Bayesian Spatio-Temporal Analysis and Statistical Computation in Very High Dimensional Problems
Abstract
Uncertainty is ubiquitous in both daily life and the grand challenges facing modern society. BayesianAnalysis (BA) harnesses the power of thinking conditionally through modeling uncertainty with sequencesof conditional probability distributions defined in a hierarchical manner, starting with thedata-generating process and ending with a prior probability distribution over model parameters.These sequences are used in Bayes’ Theorem to quantify uncertainty through the posterior probabilitydistribution, which is itself a conditional probability distribution of all the ‘unknowns’ giventhe observations. Fundamentally, BA is a coherent way of inferring an underlying, possible complexsignal from statistically noisy, incomplete, and diverse observations; and, in principle, uncertaintyquantification accompanies the estimated signal through selective summaries of the posterior distribution.Our project will develop spatio-temporal prediction in highly-complex settings through-scalable computing of a highly multivariate but marginalized posterior distribution of unknownscustomized to the question being answered; and Bayesian deep-learning models developed aroundnetwork architectures that treat uncertainty as an integral part of the network design. Posteriorinference quantifies the uncertainty of inference on the unknowns with multivariate loss functions,and we shall develop these for the two objectives given above. Solutions in these areas of research willusher in a transformative shift in the utility of Bayesian statistical models for big spatio-temporaldata with the potential for a diverse array of application areas from the geosciences to managementof public health.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 16, 2024
- Source ID
- FA23862314100
Entities
People
- Noel Cressie
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Wollongong