Fast retraction of evidence in a probabilistic expert system

We present and justify a propagation algorithm to facilitate the simultaneous calculation, for every node in a probabilistic exper system of the distribution of the associated random quantity, conditional on all the evidence obtained about the remaining nodes.     

Determination of recovery effort for a probabilistic recovery system under various inventory control policies

In this study we investigate the desired level of recovery under various inventory control policies when the success of recovery is probabilistic. All the used and returned items go into a recovery process that is modelled as a single stage operation. The recovery effort is represented by the expected time spent for it. The effect of increasing recovery effort on the success probability together with unit cost of the operation is included by assuming general forms of dependencies. Alternative to recovered items, demand is satisfied by brand-new items. Four inventory control policies that differ in timing of and information used in purchasing decision are proposed. The objective is to find the recovery level together with inventory control parameter that minimize the long-run average total cost. A numerical study covering a wide range of system parameters is carried out. Finally computational results are presented with their managerial implications.     

Consistent Probabilistic Social Choice

Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non‐probabilistic social choice, these axioms are incompatible with each other. We show that in the context of probabilistic social choice, these axioms uniquely characterize a function proposed by Fishburn (1984). Fishburn's function returns so‐called maximal lotteries, that is, lotteries that correspond to optimal mixed strategies in the symmetric zero‐sum game induced by the pairwise majority margins. Maximal lotteries are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always unique, and can be efficiently computed using linear programming.     

A probabilistic clustering method for data elements with normal distributed attributes

By considering uncertainty in the attributes common methods cannot be applicable in data clustering. In the recent years, many researches have been done by considering fuzzy concepts to interpolate the uncertainty. But when data elements attributes have probabilistic distributions, the uncertainty cannot be interpreted by fuzzy theory. In this article, a new concept for clustering of elements with predefined probabilistic distributions for their attributes has been proposed, so each observation will be as a member of a cluster with special probability. Two metaheuristic algorithms have been applied to deal with the problem. Squared Euclidean distance type has been considered to calculate the similarity of data elements to cluster centers. The sensitivity analysis shows that the proposed approach will converge to the classic approaches results when the variance of each point tends to be zero. Moreover, numerical analysis confirms that the proposed approach is efficient in clustering of probabilistic data.     

A class of weighted normal distributions and its variants useful for inequality constrained analysis

This article develops a class of the weighted normal distributions for which the probability density function has the form of a product of a normal density and a weight function. The class constitutes marginal distributions obtained from various kinds of doubly truncated bivariate normal distributions. This class of distributions strictly includes the normal, skew–normal and two-piece skew–normal and is useful for selection modelling and inequality constrained normal mean analysis. Some distributional properties and Bayesian perspectives of the class are given. Probabilistic representation of the distributions is also given. The representation is shown to be straightforward to specify distribution and to implement computation, with output readily adapted for required analysis. Necessary theories and illustrative examples are provided.     

On the Cycle-Transitivity of the Dice Model

We introduce the notion of a dice model as a framework for describing a class of probabilistic relations. We investigate the transitivity of the probabilistic relation generated by a dice model and prove that it is a special type of cycle-transitivity that is situated between moderate stochastic transitivity or product-transitivity on the one side, and ukasiewicz-transitivity on the other side. Finally, it is shown that any probabilistic relation with rational elements on a three-dimensional space of alternatives which possesses this particular type of cycle-transitivity, can be represented by a dice model. The same does not hold in higher dimensions.     

Approximating probability density functions in hybrid Bayesian networks with mixtures of truncated exponentials

Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization and Monte Carlo methods for solving hybrid Bayesian networks. Any probability density function (PDF) can be approximated by an MTE potential, which can always be marginalized in closed form. This allows propagation to be done exactly using the Shenoy-Shafer architecture for computing marginals, with no restrictions on the construction of a join tree. This paper presents MTE potentials that approximate standard PDF’s and applications of these potentials for solving inference problems in hybrid Bayesian networks. These approximations will extend the types of inference problems that can be modelled with Bayesian networks, as demonstrated using three examples.     

An analysis of two probabilistic model induction techniques

Two probabilistic model induction techniques, cart and constructor, are compared, via a series of experiments, in terms of their ability to induce models that are both interpretable and predictive. The experiments show that, although both algorithms are able to deliver classifiers with predictive performance close to that of the optimal Bayes rule,constructor is able to generate a probabilistic model that is more easily interpretable than the cart model. On the other hand, cart is a more mature algorithm and is capable of handling many more situations (e.g., real-valued training sets) thanconstructor. A variety of characteristics of both algorithms are compared, and suggestions for future research are made.     

Probabilistic Modeling—From Physics to Computing Science

It is important in computing science to estimate the number of data blocks needed to answer a query. Three different answers to this problem emerged respectively in 1975, 1977, and 1982. This article investigates the basic differences of the three models and observes that the same differences were shared a long time ago by the physicists who used different models for the behavior of elementary particles to obtain the Maxwell-Boltzmann statistics, the Bose-Einstein statistics, and the Fermi-Dirac statistics.     

概率赋范空间中的弱收敛和弱有界

本文引入了Menger-概率赋范空间中有界线性算子,泛函以及向量序列(集)的几种收敛性(有界性)概念,并研究了各种收敛性(有界性)及其相互关系。