A simple model of rational belief holds that: (i) an instantaneous snapshot of an ideally rational belief system corresponds to a probability distribution; and (ii) rational belief change occurs by Bayesian conditionalization. But a priori probability distributions of the Kolmogorov sort cannot distinguish between propositions that are simply true from propositions that are necessarily true. Fu...

I generalise the arguments of [Chow & Liu 1968] to show that a Bayesian network satisfying some arbitrary constraint that best approximates a probability distribution is one for which mutual information weight is maximised. I give a practical procedure for finding an approximation network. The plan is first to discuss the approximation problem and its link with Bayesian network theory. After id...

Probability theory can be modified in essentially one way while maintaining consistency with the basic Bayesian framework. This modification results in copies of standard probability theory for real, complex or quaternion probabilities. These copies, in turn, allow one to derive quantum theory while restoring standard probability theory in the classical limit. This sequence is presented in some...

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...

The theory of belief functions provides one way to use mathematical probability in subjective judgment. It is a generalization of the Bayesian theory of subjective probability. When we use the Bayesian theory to quantify judgments about a question, we must assign probabilities to the possible answers to that question. The theory of belief functions is more flexible; it allows us to derive degre...

The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more traditional statistical tools, offering the advantage of higher efficiency and of a consistent conceptual basis for dealing with the problem of induction in the ...

Compositional models were initially described for discrete probability theory, and later extended for possibility theory and for belief functions in Dempster-Shafer (D-S) theory of evidence. Valuation-based system (VBS) is an unifying theoretical framework generalizing some of the well known and frequently used uncertainty calculi. This generalization enables us to not only highlight the most i...

The field of Bayesian Networks has had an enormous development over the last few years and is one of the current key topics of research in the design of statistical machine learning and data mining algorithms. Bayesian networks are a natural marriage between two areas in mathematics: graph theory and probability theory. A Bayesian net encodes the probability distribution of a set of attributes ...

Bayesian networks provide a powerful intelligent information fusion architecture for modeling probabilistic and causal patterns involving multiple random variables. This paper advances a computable theory of learning discrete Bayesian networks from data. The theory is based on the MAP-MDL principles for maximizing the joint probability or interchangeably miniziming the joint description length ...

I present a straightforward objection to the view that what we know has epistemic probability 1: when combined with Bayesian decision theory, the view seems to entail implausible conclusions concerning rational choice. I consider and reject three responses. The first holds that the fault is with decision theory, rather than the view that knowledge has probability 1. The second two try to reconc...