This paper aims to find a suitable decision rule for a binary composite hypothesis-testing problem with a partial or coarse prior distribution. To alleviate the negative impact of the information uncertainty, a constraint is considered that the maximum conditional risk cannot be greater than a predefined value. Therefore, the objective of this paper becomes to find the optimal decision rule to ...

Bayes' Rule is a way of calculating conditional probabilities. It is difficult to find an explanation of its relevance that is both mathematically comprehensive and easily accessible to all readers. This article tries to fill that void, by laying out the nature of Bayes' Rule and its implications for clinicians in a way that assumes little or no background in probability theory. It builds on Me...

Bayesian statistics is has been very successful in describing behavioural data on decision making and cue integration under noisy circumstances. However, it is still an open question how the human brain actually incorporates this functionality. Here we compare three ways in which Bayes rule can be implemented using neural fields. The result is a truly dynamic framework that can easily be extend...

The Method of Maximum (relative) Entropy (ME) has been designed for updating from a prior distribution to a posterior distribution when the information being processed is in the form of a constraint on the family of allowed posteriors. This is in contrast with the usual MaxEnt which was designed as a method to assign, and not to update, probabilities. The objective of this paper is to strengthe...

Chapter 1: INTRODUCTION Chapter 2: SHAPE-BASED DESCRIPTION 2.1 Fourier Descriptors 2.2 Moment Invariants 2.3 Scalar Descriptors Chapter 3: CLASSIFICATION 3.1 Supervised v Unsupervised Classification 3.2 Classification using Bayes Theorem 3.3 Implementing Bayesian Classification Chapter 4: COMBINING CLASSIFIERS 4.1 The Fusion Model 4.2 Theory 4.2.1 The Product Rule 4.2.2 Sum Rule 4.3 Classifier ...

To this end, the so-called Bayes decision rule assigns each pattern x to the class for which the a posteriori probability P(u i Dx) is maximum. An error probability lower than the one provided by the above Bayes rule can be obtained using the so-called `rejecta option. Namely, the patterns that are the most likely to be misclassi"ed are rejected (i.e., they are not classi"ed); they are then han...