From the Publisher:
Probabilistic Reasoning in Intelligent Systems is a complete andaccessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertaintyand offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognitionin short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information.
Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

The Second Scientific American Book of Mathematical Puzzles and Diversions.

Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference

A number of problems in physics can be reduced to the study of a measure‐preserving mapping of a plane onto itself. One example is a Hamiltonian system with two degrees of freedom, i.e., two coupled nonlinear oscillators. These are among the simplest deterministic systems that can have chaotic solutions. According to a theorem of Kolmogorov, Arnol’d, and Moser, these systems may also have more ordered orbits lying on curves that divide the plane. The existence of each of these orbit types depends sensitively on both the parameters of the problem and on the initial conditions. The problem addressed in this paper is that of finding when given KAM orbits exist. The guiding hypothesis is that the disappearance of a KAM surface is associated with a sudden change from stability to instability of nearby periodic orbits. The relation between KAM surfaces and periodic orbits has been explored extensively here by the numerical computation of a particular mapping. An important part of this procedure is the introduction of two quantities, the residue and the mean residue, that permit the stability of many orbits to be estimated from the extrapolation of results obtained for a few orbits. The results are distilled into a series of assertions. These are consistent with all that is previously known, strongly supported by numerical results, and lead to a method for deciding the existence of any given KAM surface computationally.

/pdf/a-method-for-determining-a-stochastic-transition-3gx70fhol6.pdf

A method for determining a stochastic transition

http://compalg.inf.elte.hu/~tony/Kutatas/BinPacking/Johnson-BinPacking-NP-Column-JAlg-2002.pdf

The NP-completeness column: An ongoing guide

We define a new notion of conditional belief, which plays the same role for Dempster-Shafer belief functions as conditional probability does for probability functions. Our definition is different from the standard definition given by Dempster, and avoids many of the well-known problems of that definition. Just as the conditional probability Pr(.IB) is a probability function which is the result of conditioning on B being true, so too our conditional belief function BeZ(-IB) is a belief function which is the result of conditioning on B being true. We define the conditional belief as the lower envelope (that is, the inf) of a family of conditional probability functions, and provide a closedform expression for it. An alternate way of understanding our definition of conditional belief is provided by considering ideas from an earlier paper [Fagin and Halpern, 19891, where we connect belief functions with inner measures. In particular, we show here how to extend the definition of conditional probability to nonmeasurable sets, in order to get notions of inner and outer conditional probabilities, which can be viewed as best approximations to the true conditional probability, given our lack of information. Our definition of conditional belief turns out to be an exact analogue of our definition of inner conditional probability.

https://researcher.watson.ibm.com/researcher/files/us-fagin/uncai91.pdf

The Second Scientific American Book of Mathematical Puzzles and Diversions.

Citations

Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference

A method for determining a stochastic transition

The NP-completeness column: An ongoing guide

A new approach to updating beliefs

The Game of Hex and the Brouwer Fixed-Point Theorem

Related Papers (5)

Some teasers concerning conditional probabilities.

The Game of Hex and the Brouwer Fixed-Point Theorem

A Combinatorial Problem Which Is Complete in Polynomial Space

An introduction to probability theory and its applications

Winning Ways for your Mathematical Plays