Multiscale Modeling

This book presents methodology for analyzing data that cocur on multiple scales (for example, daily and monthly data, or data at zip code and state levels). This is the first such book to focus on the Bayesian approach, which allows straightforward incorporation of prior knowledge, as well as estimates of uncertainty. Two worked case studies provide detailed examples of these methods in practice.

Stochastic models for processes that live and can possibly be observed at different levels of resolution The models in this book allow different degrees of smoothness of the stochastic processes at the different levels of resolution The statistical analysis of multiscale models based on the Bayesian paradigm in the book allow a full amount of uncertainty Contains implicit multiscale models implementable with parallel computation and genetic algorithms

Inhalt
Models for Spatial Data.- Illustrative Example.- Convolutions and Wavelets.- Convolution Methods.- Wavelet Methods.- Explicit Multiscale Models.- Overview of Explicit Multiscale Models.- Gaussian Multiscale Models on Trees.- Hidden Markov Models on Trees.- Mass-Balanced Multiscale Models on Trees.- Multiscale Random Fields.- Multiscale Time Series.- Change of Support Models.- Implicit Multiscale Models.- Implicit Computationally Linked Model Overview.- Metropolis-Coupled Methods.- Genetic Algorithms.- Case Studies.- Soil Permeability Estimation.- Single Photon Emission Computed Tomography Example.- Conclusions.