Bayes’ Theorem is increasingly used as a benchmark against which to judge the quality of citizens’ thinking, but some of its implications are not well understood. A common claim is that Bayesians must agree more as they learn and that the failure of partisans to do the same is evidence of bias in their responses to new information. Formal inspection of Bayesian learning models shows that this i...

Bayes's theorem is predominantly used in diagnosing based on the results of various diagnostic tests. This statistical approach is intuitive in differential diagnosis as it explicitly takes into consideration data from medical history, physical examination, laboratory findings and imaging. Bayes's theorem states that the probability of disease occurrence (or occurrence of other outcome) after n...

A Bayesian method for incorporating probabilistic background knowledge into ILP is presented. Positive only learning is extended to allow density estimation. Estimated densities and deened prior are combined in Bayes theorem to perform relational classiication. An initial application of the technique is made to part-of-speech (POS) tagging. A novel use of Gibbs sampling for POS tagging is given.

We develop a theory of quantum rational decision making in the tradition of Anscombe and Aumann’s axiomatisation of preferences on horse lotteries. It is essentially the Bayesian decision theory generalised to the space of Hermitian matrices. Among other things, this leads us to give a representation theorem showing that quantum complete rational preferences are obtained by means of expected ut...

(Jaynes’) Method of (Shannon-Kullback’s) Relative Entropy Maximization (REM or MaxEnt) can be at least in the discrete case according to the Maximum Probability Theorem (MPT) viewed as an asymptotic instance of the Maximum Probability method (MaxProb). A simple bayesian interpretation of MaxProb is given here. MPT carries the interpretation over into REM.

This paper presents some basic topics in probability and statistics, including sample spaces, probabilistic events, expectations, the binomial and normal distributions, the Central Limit Theorem, Bayesian analysis, and statistical hypothesis testing. These topics are applied to gambling games involving dice, cards, and coins.

Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian operators and to describe both pure and mixed systems. Illustrative examples are given. The quantum version of Bayesian inference is discussed.

We develop a theory of quantum rational decision making in the tradition of Anscombe and Aumann’s axiomatisation of preferences on horse lotteries. It is essentially the Bayesian decision theory generalised to the space of Hermitian matrices. Among other things, this leads us to give a representation theorem showing that quantum complete rational preferences are obtained by means of expected ut...

A 3D super-resolution algorithm is proposed below, based on a probabilistic interpretation of the ndimensional version of Papoulis’ generalized sampling theorem. The algorithm is devised for recovering the albedo and the height map of a Lambertian surface in a Bayesian framework, using Markov Random Fields for modeling the a priori knowledge.