3 Literature Survey: Bayesian Probability Theory

Abstract

This chapter presents some basic aspects of Bayesian probability theory [21, 153]. First of all, the difference between Bayesian and classical statistics is discussed (Sect. 3.2). Section 3.3 presents Bayesian state estimation (filtering) based on data measured at discrete time steps. Section 3.4 describes Bayesian hypothesis testing. Sections 3.5 and 3.6 focus on optimal experiment design ( active sensing), i.e., the optimisation of the experiment in order to provide “optimal” state estimates. Section 3.5 presents ways to measure the “information content” of data and estimates. The algorithms for optimisation under state uncertainty are surveyed in Sect. 3.6. Section 3.7 concludes.