Model selection is the problem of distinguishing competing models, perhaps featuring different numbers of parameters. The statistics literature contains two distinct sets of tools, those based on information theory such as the Akaike Information Criterion (AIC), and those on Bayesian inference such as the Bayesian evidence and Bayesian Information Criterion (BIC). The Deviance Information Crite...

Bayesian approach to decision making is successfully applied in control theory for design of control strategy. However, it is based on on the assumption that a decision-maker is the only active part of the system. Relaxation of this assumption would allow us to build a framework for design of control strategy in multi-agent systems. In Bayesian framework, all information is represented by proba...

The Sleeping Beauty problem is test stone for theories about self-locating belief, i.e. theories about how we should reason when data or theories contain indexical information. Opinion on this problem is split between two camps, those who defend the “1/2 view” and those who advocate the “1/3 view”. I argue that both these positions are mistaken. Instead, I propose a new “hybrid” model, which av...

S u m m a r y. The main objective of this paper is to show the use of Bayesian networks in inductive research applied in an e-loyalty study and to investigate whether e-loyalty theories can be discovered by means of Bayesian networks.

The aim is to explain and explore some of the current ideas from category theory that enable various mathematical descriptions of hierarchical structures.

Bayesian bootstrap was proposed by Rubin (1981) and its theoretical properties and application to survival models without covariates was studies by Lo (1993) and others. Bayesian bootstrap, empirical likelihood and bootstrap are diierent approaches based on the same idea, approximating the nonparametric model with the family of distributions whose supports are the set of observations. Based on ...

Over the past two decades a number of different approaches to “fuzzy probabilities” have been presented. The use of the same term masks fundamental differences. This paper surveys these different theories, contrasting and relating them to one another. Problems with these existing approaches are noted and a theory of “linguistic probabilities” is developed, which seeks to retain the underlying i...

One of the most important fundamental properties of Bayesian networks is the representational power, re ecting what kind of functions they can or cannot represent. In this paper, we establish an association between the structural complexity of Bayesian networks and their representational power. We use the maximum number of nodes' parents as the measure for the Bayesian network structural comple...

The two preceding articles developed the application of Bayesian probability theory to the problems of parameter estimation, signal detection, and model selection on quadrature NMR data in some generality. Here those procedures are used to analyze free induction decay data, when the models are sinusoidal. The exact relationship between Bayesian probability theory and the discrete Fourier-transf...

Graphical Models bring together two different mathematical areas: graph theory and probability theory. Recent years have witnessed an increase in the significance of the role played by Graphical Models in solving several machine learning problems. Graphical Models can be either directed or undirected. Undirected Graphical Models are also called Bayesian networks. The manual construction of Baye...