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Showing papers on "Bayesian inference published in 1979"




01 Jan 1979
TL;DR: In this article, a procedure is proposed to derive reference posterior distributions which approximately describe the inferential content of the data without incorporating any other information, and the results obtained unify and generalize some previous work and seem to overcome criticisms to which this has been subject.
Abstract: SUMMARY A procedure is proposed to derive reference posterior distributions which approximately describe the inferential content of the data without incorporating any other information. More explicitly, operational priors, derived from informationtheoretical considerations, are used to obtain reference posteriors which may be expected to approximate the posteriors which would have been obtained with the use of proper priors describing vague initial states of knowledge. The results obtained unify and generalize some previous work and seem to overcome criticisms to which this has been subject.

177 citations


Book
01 Jan 1979

127 citations


Journal ArticleDOI
TL;DR: It is argued that neither policy is acceptable to a Bayesian since each is inconsistent with conditionalization and each appears to be symptoms of the program's inability to formulate rules for picking privileged probability distributions that serve to represent ignorance or near ignorance.
Abstract: The objective Bayesian program has as its fundamental tenet (in addition to the three Bayesian postulates) the requirement that, from a given knowledge base a particular probability function is uniquely appropriate. This amounts to fixing initial probabilities, based on relatively little information, because Bayes' theorem (conditionalization) then determines the posterior probabilities when the belief state is altered by enlarging the knowledge base. Moreover, in order to reconstruct orthodox statistical procedures within a Bayesian framework, only privileged ‘ignorance’ probability functions will work.

96 citations


Journal ArticleDOI
TL;DR: In this article, a coherent Bayesian argument for stochastic multiple regression analysis is developed, where dependent and independent variables are jointly random, without experimental control, and the resulting Bayes estimate for the population mean is closely related to Stein estimates.
Abstract: SUMMARY This paper discusses Bayesian inference procedures for a normal dispersion matrix. Structural information for the prior mean of the dispersion matrix is incorporated into the analysis through a Normal-Wishart prior distribution. Many of the resulting Bayes estimates are invariant, consistent and asymptotically efficient. Using this procedure, a coherent Bayesian argument for stochastic multiple regression analysis is developed, where dependent and independent variables are jointly random, without experimental control. It is shown that ordinary least squares, a general form of ridge regression, and factor analysis regression methods can be represented as special cases within this general framework. The preliminary report of a simulation study indicates that the Bayesian regression techniques demonstrate substantial improvements over least squares, even using frequentist criteria. Finally, the related problem of joint estimation of the normal population mean and dispersion matrix is briefly discussed in Section 5. The resulting Bayes estimate for the population mean is shown to be closely related to Stein estimates.

70 citations


Journal ArticleDOI
TL;DR: In this article, a consistent theory of system identification based on a Bayesian basis is proposed. But the analysis is restricted to one-shot and real-time identification, estimation and prediction in closed control loop, redundant and ~identifiable parameters, time-varying parameters and adaptivity.

17 citations


Journal ArticleDOI
TL;DR: Bayes' theorem is demonstrated as a means for incorporating in the prediction of the availability performance of new generations of turbine blades the limited operational data on the new blades along with the experience of the earlier generation and the knowledge of the design changes.
Abstract: Bayes' theorem is used to quantify the impact of new evidence in three energy-related decision problems. The first problem concerns the risk of radioactivity release during the railroad transport of spent nuclear fuel. This history of shipments thus far is shown to make it highly unlikely that the frequency of release is on the order of 0.001 or greater per shipment. The second and third applications involve predicting the availability performance of new generations of turbine blades. Bayes' theorem is demonstrated as a means for incorporating in the prediction the limited operational data on the new blades along with the experience of the earlier generation and the knowledge of the design changes.

14 citations


01 Aug 1979
TL;DR: In this article, the smoothness is assumed for the behavior of the coefficients viewed in the frequency domain, which leads to a smoothness prior with a particularly simple form Numerical result shows that the estimator based on this smoothness pre-condition produces good estimates of the lag coefficients where Shiller's prior produces highly biased estimates.
Abstract: : Shiller's distributed lag estimator based on a smoothness prior demonstrates the potential of the Bayesian approach to statistical model building Nevertheless, when the number of significant lag coefficients is small the assumption of smoothness of the pattern of the lag coefficients may not be appropriate In this paper, to cover such a situation, the smoothness is assumed for the behavior of the coefficients viewed in the frequency domain This definition leads to a smoothness prior with a particularly simple form Numerical result shows that the estimator based on this smoothness prior produces good estimates of the lag coefficients where Shiller's prior produces highly biased estimates It is also observed that the new estimator produces reasonable results even when the Shiller's prior is more appropriate The danger of introducing a bias by assuming a Bayesian model is stressed in the discussion (Author)

7 citations


01 Sep 1979
TL;DR: A Bayesian model has been proposed which describes the generation of an observation by a process whereby with prior probability 1-alpha the usually assumed statistical structure is correct but with small probability alpha it is incorrect (for example, the observation has a very large variance).
Abstract: : A Bayesian model has been proposed which describes the generation of an observation by a process whereby with prior probability 1-alpha the usually assumed statistical structure is correct but with small probability alpha it is incorrect (for example, the observation has a very large variance). For a simple location estimate the nature of the down weighting of outlying observations produced by this model is studied and is compared with that of the presently popular M-estimators.

4 citations



Journal ArticleDOI
TL;DR: The authors showed that such composite forecasts are normally suboptimal in the sense that there exists an alternative composite forecast with a strictly lower expected error than the original composite forecast, where the posterior probabilities are derived from Bayesian model discrimination methods.

01 Oct 1979
TL;DR: In this paper, the problem is recast into a hierarchical form in which there are strictly-ordered hyperparameters which index the admissible family of ordered distributions for the parameters; the modelling problem is then to describe an appropriate law of motion over the hyperparameter.
Abstract: : In models of reliability growth in stages, it is usual to assume that system parameters improve monotonically from stage to stage, following some postulated law of growth. This paper explores a Bayesian model where such improvement only occurs on the average, e.g., a case when the parameters are assumed to be stochastically ordered. It is shown that the problem can be recast into a hierarchical form in which there are strictly-ordered hyperparameters which index the admissible family of ordered distributions for the parameters; the modelling problem is then to describe an appropriate law of motion over the hyperparameters. (Author)

ReportDOI
01 Mar 1979
TL;DR: This paper develops consistent decision rules for choosing the neighborhood in a one-dimensional autoregressive (AR) model and the theory is extended to the case of stationary two-dimensional random fields.
Abstract: : This paper considers the application of system identification techniques using spectral representation for fitting models to textures and images and consists of two parts. In part I, we develop consistent decision rules for choosing the neighborhood in a one-dimensional autoregressive (AR) model. In part II, the theory is extended to the case of stationary two-dimensional random fields. (Author)

ReportDOI
01 Jun 1979
TL;DR: In this paper, it is argued that both kinds of inference are needed in the scientific iteration whereby knowledge is acquired, which employs a directed alternation between induction and deduction which uses model criticism on the one hand and parameter estimation on the other.
Abstract: : Sampling theory inference (e.g. inference based on sampling distributions of statistics and in particular on significance tests) and Bayesian inference are usually thought of as rivals and much effort has been spent in propounding their relative merits. In this paper it is argued that both kinds of inference are needed in the scientific iteration whereby knowledge is acquired. This iteration employs a directed alternation between induction and deduction which uses model criticism on the one hand and parameter estimation on the other. An analysis of Bayes' formula reveals model criticism as a sampling theory concept and parameter estimation as a Bayesian concept. The implications of these ideas for robust estimation are discussed.


Journal ArticleDOI
TL;DR: In this paper, a Bayesian theory for testing model adequacy is presented, which provides exact results whether the model is linear or nonlinear in the parameters, and provides a useful approximation for nonlinear models.
Abstract: We present a Bayesian theory for testing model adequacy which provides exact results whether the model is linear or nonlinear in the parameters. We consider two cases:(a) replicated data exists, and (b) no replicated data exists but an external estimate of the variance is available, Furthermore, we derive a useful approximation for testing model adequacy when the model is nonlinear in the parameters.


Journal ArticleDOI
TL;DR: In this paper, a Bayesian analysis of a model for two-group experimentation is given, where responses in one group are systematically related to responses in the other group through a general linear function using both multiplicative and additive parameters.
Abstract: A Bayesian analysis of a model for two-group experimentation is given. This model assumes that responses in one group are systematically related to responses in the other group through a general linear function using both multiplicative and additive parameters.