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Showing papers on "Bayesian probability published in 1968"


Journal ArticleDOI
TL;DR: "`But the authors can't agree whether A or B is correct,' he concluded, `and so they're collecting expert opinions, weighting them appropriately, and programming WESCAC to arbitrate the whole question.'"
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...

375 citations


Journal ArticleDOI
TL;DR: The problem of outlying observations is considered from a Bayesian viewpoint and the linear model is considered, which assumes 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.
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.

250 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that there are no countably additive exchangeable distributions on the space of observations which give ties probability 0 and for which a next observation is conditionally equally likely to fall in any of the open intervals between successive order statistics of a given sample.
Abstract: A Bayesian approach to inference about the percentiles and other characteristics of a finite population is proposed. The approach does not depend upon, though it need not exclude, the use of parametric models.Some related questions concerning the existence of exchangeable distributions are considered. It is shown that there are no countably additive exchangeable distributions on the space of observations which give ties probability 0 and for which a next observation is conditionally equally likely to fall in any of the open intervals between successive order statistics of a given sample.

248 citations



Journal ArticleDOI
TL;DR: In this paper, the problem of estimating the mean in the one-way random effect model yjk = θj+ejk is considered from a Bayesian viewpoint.
Abstract: The problem of estimating the means in the one-way random effect model yjk = θj+ejk is considered from a Bayesian viewpoint. Posterior distributions of the θj are obtained under the assumption that the θj are independently drawn from a Normal population N(θ, σ22) and that the ejk are independent random errors having a N(0, σ21) distribution. It is shown that the posterior distributions of the θj are clustered more closely together than are the corresponding distributions for a fixed effect model. A numerical example is given.

54 citations



Journal ArticleDOI
TL;DR: Some results are obtained concerning the optimum allocation of sampling effort among k strata at the second phase of a two phase sampling procedure, using information obtained from the first phase.
Abstract: : In this paper we obtain some results concerning the optimum allocation of sampling effort among k strata at the second phase of a two phase sampling procedure, using information obtained from the first phase. Two different approaches are employed; a Bayesian posterior analysis and a Bayesian preposterior analysis. Two different allocation methods are derived and illustrated with some numerical examples, for cases where some or all of the nuisance parameters are unknown. The problem when all nuisance parameters are known has been discussed by Ericson (1965). (Author)

31 citations



Journal ArticleDOI
TL;DR: In this paper, the adequacy of subjectively expected utility (SEU) models for Bayesian decision making was evaluated and the predictions were independent of individual measures of subjective probability or utility.

21 citations


Journal ArticleDOI
TL;DR: In this paper, the optimum allocation of sampling effort among k strata at the second phase of a two phase sampling procedure, using information obtained from the first phase, was investigated.
Abstract: : The authors had previously obtained some results concerning the optimum allocation of sampling effort among k strata at the second phase of a two phase sampling procedure, using information obtained from the first phase. One variable (or characteristic) was involved. Two different approaches were employed: a Bayesian posterior analysis and a Bayesian preposterior analysis. Two different allocation methods were derived and illustrated with some numerical examples, for cases where some or all of the nuisance parameters were unknown. The problem when all nuisance parameters are known had been discussed by Ericson. In this work the authors extend their results to the case of k characteristics. (Author)

18 citations


Journal ArticleDOI
TL;DR: In this article, a Bayesian solution for discriminating between two zero-mean normal populations with uniform covariance structures is derived and compared with the classical method of Bartlett & Please (1963).
Abstract: A Bayesian solution for discriminating between two zero-mean normal populations with uniform covariance structures is derived and compared with the classical method of Bartlett & Please (1963). In a particular application to some genetical data, the Bayesian and classical discriminants, though functionally different, yield similar results in the assign-, ment of new observations. For classificatory purposes, they are incompatible only in a region of low density for both populations.

Journal ArticleDOI
TL;DR: In this paper, subjective posterior odds favoring a reference hypothesis were found to be a simple power function of corresponding Bayesian posterior odds, and the value of the exponent was related to the diagnostic impact of individual evidence items.

Journal ArticleDOI
E. Gerald Hurst1
TL;DR: Two Bayesian autoregressive time series models for partially observable dynamic processes are presented and the facility for simultaneously inferring an unknown and unchanging parameter of the time series is added.
Abstract: Two Bayesian autoregressive time series models for partially observable dynamic processes are presented. In the first model, a general inference procedure is developed for the situation in which k previous values of the time series plus a change error determine the next value. This general model is specialized to an example in which the observational and change errors follow a normal probability law; the results for k = 1 are given and discussed. The second general model adds the facility for simultaneously inferring an unknown and unchanging parameter of the time series. This model is specialized to the same normal example presented earlier, with the precision of the change error as the unknown process parameter.


Journal ArticleDOI
TL;DR: To deal with the distortion in the analysis of data with response errors, a model for correcting response errors of subjects was presented and was applied to an experiment on the impression of a photograph of a young woman to illustrate the distortion.
Abstract: When the observed values fluctuated (we say that they have ‘Response Errors’) with considerably large variance, so that we can not ignore the variance of errors in observation in comparison with the variance of observation within groups, we face the possibility of committing errors in the analysis of data.To deal with the distortion in the analysis of data with response errors, a model for correcting response errors of subjects was presented. In blief our model is a probability model of response errors, considering that subjects who reacted + in a given test may react-in the re-test, when the reliability of the test is low.The Bayesian probability was employed to estimate the true distribution of each probability of response from the results of test and re-test.When the response is+, ±, or-, the model for correcting the error is as follows:We estimate the probability of p, q, r, s, t, u, in Table 4 from the results of test and re-test. Table 2 shows the true values, whereas Table 3, observed results. Unknown quantities are p, r, t, n(+), n(±), n (-).Then, we compute the Bayesian probability of these unknown quantities, and construct Table 5, in which the occurrence of response is considered as probabilistic, not as the {1, 0} pattern.This model was applied to an experiment on the impression of a photograph of a young woman to illustrate the distortion in the pattern analysis of data.Further, the distortion in the coventional scale analysis and its reliability were discussed.

Journal ArticleDOI
01 Dec 1968
TL;DR: The familiar expression for the probability of finding a stationary target is rewritten in aBayesian form, in the case where the search is carried out by a man walking along a given path.
Abstract: The familiar expression for the probability of finding a stationary target is rewritten in aBayesian form, in the case where the search is carried out by a man walking along a given path.


01 Jun 1968
TL;DR: 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.
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)

Journal ArticleDOI
TL;DR: In this paper, two groups of Ss gave successive probability estimates of coin bias in the same 12 sequences and the experimental group extracted more of the available certainty as measured by Bayesian predictions.
Abstract: Two groups of Ss gave successive probability estimates of coin bias in the same 12 sequences. The control group operated on sequences consecutively while the experimental group worked with all 12 sequences concurrently. The experimental group extracted more of the available certainty as measured by Bayesian predictions.