Annual Report 2008.pdf - SAMSI

1. Statistics Department Seminar, Colorado State University, Fort Collins, CO, November
5, 2007.
2. Application of Statistics to Numerical Models: New Methods and Case Studies, Boulder,
CO, May 21-24, 2007.
3. Joint Statistical Meetings, Salt Lake City, UT, July 29 - August 2, 2007.
4. Mathematical and Computer Sciences Departmental Colloquium, Colorado School of
Mines, Golden, CO, August 31, 2007.
5. 7 th World Congress in Probability and Statistics, Singapore, July 14-19, 2008.
Working Group II Methodology
Efficient Emulators of Computer Experiments
Collaborator(s) & Mentor(s): Derek Bingham, Katrin Heitmann
Emulators are statistical models for predicting the output of a computer model when running the
model code itself is deemed too time consuming. Emulators typically use Gaussian process
distributions as priors over function spaces, but these models can become computationally
infeasible when the training dataset is large. I am working with Derek Bingham at Simon Fraser
University to build emulators that use compactly supported correlation functions to speed
computation. The processes needed to model the computer output are often high dimensional
and nonisotropic. Therefore, the correlation structure must adapt to the anisotropy to avoid
losing predictive efficiency. Our approach is 1) to determine the minimum level of sparsity
required to efficiently manipulate the covariance matrix, 2) to include large-scale structure in the
mean of the process, so that 3) residual variation is modeled with little loss of efficiency by a
product of compactly supported correlation functions in each dimension. We are testing our
approach on a computer model for spectroscopic red shift developed by cosmologists.
Publications, Submissions, Work in Preparation:
Kaufman, C. Bingham, D., and Heitmann, K. Efficient Emulators of Computer Experiments
Using Compactly Supported Correlation Functions. In preparation.
Presentations outside SAMSI:
1. Efficient Emulators of Computer Experiments Using Covariance Tapering.
2. Statistics and Actuarial Science Seminar, Simon Fraser University, Burnaby, BC,
Canada, 2007.
Working Group III Terrestrial Models
State-space Modeling of Soil Moisture
Collaborator(s) & Mentor(s): Jim Clark, Jonathan Rougier
Working with Jim Clark's forest ecology group at Duke University, I am predicting spatial and
temporal soil moisture changes under varying climatic conditions. Soil moisture is an important
factor in tree growth and fecundity, and these predictions are part of a larger project studying the
effect of climate change on forest dynamics. Our approach has been to build a state-space model
in which the temporally evolving soil moisture field is the unknown state vector. Our initial
predictions used a simple linear model, which could be fit using a Kalman filter, but they did not
take advantage of valuable prior knowledge about the evolution of soil moisture over time. In
our new model, this process is governed by a simple, catchment-level hydrology model I
developed based on the literature, combined with a stochastic model for distributing total water
according to local topography. I am currently carrying out the first stage of model fitting,
developing an MCMC algorithm for sampling the unknown parameters with an embedded
smoothing algorithm to sample the soil moisture fields conditional on these parameters.