With data of rapidly increasing sizes in the environmental and geosciences such as satellite observations and high-resolution climate model runs, the spatial statistics community has recently focused on methods that are applicable to very large data. One such state-of-the-art method is the multi-resolution approximation (MRA), which was specifically developed with high performance computer architecture in mind.

We propose a novel statistical framework by supplementing case–control data with summary statistics on the population at risk for a subset of risk factors. Our approach is to first form two unbiased estimating equations, one based on the case–control data and the other on both the case data and the summary statistics, and then optimally combine them to derive another estimating equation to be used for the estimation.

Spatial analyses often focus on spatial smoothing using the geostatistical technique known as kriging.  Theoretical results regarding large sample convergence rates of kriging predictors remain elusive.  By casting kriging as a variational problem, we develop an equivalent kernel approximation technique that can also lead to computational feasibility for large data problems.

Workshop on Computational Space-Time Statistics

In this talk we develop a method for simultaneous estimation of density functions for a collection of populations of protein backbone angle pairs. Each log density function in the collection is modeled as a linear combination of a common set of basis functions. The shared basis functions are modeled as bivariate splines on triangulations and are estimated using data. The circular nature of angular data is taken into account by imposing appropriate smoothness constraints across boundaries of the triangles.

In this talk, we introduce a new Bayesian regression tree model that allows for possible heteroscedasticity in the variance model and devise novel MCMC samplers that appear to adequately explore the posterior tree space of this model.

In this talk, we first show various strategies for the efficient emulation of simulators having uncertain inputs, with applications to tsunami wave modelling. A fast surrogate of the simulator's time series of outputs is provided by the outer product emulator.