Bayesian Models and Methods for Dynamic and Spatio-Dynamic Systems

Duke University, Durham NC

Investigators

Abstract

The research concerns novel statistical theory, models and methods for structured dynamic and spatio-dynamic multivariate processes. The scope includes theoretical developments of new classes of stochastic process models for dynamic covariancestructures in multi- and matrix-variate time series, including novel classes of stationary Markov processes for multivariate volatility modeling. Theoretical and applied developments include new approaches to sparsity modeling for increasingly high-dimensional, time-varying parameter stochastic systems, applying to dynamic regression, time-varying vector auto-regression, dynamic factor models and covariance volatility models. Additional research focuses on new classes of spatial lattice and spatially-varying random field models, coupled with time series processes to define flexible models of spatio-temporal models for increasingly high-resolution lattice data observed through time. The investigator develops Bayesian simulation-based statistical computation-- including GPU-based parallelized algorithms-- for model implementations, and cross-disciplinary applications in financial time series as well as studies in atmospheric and biomedical sciences. Faced with increasingly high-dimensional data sets generated in studies of temporal and spatial systems, statistical science research aims to substantially advance the ability to represent, analyze and use mathematical models of increasing dimension, realism and complexity. The investigator develops mathematical and statistical modelling theory and associated simulation-based computational methods for a range of contexts, motivated in part by collaborative cross-disciplinary applications in areas of finance, atmospheric science and the neurosciences. Innovations in statistical research include: (i) new and improved models for describing and predicting change in time of the complex patterns of relationships among several or many time series-- such as financial indicators, or nano-technology based recordings of neural signals in brain imaging; (ii) new theory and methods for inducing sparsity-- i.e., controlling complexity-- of applied stochastic models, to enable scaling to increasingly high-dimensional problems, such as arise in high-resolution satellite imaging in atmospheric studies as well as large-scale financial time series;(iii) innovations in simulation techniques for statistical computing, including parallel desktop computing, to advance the ability to fit, explore and use models of increasing scale and complexity and with increasingly large data sets. With cross-disciplinary collaborators and students, the research advances core mathematical and statistical modeling theory and technology, and contributes new, refined and relevant approaches to modeling and dataanalysis in several specific applied contexts as well as generating methods for broader use.