Showing papers on "Variable-order Bayesian network published in 1993"

Bayesian Computation Via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods

Abstract: The use of the Gibbs sampler for Bayesian computation is reviewed and illustrated in the context of some canonical examples Other Markov chain Monte Carlo simulation methods are also briefly described, and comments are made on the advantages of sample-based approaches for Bayesian inference summaries

Bayesian analysis in expert systems

Abstract: We review recent developments in applying Bayesian probabilistic and statistical ideas to expert systems. Using a real, moderately complex, medical example we illustrate how qualitative and quantitative knowledge can be represented within a directed graphical model, generally known as a belief network in this context. Exact probabilistic inference on individual cases is possible using a general propagation procedure. When data on a series of cases are available, Bayesian statistical techniques can be used for updating the original subjective quantitative inputs, and we present a sets of diagnostics for identifying conflicts between the data and the prior specification. A model comparison procedure is explored, and a number of links made with mainstream statistical methods. Details are given on the use of Dirichlet prior distributions for learning about parameters and the process of transforming the original graphical model to a junction tree as the basis for efficient computation.

Spatial Statistics and Bayesian Computation

Abstract: on Wednesday, May 6th, 1992, Professor B. W. Silverman in the Chair] SUMMARY Markov chain Monte Carlo (MCMC) algorithms, such as the Gibbs sampler, have provided a Bayesian inference machine in image analysis and in other areas of spatial statistics for several years, founded on the pioneering ideas of Ulf Grenander. More recently, the observation that hyperparameters can be included as part of the updating schedule and the fact that almost any multivariate distribution is equivalently a Markov random field has opened the way to the use of MCMC in general Bayesian computation. In this paper, we trace the early development of MCMC in Bayesian inference, review some recent computational progress in statistical physics, based on the introduction of auxiliary variables, and discuss its current and future relevance in Bayesian applications. We briefly describe a simple MCMC implementation for the Bayesian analysis of agricultural field experiments, with which we have some practical experience.

A survey of Markov decision models for control of networks of queues

Abstract: We review models for the optimal control of networks of queues. Our main emphasis is on models based on Markov decision theory and the characterization of the structure of optimal control policies.

Towards Bayesian image analysis

Abstract: Many of the tasks encountered in image processing can be considered as problems in statistical inference. In particular, they fit naturally into a subjectivist Bayesis framework. In this paper, we describe the Bayesian approach to image analysis. Numerical examples are not included but references are given. It is argued that the Bayesian approach, still in its infancy, has considerable potential for future development.

An algorithm for the construction of Bayesian network structures from data

Abstract: Previous algorithms for the construction of Bayesian belief network structures from data have been either highly dependent on conditional independence (CI) tests, or have required an ordering on the nodes to be supplied by the user. We present an algorithm that integrates these two approaches - CI tests are used to generate an ordering on the nodes from the database which is then used to recover the underlying Bayesian network structure using a non CI based method. Results of preliminary evaluation of the algorithm on two networks (ALARM and LED) are presented. We also discuss some algorithm performance issues and open problems.

Temporal-difference methods and Markov models

Abstract: The relation between temporal-difference training methods and Markov models is explored. This relation is derived from a new perspective, and in this way the particular association between conventional temporal-difference methods and first-order Markov models is explained. The authors then derive a generalization of temporal-difference methods that is suitable for Markov models of higher order. Several issues related to the performance of mismatched temporal-difference methods (i.e., the performance when the temporal-difference method is not specifically designed to match the order of the Markov model) are investigated numerically. >

Morphological Tagging Based Entirely on Bayesian Inference

Abstract: The influence of various information sources on the ability of a statistical tagger to assign lexical categories to unknown words is investigated. The literal word form is found to be very much more important than other information sources such as the local syntactic context. Different ways of combining information sources are discussed. Methods for improving estimates based on scarce data are proposed and examined experimentally.

Bayesian updating in hierarchic Markov processes applied to the animal replacement problem

Abstract: The observed level of milk yield of a dairy cow or the litter size of a sow is only partially the result of a permanent characteristic of the animal; temporary effects are also involved. Thus, we face a problem concerning the proper definition and measurement of the traits in order to give the best possible prediction of the future revenues from an animal considered for replacement. A trait model describing the underlying effects is built into a model combining a Bayesian approach with hierarchic Markov process in order to be able to calculate optimal replacement policies under various conditions. Copyright 1993 by Oxford University Press.

A Bayesian method for learning belief networks that contain hidden variables

Abstract: This paper presents a Bayesian method for computing the probability of a Bayesian belief-network structure from a database In particular, the paper focuses on computing the probability of a belief-network structure that contains a hidden (latent) variable A hidden variable represents a postulated entity that has not been directly measured After reviewing related techniques, which previously were reported, this paper presents a new, more efficient method for handling hidden variables in belief networks

Bayesian testing and testing bayesians

Abstract: This chapter focuses on Bayesian methods and illustrates both the intrinsic unity of Bayesian thinking, and its basic flexibility to adjust to and to cope with a wide range of circumstances. Two ideas are emphasized in the chapter. Firstly hypothesis testing and model choice have been dealt with as a single class of problems met with so strikingly varied motivations that no clear distinction among them seems to be operationally fruitful. Secondly Bayesian thinking is rich enough to accommodate to that variety of situations and is much more flexible than a mechanical prior-to-posterior transformation; in particular, the predictive distributions have been shown to play an important role for this class of problems. Putting emphasis on general inference, on model label or on parameters of interest, has led to put less emphasis on solving specific decision problems. Thus strictly decision oriented procedures have at time been alluded to but not dealt with in any systematic way. This is the case of model choice procedures based on specific criteria such as Akaike information criterion (AIC) or Bayesian information criterion (BIC) with different degrees of involvement with the Bayesian idea. The chapter also provides some examples to examine how testing problems may be handled by statisticians open-minded towards Bayesian ideas.

Bayesian D-Optimal and Model Robust Designs in Linear Regression Models

Abstract: We consider the Bayesian optimal design problem in the usual linear regression model. A version of Elfving’s Theorem is proved for a model robust Bayesian c-optimality criterion. The optimal design minimizes a weighted product where the factors are proportional to the expected posterior risks of the Bayesian estimators for the linear combinations of the parameters in different models. The geometric characterizations are used to state sufficient conditions which guarantee that the classical and the Bayesian optimal designs are supported at the same set of points or are identical. The Bayesian D-optimal design problem appears as a special case in this setup considering “nested” models and special linear combinations for the paramater of the “highest coefficients” in different models. Thus sufficient conditions on the precision matrices of the prior distribution are found that the Bayesian D-optimal and the classical optimal design are supported at the same set of points or are identical. The results are ill...

Generalized exponential growth models a bayesian approach

Abstract: A broad class of normal and non-normal models for processes with non-negative and non-decreasing mean function is presented. This class is called exponential growth models and the inferential procedure is based on dynamic Bayesian forecasting techniques. The aim is to produce the analysis on the original variable avoiding transformation and giving to the practitioner the opportunity to communicate easily with the model. This class of models includes the well-known exponential, logistic and Gompertz models. Models for counting data are compared with the Normal models using the appropriate variance law. In the examples, the novel aspects of this class of models are illustrated showing an improved performance over simple, standard linear models.

Case Studies in Bayesian Statistics

Abstract: The past few years have witnessed dramatic advances in computational methods for Bayesian inference. As a result, Bayesian approaches to solving a wide variety of problems in data analysis and decision-making have become feasible. The purpose of this volume is to present several detailed examples of the applications of Bayesian methods. The emphasis of each article is on the scientific or technological context of the problem being solved, and much background material is provided to complete the description of the analysis. This collection illustrates the ways in which Bayesian methods are permeating statistical practice. Noteworthy in the articles are the construction of explicit and conceptually simple models, the use of information other than the data under analysis, and the representation of uncertainty from various sources in the model.

Dynamic image analysis using Bayesian shape and texture models

Abstract: In this paper, we discuss the implementation of fully Bayesian analysis of dynamic image sequences in the context of stochastic deformable templates for shape modelling, Markov/Gibbs random fields for modelling textures, and dynomation. Throughout, Markov chain Monte Carlo algorithms are used to perform the Bayesian calculations.

Distributed propagation of a-priori constraints in a Bayesian network of Markov random fields

Abstract: In this paper, Bayesian networks of Markov random fields (BN-MRFs) are proposed as a technique for representing and applying apriori knowledge at different abstraction levels inside a distributed image processing framework. It is shown that this approach, thanks to the common probabilistic basis of the two techniques, is able to combine in a natural way causal inference properties at different abstraction levels as provided by Bayesian networks with optimisation criteria usually applied to find the best configuration for an MRF. Examples of two-level BN-MRFs are given, where each node uses a coupled Markov random field which has to solve a coupled restoration and segmentation problem. Experiments are concerned with expert-driven registered segmentation and tracking of regions from image sequences.

Ranking, estimation and hypothesis testing in unbalanced two-way additive models - a bayesian approach

Abstract: For the usual 2-factor additive model, there has been comparatively little work in the ranking and selection literature for the case of unequal sample sizes (unequal variances). The existing papers (e.g., Huang and Panchapakesan (1976), Dudewicz (1977), Gupta and Hsu (1980), Taneja and Dudewicz (1982), and Bechhofer and Dunnett (1987)) do not give explicit procedures unless assuming an equal number of observations and equal variances. (In the 2 x 2 case, classical ranking and selection procedures do exist even for more complicated models. See Taneja and Dudewicz (1984, 1987).) However the case of unequal sample sizes may arise in many natural settings, say in the problem of designing an experiment for comparing treatments in the presence of blocks of different fixed sizes, where one may assign an equal number of experimental units to each treatment within the same block. Unequal sample sizes can be handled in the classical analysis of variance (AOV) model (see Bishop and Dudewicz (1978, 1981) and Dudewicz and Bishop (1981)), which may partly explain the popularity of AOV. A Bayesian approach to the problem is taken here, leading to computation of the posterior probabilities that each treatment mean is the largest. In addition, a Bayesian version of AOV will be considered. Calculation of the quantities of interest involves, at worst, 5-dimensional numerical integration, for which an efficient Monte Carlo method of evaluation is given. An example is presented to illustrate the methodology. AMS 1970 subject classifications: 62F05, 62F07, 62F10, 62F15, 65C05

An evaluation of factors influencing Bayesian learning systems.

Abstract: This paper examines the influences of situational and model factors upon the accuracy of Bayesian learning systems. In particular, it is concerned with the impact of variations in training sample size, number of attributes, choice of Bayesian model, and criteria for excluding model attributes upon the overall accuracy of the simple and proper Bayes models.

A bayesian interpretation of the linearly-constrained cross-entropy minimization problem

Abstract: Both the linearly-constrained minimum cross-entropy (LCMXE) method and the Bayesian parameter estimation procedure have been widely used for solving various engineering problems. From the viewpoint of the information/decision theory, both approaches start with a prior distribution for a random variable, “absorb” new information, and finally produce a posterior distribution. In this paper, an equivalence relationship between these two approaches is established by identifying certain statistical experiments “embedded” in the LCMXE framework. Interestingly, the dual of the LCMXE problem actually “translates” the new information into its Bayesian counterpart. It is also shown that, while new information may come in stages, the identical final posterior can be obtained by applying the LCMXE method either stagewise or collectively. The equivalence further implies that the LCMXE method can help select a proper exponential family as the statistical model for the Bayesian experiments.

Learning Bayesian classification rules through genetic algorithms

Abstract: The paper surveys the features of an inductive learning environment named DELVAUX that learns prospector. style, Bayesian classification rules from sets of examples. A genetic algorithm approach is used for learning Bayesian rule-sets, in which a population consists of sets of rule-sets that generate offsprings through the exchange of rules, permitting fitter rule-sets to produce offsprings with a higher probability. The various genetic operators of our leazning environment, such crossover, mutation, inversion and selection operators are described. Finally, empirical results we obtained when using the DELVAUX rule learning environment for the classification of Iris flowers, for the classification of edible mushrooms, and for the classification of different kinds of glass are surveyed.

Compiling Bayesian networks into neural networks

Abstract: The criticism on the usage of Bayesian Networks in expert systems was centered around the claim that the use of probability requires a massive amount of data in the form of conditional probabilities. This paper shows that given information easily obtained from experts, the dependence model and some observations, the conditional probabilities can be estimated using backpropagation, such that during training the Bayesian characteristic of the network is preserved. Applying the Occam's razor principal results in defining a partial order among neural network structures. Experiments show that for the Multiplexer problem, the network compiled from the more succinct causal model generalized better than the one compiled from the less succinct model.