Showing papers on "Bayesian inference published in 1986"

Decision analysis and behavioral research

Abstract: Decision analysis is a technology designed to help individuals and organizations make wise inferences and decisions. It synthesises ideas from economics, statistics, psychology, operations research, and other disciplines. A great deal of behavioural research is relevant to decision analysis; behavioural scientists have both suggested easy and natural ways to describe and quantify problems and shown the kind of errors to which unaided intuitive judgements can lead. This long-awaited book offers the4first integrative presentation of the principles of decision analysis in a behavioural context. The authors break new ground on a variety of technical topics (sensitivity analysis, the value-utility distinction, multistage inference, attitudes toward risk), and attempt to make intuitive sense out of what have been treated in the literature as endemic biases and other errors of human judgement. Those interested in artificial intelligence will find it the easiest presentation of hierarchical Bayesian inference available.

Combining Economic Forecasts

Abstract: A method for combining forecasts may or may not account for dependence and differing precision among forecasts. In this article we test a variety of such methods in the context of combining forecasts of GNP from four major econometric models. The methods include one in which forecasting errors are jointly normally distributed and several variants of this model as well as some simpler procedures and a Bayesian approach with a prior distribution based on exchangeability of forecasters. The results indicate that a simple average, the normal model with an independence assumption, and the Bayesian model perform better than the other approaches that are studied here.

Why Isn't Everyone a Bayesian?

Abstract: Originally a talk delivered at a conference on Bayesian statistics, this article attempts to answer the following question: why is most scientific data analysis carried out in a non-Bayesian framework? The argument consists mainly of some practical examples of data analysis, in which the Bayesian approach is difficult but Fisherian/frequentist solutions are relatively easy. There is a brief discussion of objectivity in statistical analyses and of the difficulties of achieving objectivity within a Bayesian framework. The article ends with a list of practical advantages of Fisherian/frequentist methods, which so far seem to have outweighed the philosophical superiority of Bayesianism.

Exact inference in the inequality constrained normal linear regression model

Abstract: Inference in the inequality constrained normal linear regression model is approached as a problem in Bayesian inference, using a prior that is the product of a conventional uninformative distribution and an indicator function representing the inequality constraints. The posterior distribution is calculated using Monte Carlo numerical integration, which leads directly to the evaluation of expected values of functions of interest. This approach is compared with others that have been proposed. Three empirical examples illustrate the utility of the proposed methods using an inexpensive 32-bit microcomputer.

The Formation of Maintenance of Delusions: a Bayesian Analysis

Abstract: This paper argues that recent research on normal-belief formation is relevant to our understanding of the establishment and maintenance of delusions. Bayesian theory provides a normative model of the way in which evidence relevant to normal beliefs may be evaluated: this makes it possible to classify delusional beliefs in terms of deviations from optimal Bayesian inference. Some hypothetical forms of deviation appear to correspond closely to cognitive processes observed in some groups of deluded patients. Theories of the precise nature of the abnormal judgemental processes also have implications for psychological approaches to treatment of deluded patients. The role of hallucinations in the formation and/or maintenance of delusions and the extent to which the distortions of cognitive processes associated with delusions are content-specific or mood-specific are also considered.

Entropy and Uncertainty

Abstract: This essay is, primarily, a discussion of four results about the principle of maximizing entropy (MAXENT) and its connections with Bayesian theory. Result 1 provides a restricted equivalence between the two where the Bayesian model for MAXENT inference uses an a priori probability that is uniform, and where all MAXENT constraints are limited to 0–1 expectations for simple indicator-variables. The other three results report on an inability to extend the equivalence beyond these specialized constraints. Result 2 establishes a sensitivity of MAXENT inference to the choice of the algebra of possibilities even though all empirical constraints imposed on the MAXENT solution are satisfied in each measure space considered. The resulting MAXENT distribution is not invariant over the choice of measure space. Thus, old and familiar problems with the Laplacean principle of Insufficient Reason also plague MAXENT theory. Result 3 builds upon the findings of Friedman and Shimony (1971,1973) and demonstrates the absence of an exchangeable, Bayesian model for predictive MAXENT distributions when the MAXENT constraints are interpreted according to Jaynes’ (1978) prescription for his (1963) Brandeis Dice problem. Last, Result 4 generalizes the Friedman and Shimony objection to cross-entropy (Kullback-information) shifts subject to a constraint of a new odds-ratio for two disjoint events.

Bayesian Model Monitoring

Abstract: On presente une approche bayesienne basee sur des comparaisons des predictions a partir du modele standard avec celles d'un modele alternatif simple

On discrete weighted distributions and their use in model choice for observed data

Abstract: This paper provides a brief structural perspective of discrete weighted distributions in theory and practice.. It develops a unified view of previous work involving univariate and bivariate models with some new results pertaining to mixtures, form-invariance and Bayesian inference

Case-Control Studies and Bayesian Inference

Abstract: We outline the methods of Bayesian inference for applications to case-control studies. These methods appear as the natural way of making inferences, since much of the controversy that surrounds a specific case-control study is subjective. We derive conjugate prior distributions of exposure, posterior distributions of the ratio of the odds of being incident with a disease both with and without exposure to a potential causal agent, and convenient approximations. In particular, we show how one may carry out ‘case-control studies’ without necessarily having a control group. We illustrate these ideas with the data that first showed the relationship between in utero exposure to diethylstilbestrol and cancer of the vagina in young girls

Tests of Significance in Theory and Practice

Abstract: The best (most widely) received theory for tests of significance is that due largely to Fisher. Embellished with Neyman's mathematics, Fisher's theory is very well received. But Fisher's logic is not consistent with Bayes' theorem. And Bayes' theorem is beyond reproach. Thus, Fisher's logic is deficient. However, in practice, there is often some redress. Indeed, sometimes Fisher's level of significance P coincides mathematically with the posterior probability of the null hypothesis, i.e. P=p(hOIE), where E is the sample event (evidence). More generally, a good Fisherian tends intuitively (although certainly not inevitably) toward the inference he would make if he employed Bayes' theorem with explicit subjective priors. In effect, he is almost Bayesian. 1 In theory

Bayesian Statistics for Evaluation Research: An Introduction

Abstract: Introduction Overview of Classical Methods Probability and Its Interpretation Bayes' Theorem Principles of Bayesian Inference Normal Means and Variances Inference in Linear Regression Inference for Binomial Proportions Decision Analysis Summary and Perspective

Bayesian inference without point estimates

Abstract: It is conventional to apply Bayes' formula only to point estimates of the prior probabilities. This convention is unnecessarily restrictive. The analyst may prefer to estimate that the priors belong to some set of probability vectors. Set estimates allow the non-paradoxical expression of ignorance and support rigorous inference on such everyday assertions as "one event is more likely than another" or that an event "usually" occurs. Bayes' formula can revise set estimates, often at little computational cost beyond that needed for point priors. Set estimates can also inform statistical decisions, although disagreement exists about what decision methods are best.

The Bayesian Approach to Causality Assessment: An Introduction

Abstract: This paper outlines an approach to causality assessment that is based on the logic of uncertainty, Bayesian probability theory. The goal of causality assessment is taken to be the calculation of the posterior odds in favor of drug causation, given all available background and case information. There are two stages to the Bayesian approach: collecting the facts and evaluating the evidence. The evaluation proceeds by a series of probability assessments that decompose the overall causality assessment into a series of component evaluations, each of which focuses on one factor or source of information. The solutions to these component problems are then combined according to the rules of probability theory to give a solution to the overall causality assessment.

Probabilistic reasoning about ship images

Abstract: One of the most important aspects of current expert systems technology is the ability to make causal inferences about the impact of new evidence. When the domain knowledge and problem knowledge are uncertain and incomplete, Bayesian reasoning has proven to be an effective way of forming such inferences [3,4,8]. While several reasoning schemes have been developed. based on Bayes Rule, there has been very little work examining the comparative effectiveness of these schemes in a real application. This paper describes a knowledge based system for ship classification [1], originally developed using the PROSPECTOR updating method [2], that has been reimplemented to use the inference procedure developed by Pearl and Kim [4,5|. We discuss our reasons for making this change, the implementation of the new inference engine, and the comparative performance of the two versions of the system.

A note on the construction of highest posterior density intervals

Abstract: On decrit des methodes applicables aux fonctions de densite de probabilite unimodales univariables

A causal Bayesian model for the diagnosis of appendicitis

Abstract: The causal Bayesian approach is based on the assumption that effects (e.g., symptoms) that are not conditionally independent with respect to some causal agent (e.g., a disease) are conditionally independent with respect to some intermediate state caused by the agent, (e.g., a pathological condition). This paper describes the development of a causal Bayesian model for the diagnosis of appendicitis. The paper begins with a description of the standard Bayesian approach to reasoning about uncertainty and the major critiques it faces. The paper then lays the theoretical groundwork for the causal extension of the Bayesian approach, and details specific improvements we have developed. The paper then goes on to describe our knowledge engineering and implementation and the results of a test of the system. The paper concludes with a discussion of how the causal Bayesian approach deals with the criticisms of the standard Bayesian model and why it is superior to alternative approaches to reasoning about uncertainty popular in the AI community.

Bayesian inference for radar imagery based surveillance

Abstract: Publisher Summary This chapter discusses Bayesian inference for radar imagery based surveillance. Inference is performed over a space of hierarchically linked hypotheses. The hypotheses represent statements of the form there is a military force of type F in deployment D at world location L at time T . The hierarchy in the hypothesis space corresponds to the hierarchy inherent in military doctrine of force structuring. Thus, array-level hypotheses of military units, such as companies, artillery batteries, and missile sites, are linked to their component unit hypotheses of vehicles batteries and missile launchers. Similarly, companies are grouped to form battalion hypotheses and battalions to form regiments. The structure of inference follows a pattern based on the models that are matched to generate hypotheses of the presence of military forces on the battlefield. The chapter discusses a general problem of symbolic hierarchical Bayesian inference for military force inference. It presents a method for approximate hierarchical accrual that can be used to selectively avoid unnecessary conflict resolution depending on the system's focus of attention in processing tasks.

Is the Reference in Hartley (1749) to Bayesian Inference

Abstract: (1986). Is the Reference in Hartley (1749) to Bayesian Inference? The American Statistician: Vol. 40, No. 2, pp. 109-110.

Structural inference for parameters of a power function distribution

Abstract: We consider the problem of statistical inference on the parameters of the three parameter power function distribution based on a full unordered sample of observations or a type II censored ordered sample of observations. The inference philosophy used is the theory of structural inference. We state inference procedures which yield inferential statements about the three unknown parameters. A numerical example is given to illustrate these procedures. It is seen that within the context of this example the inference procedures of this paper do not encounter certain difficulties associated with classical maximum likelihood based procedures. Indeed it has been our numerical experience that this behavior is typical within the context of that subclass of the three parameter power function distribution to which this example belongs.

Asset Prices in an Economy with Latent Technological Shocks - Econometric Implications of a Discrete Time General Equilibrium Model

Abstract: The Paper Has Two Major Parts. the First Part Focuses on the Theoretical Properties of a General Equilibrium Asset Price Model Describing an Economy with Actual Output Stochastically Generated by a Markovian Latent Process of Technolgical Shocks. with a Concealed State Space Economy, Agents Make Use of the Entire Observed History to Make Inference About the Latent Technological Shock. Instead of Focussing on the Entire History of Output, Past Events Are Summarized by a Conditional Probability Distribution Defined on the Space of All Possible States of Technology. Bayesian Updating Reestablishes Markovian Recursive Dynamics, and Allows One to Exploit the Analytical Tools Introduced by Lucas (1978) in Solving for Equilibrium Asset Prices. the Second Part of the Paper Deals with the Econometric Implications of the Model. the Consumption and Portfolio Decisions Can Be Expressed As Time Invariant Functions Defined on the Transformed State Space, I.E. the Space of Conditional Probability Distributions on the State of Nature At Any Point in Time. This Does Not Necessarily Imply That the Co-Movements of Consumption, Portfolio Decisions, Output and Asset Prices Are Stationary. We Formulate a Gaussian Model, Very Similar to Hansen and Singleton (1983) and Estimate It Via a State Space Representation Which Incorporates the Rational Expectations Equilibrium Cross-Equation Restriction.

Bayes and empirical bayes estimation of the probability that z > x + y

Abstract: Let X, Y and Z be independent random variables with common unknown distribution F. Using the Dirichlet process prior for F and squared erro loss function, the Bayes and empirical Bayes estimators of the parameters λ(F). the probability that Z > X + Y, are derived. The limiting Bayes estimator of λ(F) under some conditions on the parameter of the process is shown to be asymptotically normal. The aysmptotic optimality of the empirical Bayes estimator of λ(F) is established. When X, Y and Z have support on the positive real line, these results are derived for randomly right censored data. This problem relates to testing whether than used discussed by Hollander and Proshcan (1972) and Chen, Hollander and Langberg (1983).

Estimation of multiple gamma scale-parameters: bayes estimation subject to uniform domination

Abstract: Simultaneous estimation of p gamma scale-parameters is considered under squared-error loss. The problem of minimizing, subject to uniform risk domination, the Bayes risk (or more generally the posterior expected loss) against certain conjugate or mixtures of conjugate priors is considered. Rather surprisingly, it is shown that the minimization can be done conditionally, thus avoiding variational arguments. Relative savings loss (and a posterior version thereof) are found, and it is found that in the most favorable situations, Bayesian robustness can be achieved without sacrificing substantial subjective Bayesian gains.

Sensitivity of a Bayesian inference to prior assumptions

Abstract: The sensitivity of-a Bayesian inference to prior assumptions is examined by Monte Carlo simulation for the beta-binomial conjugate family of distributions Results for the effect on a Bayesian probability interval of the binomial parameter indicate that the Bayesian inference is for the most part quite sensitive to misspecification of the prior distribution The magnitude of the sensitivity depends primarily on the difference of assigned means and variances from the respective means and variances of the actually-sampled prior distributions The effect of a disparity in form between the assigned prior and actually-sampled distributions was less important for the cases tested

Optimal Likelihood Generators for Edge Detection under Gaussian Additive Noise.

Abstract: : A technique is presented for determining the probability of an edge at a point in an image that is convolve with a linear blurring function and also with uncorrelated Gaussian additive noise The ideal image is modeled by a set of templates for local neighborhoods Every neighborhood in the ideal image is assumed to fit one of the templates with height probability A computationally feasible scheme to compute the probability of edges is given The output of several of the likelihood generators based on this model can be combined to form a more robust likelihood generator Keywords: Edge detection; Template; Likelihood; Bayesian reasoning

An Efficient Algorithm for Time Series Decomposition

Abstract: The aim of this work is to present an efficient algorithm for time series decomposition. Following Akaike (1980), who uses a linear bayesian model, it is possible to take advantage of the model structure to reduce the computational effort.

On Bayes and Empirical Bayes Procedures for Selection Problems

Abstract: : This paper describes selection and ranking procedures using Bayesian or Empirical Bayes approaches. Section 2 of this paper deals with the problem of selecting the best population or selecting a subset containing the best population through Bayesian approach. An essentially complete class is obtained for a class of reasonable loss functions. A control condition, called P* - condition, is used to filter out poor procedures. Section 3 set up a general formation of empirical Bayes framework for selection problems. Several empirical Bayes frameworks are discussed based on the underlying statistical models. Two selection problems dealing with binomial and uniform distributions are discussed in detail.