Title: Hierarchical Modeling and Analysis for Spatial Data

Instructor: Bradley P. Carlin Division of Biostatistics, University of Minnesota [ bio ]

Course description: As recently as two decades ago, the impact of hierarchical Bayesian methods outside of a small group of theoretical probabilists and statisticians was minimal at best. Suddenly, around 1990, the ``Markov chain Monte Carlo (MCMC) revolution'' enabled hierarchical models to become not only feasible, but the preferred approach for almost any model involving multiple levels incorporating random effects or complicated dependence structures.

In this course we will describe hierarchical modeling methods for an area of application in which they can pay substantial dividends: spatial statistics. We will begin by outlining and providing illustrative examples of the three types of spatial data: point-level (geostatistical), areal (lattice), and spatial point process.

We then describe both exploratory data analysis tools and traditional modeling approaches for point-referenced data. Modeling approaches from traditional geostatistics (variogram fitting, kriging, and so forth) will be covered here. We shall then offer a similar presentation for areal data models, again starting with choropleth maps and other displays and progressing towards more formal statistical concepts, such as Brook's Lemma and the Markov random field topics that underlie the conditional, intrinsic, and simultaneous autoregressive (CAR, IAR, and SAR) models so often used in areal data settings.

The remainder of our presentation will cover hierarchical modeling for both univariate and multivariate spatial response data, including Bayesian kriging and lattice modeling, as well as more advanced issues such as anisotropy and nonstationarity. Bayesian methods will also be suggested for modeling data that are spatially misaligned (say, with one variable measured by census tract but another by zip code), since they are particularly well-suited to sorting out complex interrelationships and constraints.

We also include a discussion of spatially varying coefficient, spatio-temporal, and spatial survival models. The class will also include instructor demonstrations of the geoR and WinBUGS programs for carrying out spatial analyses. Since both of these programs are freely available, students are encouraged to download both onto their laptop computers if they would like to follow along with this part of the presentation.

Prerequisites: Short course participants should have an M.S. understanding of mathematical statistics at, say, the Hogg and Craig (1978) level, as well as basic familiarity with standard statistical models and computing.

We will not assume any significant previous exposure to spatial or Bayesian methods, although students with basic knowledge of these areas (say, based on the books by Cressie, 1993, and Carlin and Louis, 2000, respectively) will certainly face a gentler learning curve.

Short Course Fees :

Participants are expected to purchase the book "Hierarchical Modeling and Analysis for Spatial Data'' by Banerjee, Carlin and Gelfand prior to beginning the course. This can be done via the CRC Press website (www.crcpress.com), from amazon.com, or from the CRC representative Mr. Bob Stern the morning of the course. Course fee does not include the cost of the book (approximately US$65.00).