Displaying similar documents to “Approximations: Discussion.”

Likelihood, sufficiency and ancillarity: Discussion.

George A. Barnard, P. R. Freeman, Daniel Peña, James M. Dickey, Seymour Geisser, Dennis V. Lindley, Anthony O'Hagan, Adrian F. M. Smith (1980)

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Discussion on the papers by Akaike, Hirotugu, Likelihood and the Bayes procedure and by Dawid, A. Philip, A Bayesian look at nuisance parameters, both of them part of a round table on Likelihood, sufficiency and ancillarity held in the First International Congress on Bayesian Methods (Valencia, Spain, 28 May - 2 June 1979).

Predictive sample reuse: Discussion.

Irwin Guttman, S. James Press (1980)

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Discussion on the paper by Geisser, Seymour, Predictive sample reuse techniques for censored data, part of a round table on Bayesian and non-Bayesian conditional inference held in the First International Congress on Bayesian Methods (Valencia, Spain, 28 May - 2 June 1979).

Hypothesis testing: Discussion.

Edwin T. Jaynes, David J. Spiegelhalter, Hirotugu Akaike, Arthur P. Dempster, James M. Dickey, Seymour Geisser, Irving John Good, Dennis V. Lindley, Anthony O'Hagan, Arnold Zellner (1980)

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Discussion on the papers by Zellner, Arnold and Siow, Aloysius, Posterior odds ratios for selected regression hypotheses and by Bernardo, José M., A Bayesian analysis of classical hypotheses testing, both of them part of a round table on Hypothesis testing held in the First International Congress on Bayesian Methods (Valencia, Spain, 28 May - 2 June 1979).

Coherence of models and utilities: Discussion.

James M. Dickey, William H. DuMouchel, José M. Bernardo, Simon French, Joseph B. Kadane, Dennis V. Lindley, Anthony O'Hagan, Adrian F. M. Smith, Thomas W. F. Stroud (1980)

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Discussion on the papers by Leonard, Tom, The roles of inductive modelling and coherence in Bayesian statistics and by Novick, Melvin R., Dekeyrel, D.F. and Chuang, D.T., Local and regional coherence utility assessment procedures, both of them part of a round table on Coherence of models and utilities held in the First International Congress on Bayesian Methods (Valencia, Spain, 28 May - 2 June 1979).

Least squares approximation in Bayesian analysis.

Michel Mouchart, Léopold Simar (1980)

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This paper presents in a simple and unified framework the Least-Squares approximation of posterior expectations. Particular structures of the sampling process and of the prior distribution are used to organize and to generalize previous results. The two basic structures are obtained by considering unbiased estimators and exchangeable processes. These ideas are applied to the estimation of the mean. Sufficient reduction of the data is analysed when only the Least-Squares approximation...

Approximate Bayesian methods.

Dennis V. Lindley (1980)

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This paper develops asymptotic expensions for the ratios of integrals that occur in Bayesian analysis: for example, the posterior mean. The first term omitted is 0(n) and it is shown how the term 0(n) can be of importance.

Posterior odds ratios for selected regression hypotheses.

Arnold Zellner, Aloysius Siow (1980)

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Bayesian posterior odds ratios for frequently encountered hypotheses about parameters of the normal linear multiple regression model are derived and discussed. For the particular prior distributions utilized, it is found that the posterior odds ratios can be well approximated by functions that are monotonic in usual sampling theory F statistics. Some implications of these finding and the relation of our work to the pioneering work of Jeffreys and others are considered. Tabulations of...

Sequential learning, discontinuities and changes: Discussion.

Stephen E. Fienberg, José M. Bernardo, Philip J. Brown, A. Philip Dawid, James M. Dickey, Joseph B. Kadane, Tom Leonard (1980)

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Discussion on the papers by Makov, Udi E., Approximation of unsupervised Bayes learning procedures, Smith, Adrian F. M., Change-Point problems: approaches and applications and by Harrison, P. J. and Smith Jim Q., Discontinuity, decision and conflict, the three of them part of a round table on Sequential learning, discontinuities and changes held in the First International Congress on Bayesian Methods (Valencia, Spain, 28 May - 2 June 1979).

Bayesian and non-Bayesian conditional inference: Discussion.

A. Philip Dawid, Morris H. DeGroot, James M. Dickey, Irving John Good, Bruce M. Hill, Joseph B. Kadane, Tom Leonard, Dennis B. Lindley, Arnold Zellner (1980)

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Discussion on the paper by Barnard, George A., Pivotal inference and the Bayesian controversy, part of a round table on Bayesian and non-Bayesian conditional inference held in the First International Congress on Bayesian Methods (Valencia, Spain, 28 May - 2 June 1979).

Likelihood and the Bayes procedure.

Hirotugu Akaike (1980)

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In this paper the likelihood function is considered to be the primary source of the objectivity of a Bayesian method. The necessity of using the expected behaviour of the likelihood function for the choice of the prior distribution is emphasized. Numerical examples, including seasonal adjustment of time series, are given to illustrate the practical utility of the common-sense approach to Bayesian statistics proposed in this paper.

Some history of the hierarchical Bayesian methodology.

Irving John Good (1980)

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A standard tecnique in subjective Bayesian methodology is for a subject (you) to make judgements of the probabilities that a physical probability lies in various intervals. In the Bayesian hierarchical technique you make probability judgements (of a higher type, order, level or stage) concerning the judgements of lower type. The paper will outline some of the history of this hierarchical technique with emphasis on the contributions by I. J. Good because I have read every word written...