Showing papers on "Bayesian inference published in 1968"

A generalization of bayesian inference

Abstract: Procedures of statistical inference are described which generalize Bayesian inference in specific ways Probability is used in such a way that in general only bounds may be placed on the probabilities of given events, and probability systems of this kind are suggested both for sample information and for prior information These systems are then combined using a specified rule Illustrations are given for inferences about trinomial probabilities, and for inferences about a monotone sequence of binomial pi Finally, some comments are made on the general class of models which produce upper and lower probabilities, and on the specific models which underlie the suggested inference procedures

The Consensus of Subjective Probability Distributions

Abstract: “‘But we can't agree whether A or B is correct,' he concluded, ‘and so we're collecting expert opinions, weighting them appropriately, and programming WESCAC to arbitrate the whole question.’” (John Barth, Giles Goat-Boy, p. 664.) In the Bayesian framework, quantified judgments about uncertainty are an indispensable input to methods of statistical inference and decision. If a decision maker has little knowledge with regard to the parameters of interest, he may decide to consult a number of experts and obtain their quantified judgments in the form of subjective probability distributions. If this is the case, the decision maker must somehow combine the distributions assessed by the experts and form a single distribution to be used as an input to a formal Bayesian analysis. Several methods for combining the distributions are suggested, some involving mathematical formulae and some involving feedback and/or group discussion. These methods are compared under certain assumptions regarding the form of the distri...

A bayesian approach to some outlier problems.

Abstract: The problem of outlying observations is considered from a Bayesian viewpoint. We suppose that each of the observations in an experiment may come from either a 'good' run or a 'bad' run. By specifying the models corresponding to good and bad runs and the prior probabilities of which runs being bad, we then employ standard Bayesian inference procedures to derive the appropriate analysis. In particular, we consider the linear model and assume that a good observation is normally distributed about its mean with variance o.2, and a bad one is normal with the same mean but a larger variance k2o-2. An example is given.

Asymptotically Optimal Bayes and Minimax Procedures in Sequential Estimation

Abstract: In [4] we introduced a general method for obtaining asymptotically pointwise optimal procedures in sequential analysis when the cost of observation is constant The validity of this method in both estimation and testing was established in [4] for Koopman-Darmois families, and in [5] for the general case Section 2 of this paper generalizes Theorem 21 of [4] to cover essentially the case of estimation with variable cost of observation In Section 3 we show that in estimation problems, under a very weak condition, for constant cost of observation, the asymptotically pointwise optimal rules we propose are optimal in the sense of Kiefer and Sacks [9] The condition given is further investigated in the context of Bayesian sequential estimation in Section 4 and is shown to be satisfied if reasonable estimates based on the method of moments exist In Section 5 we consider the robustness of our rules under a change of prior The main result of this section is given by Theorem 51 Finally Theorem 52 deals with a generalization of Wald's [12] theory of asymptotically minimax rules and an application of that theory to the Bayesian model

A Generalization of Bayesian Inference

Abstract: Procedures of statistical inference are described which generalize Bayesian inference in specific ways. Probability is used in such a way that in general only bounds may be placed on the probabilities of given events, and probability systems of this kind are suggested both for sample information and for prior information. These systems are then combined using a specified rule. Illustrations are given for inferences about trinomial probabilities, and for inferences about a monotone sequence of binomial pi. Finally, some comments are made on the general class of models which produce upper and lower probabilities, and on the specific models which underlie the suggested inference procedures.

Investigation of a bayesian approach applied to a specific intelligence problem

Abstract: : Although it appears theoretically possible that many problems of intelligence could be profitably attacked by a Bayesian approach, several difficulties must be overcome before such an approach can be used as an operational tool. Because test applications of a Bayesian approach to real problems of intelligence offer insight into the areas of difficulty, a specific previously 'solved' intelligence problem was explored with the aid of a cooperating intelligence analyst who used a Bayesian approach. This report discusses the salient aspects of the intelligence problem area, the specific difficulties encountered in the implementation of a Bayesian approach, and the techniques used to eliminate or diminish these difficulties. In addition, the solutions obtained with and without the aid of a Bayesian model are compared and causes of discrepancies are postulated. (Author)