Showing papers on "Bayesian probability published in 1985"
TL;DR: In this article, a formal model of Harsanyi's infinite hierarchies of beliefs is given, and it is shown that the model closes with some Bayesian game with incomplete information, and any such game can be approximated by one with a finite number of states of world.
Abstract: A formal model is given of Harsanyi's infinite hierarchies of beliefs. It is shown that the model closes with some Bayesian game with incomplete information, and that any such game can be approximated by one with a finite number of states of world.
750 citations
TL;DR: In this article, a Bayesian procedure is developed for the estimation of parameters in the two-parameter logistic item response model, and joint modal estimates of the parameters are obtained and procedures for the specification of prior information are described.
Abstract: A Bayesian procedure is developed for the estimation of parameters in the two-parameter logistic item response model. Joint modal estimates of the parameters are obtained and procedures for the specification of prior information are described. Through simulation studies it is shown that Bayesian estimates of the parameters are superior to maximum likelihood estimates in the sense that they are (a) more meaningful since they do not drift out of range, and (b) more accurate in that they result in smaller mean squared differences between estimates and true values.
175 citations
TL;DR: A numerical integration strategy based on Gaussian quadrature, and an associated strategy for the reconstruction and display of distributions based on spline techniques are described.
Abstract: Routine implementation of the Bayesian paradigm requires an efficient approach to the calculation and display of posterior or predictive distributions for given likelihood and prior specifi- cations. In this paper we shall review some of the analytic and numerical approaches currently available, describing in detail a numerical integration strategy based on Gaussian quadrature, and an associated strategy for the reconstruction and display of distributions based on spline techniques.
110 citations
TL;DR: This article developed a new test that reconciles these findings with the Bayesian learning approach frequently used in economic analysis, showing that individuals overassess low frequency events and underassess high frequency events.
104 citations
TL;DR: The classical hypothesis testing in clinical trials involving two treatments is criticized and a Bayesian approach in which sampling stops when the probability that one treatment is the better exceeds a specified value is recommended.
Abstract: This paper concerns interim analysis in clinical trials involving two treatments from the points of view of both classical and Bayesian inference. I criticize classical hypothesis testing in this setting and describe and recommend a Bayesian approach in which sampling stops when the probability that one treatment is the better exceeds a specified value. I consider application to normal sampling analysed in stages and evaluate the gain in average sample number as a function of the number of interim analyses.
98 citations
TL;DR: A Bayesian cross-validated likelihood BCVL method for comparing quantitative models, which can be used when the models are either nested or nonnested, and is especially useful for nonn nested models.
Abstract: There are many situations in marketing in which several alternative quantitative models may be built to model a particular marketing phenomenon or system Few methods exist for comparing the fit of such models if the models are not nested, especially if their performance on each of several criteria is important
This paper proposes a Bayesian cross-validated likelihood BCVL method for comparing quantitative models It can be used when the models are either nested or nonnested, and is especially useful for nonnested models A simulation based upon a typical marketing modeling situation shows the incremental benefit of using the BCVL method rather than existing techniques, and explores the circumstances under which BCVL works best The applicability of the BCVL method is demonstrated using several typical marketing modeling situations
83 citations
TL;DR: Experimental results are presented demonstrating that humans can make effective use of prior knowledge for detecting and identifying visual signals in static noise using cross correlation (or matched filtering) of expected signal profiles with those present in the display.
Abstract: Experimental results are presented demonstrating that humans can make effective use of prior knowledge for detecting and identifying visual signals in static noise. The signals were selected from an orthogonal Hadamard set. There was a marked drop in detection performance when observers did not know which signal was present. The drop was in excellent quantitative agreement with that predicted by the theory of signal detectability. The statistical efficiency of the human observers was 33% in both cases (detection with and without prior knowledge). When interpreted in terms of channel uncertainty, the detection results demonstrated an upper limit of 10 orthogonal, uncertain channels. The statistical efficiency for the Hadamard signal-identification task was 40%. All the results are consistent with the standard theory of signal detectability based on a Bayesian maximum a posteriori probability decision strategy using cross correlation (or matched filtering) of expected signal profiles with those present in the display.
78 citations
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66 citations
TL;DR: The authors argue that both averaging and conservatism in the Bayesian task occur because subjects produce their judgments by using an adjustment strategy that is qualitatively equivalent to averaging, and two experiments are presented that show qualitative errors in the direction of revisions in Bayesian inference tasks that are well accounted for by the simple adjustment strategy.
Abstract: Two empirically well-supported research findings in the judgment literature are (1) that human judgments often appear to follow an averaging rule, and (2) that judgments in Bayesian inference tasks are usually conservative relative to optimal judgments. This paper argues that both averaging and conservatism in the Bayesian task occur because subjects produce their judgments by using an adjustment strategy that is qualitatively equivalent to averaging. Two experiments are presented that show qualitative errors in the direction of revisions in the Bayesian task that are well accounted for by the simple adjustment strategy. Also noted is the tendency for subjects in one experiment to evaluate sample evidence according to representativeness rather than according to relative likelihood. The final discussion describes task variables that predispose subjects toward averaging processes.
63 citations
TL;DR: A new approach to the applied econometric problems of adjusting and forecasting univariate time series with component models with particular emphasis placed on assessing sensitivity of conclusions to model assumptions is described.
TL;DR: In this article, the authors proposed a framework and the resultant methods for the problem of detecting and characterizing influential subsets of observations when the goal is to estimate parameters using a Bayesian formulation and Kullback-Leibler divergences.
10 Jul 1985
TL;DR: This paper is concerned with two theories of probability judgment: the Bayesian theory and the theory of belief functions and illustrates these theories with some simple examples and discusses some of the issues that arise when the authors try to implement them in expert systems.
Abstract: This paper is concerned with two theories of probability judgment: the Bayesian theory and the theory of belief functions. It illustrates these theories with some simple examples and discusses some of the issues that arise when we try to implement them in expert systems. The Bayesian theory is well known; its main ideas go back to the work of Thomas Bayes (1702–1761). The theory of belief functions, often called the Dempster-Shafer theory in the artificial intelligence community, is less well known, but it has even older antecedents; belief-function arguments appear in the work of George Hooper (1640–1723) and James Bernoulli (1654–1705). For elementary expositions of the theory of belief functions, see Shafer (1976, 1985).
TL;DR: In this paper, some difficulties with orthodox theory, implementation of the likelihood principle, and Bayesian tests of hypotheses are discussed, and some considerations relating to the post-data selection of models are discussed.
Abstract: Some considerations relating to the post–data selection of models are discussed. These include some difficulties with orthodox theory, implementation of the likelihood principle, and Bayesian tests of hypotheses.
TL;DR: The Methodological Foundation of Mach's Anti-Atomism and Their Historical Roots are described, in Motion and Time Space and Matter, ed.
Abstract: BLACKMORE, J. T. [1972]: Ernst Mach—His Life, Work 8c Influence. University of California Press. CLARK, P. [1976]: 'Atomism versus Thermodynamics', in Method and Appraisal in the Physical Science, ed. C. Howson, pp. 41-105. Cambridge University Press. CLARK, P. [1982]: 'Matter, Motion & Irreversibility' (Review of S. G. Brush The Kind of Motion We Call Heat) British Journal for the Philosophy of Science, 33, pp. 165-86. FEYERABEND, P. [1980]: 'Zahar on Mach, Einstein and Modern Science', British Journal for the Philosophy of Science, 31, pp. 273—82. GARDNER, M. [1979]: 'Realism and Instrumentalism in 19th Century Atomism', Philosophy of Science, 46, pp. 1—34. LAUDAN, L. [1976]: 'The Methodological Foundation of Mach's Anti-Atomism and Their Historical Roots', in Motion and Time Space and Matter, ed. P. K. Machamer and R. G. Tumbull, pp. 390-417. Ohio State Universtiy Press. MACH, E. [1896]: Die Prindpien der Warmelehre—historisch-kritisch entxcickclt. 4. Auflage 1923. Verlag von Johann Ambrosius Barth. MACH, E. [1910]: 'Die Leitgedanken meiner naturwissenschaftlichen Erkenntnislehre und ihre Aufnahme durch die Zwitgenossen' Physikalische Zeitschrift, n , pp. 599-606. MACH, E. [1919]: Die Leitgedanken meiner naturwissenschaftlichen Erkenntnislehre und ihre Aufnahme durch die Zeitgenossen. Simtliche Elemente und naturzcissenschaftliche Begriffe. Verlag von Johann Ambrosius Barth. MEYER, S. [1950]: 'Die VorgeschichtederGrundungunddasersteJahrzehntdes Institutes fur Radiumforschung' Sitxungsberichte der Osterreichischen Akademie der Wissenschaft, 159, pp. 5-00. NYHOF, J. [1981]: Instrumentalism and Beyond, Doctoral Dissertation, University of Otago, Dunedin, New Zealand. OSTWALD, W. [1901]: Vorlesungen uber Naturphilosophie. 2. Auflage, 1902, p. 4. Verlag von Johann Ambrosius Barth. POPPER, K. R. [1974]: 'Autobiography of Karl Popper', in The Philosophy of Karl Popper, ed. P. A. Schilpp, pp. 156-67. Later published as Unended Quest [1976]. Fifth Impression [1980]. Fontana/Collins. TRAVERS, M. [1951]: Sir William Ramsay, pp. 251—2. London. TREVOR, J. E. [1897]: Journal of Physical Chemistry, 1, p. 431.
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TL;DR: In this paper, the authors consider the problem of economic forecasting, the justification for the Bayesian approach, its implementation, and the performance of one small BVAR model over the past five years.
Abstract: The results obtained in five years of forecasting with Bayesian vector autoregressions (BVAR's) demonstrate that this inexpensive, reproducible statistical technique is as accurate, on average, as those used by the best known commercial forecasting services. This article considers the problem of economic forecasting, the justification for the Bayesian approach, its implementation, and the performance of one small BVAR model over the past five years.
TL;DR: In this paper, a Bayesian method for estimation of finite population parameters in general population surveys where acceptable regression-type models are typically unavailable is described, and the posterior moments and probabilities are evaluated using Monte Carlo integration with importance sampling.
Abstract: This note describes a Bayesian method for estimation of finite population parameters in general population surveys where acceptable regression-type models are typically unavailable. A categorical data model is adopted as in Ericson (1969, Section 4). However, specifications of smoothness are incorporated into the prior distribution. These smoothness conditions are expressed as unimodal or, possibly, multi-modal order relations among the category probabilities. Emphasis is placed on posterior inference about the finite population mean. Of independent interest is the methodology for evaluating the posterior moments and probabilities using Monte Carlo integration with importance sampling.
TL;DR: In this paper, it is shown that conservative prior parameter values for the Cox and Snell bound can be found such that this bound possesses classical confidence properties in repeated sampling from a wide variety of possible realized populations.
Abstract: Mixture distributions combining a probability mass at zero and a continuous density function for positive outcomes are frequently found in auditing. The Cox and Snell bound for evaluating the results of monetary unit sampling is a Bayesian bound utilizing prior information designed for such mixture distributions. In this paper it is shown that conservative prior parameter values for the Cox and Snell bound can be found such that this bound possesses classical confidence properties in repeated sampling from a wide variety of possible realized populations.
TL;DR: It is shown that the Bayesian approach solves the non-uniqueness problem which affects maximum likelihood prediction in certain situations and the maximum likelihood and Bayesian methodologies for inference and prediction are compared.
TL;DR: In this article, a mixture of a product of beta prior distributions is used to estimate the posterior mean and credible regions of a sample survey problem in which there is significant nonresponse.
Abstract: In this article, Bayesian estimation methods for several binomial probabilities are studied by using a mixture of a product of beta prior distributions. Approximations to the posterior means and credible regions are derived. The results obtained are applied to a sample survey problem in which there is significant nonresponse.
TL;DR: This article uses Bayesian methods for the analysis of survival data and describes posterior distributions for various parameters of clinical interest in the presence of arbitrary right censorship to suggest an approach for checking adequacy.
Abstract: Posterior distributions can provide effective summaries of the main conclusions of medical follow-up studies. In this article, we use Bayesian methods for the analysis of survival data. We describe posterior distributions for various parameters of clinical interest in the presence of arbitrary right censorship. Non-informative reference priors result from transformation of a two-parameter Weibull model into a location-scale family. We suggest an approach for checking adequacy. For illustration, we apply the methods to a well-known acute leukemia data set.
TL;DR: The proposed method employs Bayesian statistical theory and incorporates weighting of expert judgements in evaluating the consessus distributions and contains no error due to discretization.
TL;DR: In this article, a Monte Carlo procedure is proposed to compute posterior moments with an importance function based on an approximate posterior density of the model, which is shown in a numerical example and then in an economic example.
01 Jan 1985
TL;DR: Since the Bayesian Approach does provide a means for producing a probability for system survival, conditional on data, which can be used for decision, this approach focuses on this approach.
Abstract: In system reliability prediction, one of the most difficult problems (especially if the classical statistics approach is used) is to combine component and system failure data. Asymptotic and approximate methods to calculate classical confidence intervals on system reliability continue to be produced each year [cf Martz and Waller (1982), Chapter 11]. However, since classical confidence intervals do not produce a probability for system survival conditional on data, they c a n n o t provide the basis for action in the decision theory sense [see Lindley (1972), p. 16 for a discussion of confidence intervals]. Since the Bayesian Approach does provide a means for producing a probability for system survival, conditional on data, which can be used for decision, we concentrate on this approach.
TL;DR: In this article, the populations are exchangeable, in the sense that the joint prior probability dis- tribution of their parameters is invariant under permutation of their mean vectors (given their dispersion matrices are the same) by using the exchangeability assumption the problem of assessing hyperparameters is substantially reduced.
Abstract: This paper broadens earlier Bayesian statistical procedures for problems in the multivariate analysis of variance and covari- ance which were developed for general families of prior distribu- tions. In this paper, we assume that the populations are exchangeable, in the sense that the joint prior probability dis- tribution of their parameters is invariant under permutation of their mean vectors (given their dispersion matrices are the same) By using the exchangeability assumption the problem of assessing hyperparameters is substantially reduced. Under vague prior assumptions, results are comparable to those of classical random effects models; with other prior assumptions they differ. Stein- type shrinkage estimators are obtained for cases in which hyper- parameters are known through subjective assessment, and for cases in which hyperparameters are imperfectly known. We develop results for both one- and two-way classifications.