Multiscale Statistical Models for Hierarchical Spatial Aggregation

Evaluation of Diagnostics for Hierarchical Spatial Statistical Models

Spatial-Temporal Nonlinear Filtering Based on Hierarchical Statistical Models

A hierarchical statistical model is made up generically of a data model, a process model, and occasionally a prior model for all the unknown parameters. The process model, known as the state equations in the filtering literature, is where most of the scientist’s physical/chemical/biological knowledge about the problem is used. In the case of a dynamically changing configuration of objects movin...

Hierarchical Spatial Models

Methods for spatial and spatio-temporal modeling are becoming increasingly important in environmental sciences and other sciences where data arise from a process in an inherent spatial setting. Technological advances in remote sensing, monitoring networks, and other methods of collecting spatial data in recent decades have revolutionized scientific endeavor in fields such as agriculture, climat...

Bayesian hierarchical statistical SIRS models

The classic SIR (susceptible-infectious-recovered) model, has been used extensively to study the dynamical evolution of an infectious disease in a large population. The SIR-susceptible (SIRS) model is an extension of the SIR model to allow modeling imperfect immunity (those who have recovered might become susceptible again). SIR(S) models assume observed counts are “mass balanced.” Here, mass b...

Multiscale Statistical Image Models and Bayesian Methods

Multiscale statistical signal and image models resulted in major advances in many signal processing disciplines. This paper focuses on Bayesian image denoising. We discuss two important problems in specifying priors for image wavelet coefficients. The first problem is the characterization of the marginal subband statistics. Different existing models include highly kurtotic heavy-tailed distribu...