PhD Candidate, Statistics
Sufficient dimension folding is the technology to reduce the dimensions of matrix- or array-valued objects as well as keep their data structure. In this talk, I consider the sufficient dimension folding for the regression mean function when predictors are matrix- or array-valued. I propose the concept of central mean folding subspace and its two local estimation methods: folded outer product of gradients estimation (folded-OPG) and folded minimum average variance estimation (folded-MAVE). The asymptotic property for folded-MAVE is established.
University of Illinois at Urbana-Champaign
Recently, a low cost yet highly sensitive colorimetric sensor array (CSA) for the detection and identification of volatile chemical toxicants has been developed. Classification analysis holds the key to the success of the array in discriminating multiple toxicants. The data output by the CSA are in the form of matrices, which render many traditional classification methods inapplicable. In this talk, I will introduce a matrix discriminant analysis method which can be viewed as a generalization of the conventional LDA method to the data in matrices form.
University of Illinois at Urbana-Champaign
At a depth of 2890 km, the core-mantle boundary (CMB) separates turbulent flow of liquid metals in the outer core from slowly convecting, highly viscous mantle silicates. The CMB marks the most dramatic change in dynamic processes and material properties in our planet, and accurate images of the structure at or near the CMB--over large areas--are crucially important for our understanding of present day geodynamical processes and the thermo-chemical structure and history of the mantle and mantle-core system.
Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Max-stable processes are a class of asymptotically-justified models that are capable of representing spatial dependence among extreme values. While these models satisfy modeling requirements, they are limited in their utility because their corresponding joint likelihoods are unknown for more than a trivial number of spatial locations, preventing, in particular, Bayesian analyses. In this paper, we propose a new random effects model to account for spatial dependence.
We analyze the mathematical foundations of three types of structured financial products: return optimization securities, yield magnet notes, and reverse exchangeable notes. These products were sold widely to retail "investors" in the mid-2000s. On the basis of their mathematical structure, we infer that these products could provide positive returns to a purchaser only if the stock market had continued on an enormous upward climb for most or all of the holding period.
Georgia Health Sciences University
We propose nonparametric estimators for the state occupation probabilities in a given state adjusting for the informative cluster size and one covariate at a time in a multistate model. This is a non-trivial problem since the state occupied is determined at a single inspection time for each subject and a group of subjects belongs to a cluster where cluster size is informative to their state status.
Many modern processes are capable of generating rich and complex data records not readily analyzed by traditional techniques. A single observation from a process might consist of n pairs of bivariate data that can be described via some functional relation (for example, a sequence of radar reflection signals measured over time). Or, each observation in a process may be a sample of data from some distribution. Methods are proposed here for detecting changes in such sequences from some known or estimated nominal state.
This talk provides an introduction to challenging statistical problems arising in the study of celestial objects: planets, stars, galaxies and the Universe as a whole. We start with a review of the close historical links between astronomy and statistics, from the ancient Greeks through Laplace and Gauss. However, the communities diverged during the 20th century, developing into a poor state with great needs for advanced methodology but weak links between the fields. This is ameliorating today with a vibrant subfield of astrostatistics.
Gas hydrate, which is essentially methane in ice, is a potentially important worldwide energy resource. There is evidence of significant in-place gas hydrate resources in offshore deepwater areas of the world. Southwest Statistical Consulting under grants from U.S Bureau of Ocean Energy Management (BOEM) is developing a mass-balance cell-based model using stochastic simulation to obtain estimates of in-place gas hydrate resources in U.S. Federal off-shore areas.