This paper presents a natural extension of Bayesian decision theory from the domain of individual decisions to the domain of group decisions. We assume that each group member accepts the assumptions of subjective expected utility theory with respect to the alternatives from which they must choose, but we do not assume, a priori, that the group as a whole accepts those assumptions. Instead, we i...

The problem of learning Markov equivalence classes of Bayesian network structures may be solved by searching for the maximum of a scoring metric in a space of these classes. This paper deals with the definition and analysis of one such search space. We use a theoretically motivated neighbourhood, the inclusion boundary, and represent equivalence classes by essential graphs. We show that this se...

D. Trafimow (2003) presented an analysis of null hypothesis significance testing (NHST) using Bayes's theorem. Among other points, he concluded that NHST is logically invalid, but that logically valid Bayesian analyses are often not possible. The latter conclusion reflects a fundamental misunderstanding of the nature of Bayesian inference. This view needs correction, because Bayesian methods ha...

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Approximate Bayesian Gaussian process (GP) classification techniques are powerful nonparametric learning methods, similar in appearance and performance to support vector machines. Based on simple probabilistic models, they render interpretable results and can be embedded in Bayesian frameworks for model selection, feature selection, etc. In this paper, by applying the PAC-Bayesian theorem of Mc...

Owing to the popularity of World Wide Web, many enterprises have changed the ways of doing business, which enhance the rapid development of E-commerce directly and makes the development of web usage mining skills important. It becomes a crucial issue to predict exactly the ways how users and customers browse websites. The prediction result can be used for personalization, building proper websit...

Clarke and Barron analysed the relative entropy between an i.i.d. source and a Bayesian mixture over a continuous class containing that source. In this paper a comparable result is obtained when the source is permitted to be both non-stationary and dependent. The main theorem shows that Bayesian methods perform well for both compression and sequence prediction even in this most general setting ...

The Bayesian approach to inductive reasoning originated in two brilliant insights. In 1654 Blaise Pascal, while in the course of a correspondence with Fermat [1769], recognized that states of uncertainty can be quantified using probabilities and expectations. In the early 1760s Thomas Bayes [1763] first understood that learning can be represented probabilistically using what is now called Bayes...