Speaker:

Debashis Mondal (Oregon State University, Statistics Department)
Web page: http://stat.oregonstate.edu/people/mondal-debashis

Title:

Markov random fields, geostatistics, and matrix-free computation

Abstract:

Since their introduction in statistics through the seminal works of
Julian Besag, Gaussian Markov random fields have become central to
spatial statistics, with applications in agriculture, epidemiology,
geology, image analysis and other areas of environmental science.
Specified by a set of conditional distributions, these Markov random
fields provide a very rich and flexible class of spatial processes,
and their adaptability to fast statistical calculations, including
those based on Markov chain Monte Carlo computations, makes them very
attractive to statisticians. In recent years, new perspectives have
emerged in connecting Gaussian Markov random fields with
geostatistical models, and in advancing vast statistical computations.
In this talk, I will briefly discuss the scaling limit of
lattice-based Gaussian Markov random fields, namely,  the de Wijs
process that originates in the famous work of George Matheron on gold
mines in South Africa. I will then explore how this continuum limit
connection holds out further possibilities to fit a wide range of new
continuum models by using Gaussian Markov random fields. The main
focus of the talk will be on matrix-free computation for these models.
In particular, for spatial mixed linear models, I will present
frequentist residual maximum likelihood inference via matrix-free
h-likelihood computation. I will draw applications both from
areal-unit and point-referenced spatial data.

The work resulted from collaborations with (late) Julian Besag, and
Ph.D.students Somak Dutta (former) and Chunxiao Wang (current).