Distribution design for Bayesian knowledge processing in multiple participant systems

Abstract

Knowledge processing in an optimal way is of great importance in decision making. In this thesis, we propose a consistent Bayesian mechanism for processing knowledge via the design of the probability distribution. Bayes' rule is exploited as a consistent mechanism when a complete model is available. In this thesis, we examine an important context for this, namely conjugate Bayesian inference for the autoregressive (AR) model. We characterise this as an example of uniquely specified distributional design, and we provide some novel results related to the computation of the associated statistics within fully tractable signal processing algorithms.