; particularly when the target distribution is multimodal. My interest in Monte Carlo methodology has to do with developing new ways of implementing algorithms which will minimize researcher overhead. Specifically, I am working on developing adaptive algorithms which automatically tune proposal distributions to effectively sample from the target distribution. I also work on new ways of implementing reversible jump MCMC which will effectively explore model and parameter space. My work is done as a research assistant to Scott Schmidler.

MCMC Publications

Bayesian Latent Variable Modeling

Latent variable modeling is the science of finding unmeasureable quantities (latent variables) that explain the measured response. For example, a students final grade in a course is determined by a students test taking abilities, homework ability, underlying intelligence, etc. However, each of these variables are unmeasureable. Latent variable modeling, in this case, would seek to determine a score for each of the mentioned variables and determine how each of these unmeasureable quantities factor into a students overall grade. Common techniques used in latent variable modeling include (but are not limited to) structural equation models, factor analysis, exploratory factor analysis, and principal component analysis. My interest in latent variable modeling lies in Bayesian techniques to identify the latent variables. Bayesian techniques provide a flexible approach to latent variable modeling by placing prior distributions on unknown latent variables and estimating the underlying parameters via MCMC and other methods. My current research involves an application of factor analytic methods in identifying pollution sources from measurements of chemical concentrations in ambient air. My work is part of a collaboration with Dr. Shane Reese and Dr. William Christensen of Brigham Young University.

Bayesian Latent Variable Publications