Organizer:

Timothy C. Haas, haas@uwm.edu

Speakers

1:30 p.m.
Statistical Supercomputing for Gibbs Sampling of Massive Spatio-temporal Models
Chris Wikle, University of Missouri - Columbia
(with Tim Hoar, Ralph Milliff, and Doug Nychka, National Center for Atmospheric Research)

Spatio-temporal processes are ubiquitous in the environmental and physical sciences. This is certainly true of atmospheric and oceanic processes, which typically exhibit many different scales of spatial and temporal variability. The complexity of these processes and large number of observation/prediction locations preclude the use of traditional covariance-based space-time statistical methods. Alternatively, we have investigated conditionally-specified (i.e., hierarchical) spatio-temporal models. These models are advantageous in that physical and dynamical constraints are easily incorporated into the conditional formulation, so that the series of relatively simple, yet physically realistic, conditional models leads to a much more complicated joint space-time covariance structure than can be specified directly. Furthermore, by making use of the sparse structure inherent in the hierarchical approach, multiresolution (wavelet) bases, and specialized conjugate gradient sampling procedures, these models are computable with a Gibbs Sampler for reasonably large data sets on a standard workstation. However, for the massive space-time domains (order 10^6 locations) and data sets (order 10^7 observations) useful to atmospheric/oceanic scientists , this model must be ported to a "super-computer". We describe the implementation of such a model on the 24 processor, 1.5 GFLOPS, 1024 Mword, Cray J924se super-computer at the National Center for Atmospheric Research (NCAR). Specifically, we focus on a problem concerning spatio-temporal prediction of near surface wind fields over the tropics given "data" from weather center deterministic models and remotely sensed satellite observations.

2:00 p.m.
Reversible Jump MCMC Analysis of Spatial Poisson Cluster Processes with Bivariate Normal Displacement
John Castelloe, SAS Institute and University of Iowa
Keywords: convergence assessment, bivariate normal mixture model, reversible jump MCMC, spatial point patterns

A reversible jump Markov chain Monte Carlo (RJMCMC) technique for bivariate normal mixtures with common covariance matrix is developed and applied to a special type of spatial point process, namely the Poisson cluster process with bivariate normal offspring dispersal. Inference for this type of process focuses on the common covariance matrix of the offspring dispersal distribution. RJMCMC extends the traditional MCMC capabilities by providing for transitions between different parameter spaces, which are needed in our situation due to the unknown number of clusters. A new convergence assessment method, applicable to any RJMCMC situation in which distinct models can be identified, is designed and theoretically justified. A ``model'' in our case is a given number of clusters, in other words, the number of components in a mixture. Output analysis methods are also developed, including anisotropy testing/estimation, model checking and inference for number of clusters. The RJMCMC technique is flexible and has potential to apply to more complicated spatial point processes, and also other mixture-related problems.

2:30 p.m.
Combining Expert Beliefs, Nongaussian Continuous Random Variables, and Decision Option Variables with a Simulation-Based Influence Diagram
Timothy C. Haas, University of Wisconsin - Milwaukee

Ecosystem dynamics often include systems of stochastic differential equations and/or birth-death processes. The theory of influence diagrams (ID's) will be extended to allow inclusion of such random processes. An example ID that represents cheetah population dynamics in Kenya that consists of collections of both discrete and continuous but nongaussian random variables will be given. The joint distribution, called the probability density-probability function (PDPF) (Koopmans 1969) will often have no analytical form. Simulation is used to approximate the PDPF for purposes of finding constrained minimum distance estimates of the distribution's parameters.