Toward general solutions to time-series problems: Notes on obstacles and noise

Abstract

Computational difficulties in the general application of Bretthorsts formalism to time-series problems, posed by the large number of possible models and the use of models with nonorthogonal base-functions are discussed. The specific problem under consideration is a Bayesian procedure for model selection, parameter estimation, and classification, that was applied to the search for the {\it {In Vivo}} $T_2$ decay rate distributions in brain tissues. Through the estimation of the meta-parameter $\sigma$ in the process, we also gain a better understanding of the meaning and estimation of "noise" in the frame-work of probability theory as logic.