This paper provides new foundations for Bayesian Decision Theory based on a representation theorem for preferences de…ned on a set of prospects containing both factual and conditional possibilities. This use of a rich set of prospects not only provides a framework within which the main theoretical claims of Savage, Ramsey, Je¤rey and others can be stated and compared, but also allows for the po...

Gelman and Shalizi (2012) criticize what they call the 'usual story' in Bayesian statistics: that the distribution over hypotheses or models is the sole means of statistical inference, thus excluding model checking and revision, and that inference is inductivist rather than deductivist. They present an alternative hypothetico-deductive approach to remedy both shortcomings. We agree with Gelman ...

An introduction is provided to Multi-Entity Bayesian Networks (MEBN), a logic system that integrates First Order Logic (FOL) with Bayesian probability theory. MEBN extends ordinary Bayesian networks to allow representation of graphical models with repeated sub-structures. Knowledge is encoded as a collection of Bayesian network fragments (MFrags) that can be instantiated and combined to form hi...

This paper develops a theory for the convergence rates of A* algorithms for real-world vision problems, such as road tracking, which can be formulated in terms of maximizing a reward function derived using Bayesian probability theory. Such problems are well suited to A* tree search and it can be shown that many algorithms proposed to solve them are special cases, or variants, of A*. Moreover, t...

In statistical inference, the point estimation problem is very crucial and has a wide range of applications. When, we deal with some concepts such as random variables, the parameters of interest and estimates may be reported/observed as imprecise. Therefore, the theory of fuzzy sets plays an important role in formulating such situations. In this paper, we rst recall the crisp uniformly minimum ...

The authors present a Bayesian framework for understanding how adults and children learn the meanings of words. The theory explains how learners can generalize meaningfully from just one or a few positive examples of a novel word's referents, by making rational inductive inferences that integrate prior knowledge about plausible word meanings with the statistical structure of the observed exampl...

An often mentioned obstacle for the use of Dempster-Shafer theory for the handling of uncertainty in expert systems is the computational complexity of the theory. One cause of this complexity is the fact that in Dempster-Shafer theory the evidence is represented by a belief function which is induced by a basic probability assignment, i.e. a probability measure on the powerset of possible answer...

Quasi-Bayesian theory uses convex sets of probability distributions and expected loss to represent preferences about plans. The theory focuses on decision robustness, i.e., the extent to which plans are a ected by deviations in subjective assessments of probability. Generating a plan means enumerating the actions to be taken and providing information about the robustness of the actions. The pre...

It has been shown that human problem solving obeys Bayesian theory, where this theory makes strong assumptions about prior knowledge. Distributed adaptive control (DAC) is a modeling series approaching the biological processes of acquisition, retention and expression of knowledge. In this project the question is investigated, whether the mechanisms of DAC to express its knowledge of the world f...