I used a Bayesian approach to do nonparametric regression and spatial smoothing. I used Gaussian process priors to estimate smooth fields and used both stationary and nonstationary covariance models. The nonstationary covariance models allow the degree of smoothness in the field to vary depending on where you are in covariate space or geographic space. In particular, I used the convolution method of Dave Higdon (formerly of Duke, now at Los Alamos National Lab) to create nonstationary covariance models. I extended Dave's work to create, among other things, a Matern version of his kernel covariance structure. If you'd like more information, please get in contact with me.

The dissertation won the 2003 Leonard J. Savage Award for the best Bayesian dissertation in Theory and Methods.

Here is the thesis[bibtex]. You can also download chapter by chapter. I have discovered a few errors in the text of the dissertation.

I have a NIPS paper summarizing the nonparametric regression aspect of the thesis. You can download this in ps or pdf formats.

Here are the data files in flat, space-delimited ascii format. Files marked `x' have the covariate values, one covariate per row, those marked `y' have noisy response values, and those marked `fun' have the true function from which data were simulated (for the simulated datasets). New covariates and noisy observations for the Hwang dataset and new noisy observations for the DiMatteo et al. (2002) datasets were generated for each of 50 sample datasets, so I do not include those here.

The code used in the thesis is also available. The regression code for normal data and binomial data is available here. Simply run `make' on a Unix/linux system in the directory containing the code to produce an executable named `nsgp'. Example initial value and parameter value files, as well as an example script file, are included with the code. The data files indicated in the previous paragraph contain example input files for the covariates, observations, and true function values. The code for the spatial model in the thesis is also available, but is not intended for public use, as it is not well-documented.

Last updated: September 2004.