Some history of the hierarchical Bayesian methodology

SummaryA standard technique 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 hierarchical Bayesian technique you make probability judgements (of a higher type, order, level, or stage) concerning the judgements of lower type. The paper will outlinesome of the history of this hierarchical technique with emphasis on the contributions by I. J. Good because I have read every word written by him.

[1]  H. Jeffreys,et al.  Theory of probability , 1896 .

[2]  J. Keynes.  A Treatise on Probability. , 1923 .

[3]  Hans Reichenbach,et al.  The theory of probability , 1968 .

[4]  B. O. Koopman.  The bases of probability , 1940 .

[5]  B. O. Koopman.  The Axioms and Algebra of Intuitive Probability , 1940 .

[6]  E. C. Kemble.  The Probability Concept , 1941, Philosophy of Science.

[7]  R. V. Mises.  On the Correct Use of Bayes' Formula , 1942 .

[8]  H. Jeffreys.  An invariant form for the prior probability in estimation problems , 1946, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[9]  Wilfred Perks,et al.  Some observations on inverse probability including a new indifference rule , 1947 .

[10]  J. Wolfowitz,et al.  Probability Theory for Statistical Methods. , 1950 .

[11]  L. J. Savage,et al.  Probability and the weighing of evidence , 1951 .

[12]  A. R. Davidson.  Theory of Probabilities. , 1953 .

[13]  I. Good.  THE POPULATION FREQUENCIES OF SPECIES AND THE ESTIMATION OF POPULATION PARAMETERS , 1953 .

[14]  L. J. Savage,et al.  The Foundations of Statistics , 1955 .

[15]  H. Robbins.  An Empirical Bayes Approach to Statistics , 1956 .

[16]  I. Good.  On the Estimation of Small Frequencies in Contingency Tables , 1956 .

[17]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[18]  I. Good.  Saddle-point Methods for the Multinomial Distribution , 1957 .

[19]  I J Good,et al.  Kinds of Probability: Although there are at least five kinds of probability, we can get along with just one kind. , 1959, Science.

[20]  Cedric A. B. Smith,et al.  Consistency in Statistical Inference and Decision , 1961 .

[21]  I. Good.  Maximum Entropy for Hypothesis Formulation, Especially for Multidimensional Contingency Tables , 1963 .

[22]  Irving John Good,et al.  The Estimation of Probabilities: An Essay on Modern Bayesian Methods , 1965 .

[23]  I. J. Good,et al.  Speculations Concerning the First Ultraintelligent Machine , 1965, Adv. Comput..

[24]  I. J. Good,et al.  How to Estimate Probabilities , 1966 .

[25]  I. Good.  A Bayesian Significance Test for Multinomial Distributions , 1967 .

[26]  Irving John Good,et al.  A Subjective Evaluation of Bode's Law and an ‘Objective’ Test for Approximate Numerical Rationality , 1969 .

[27]  David Lindley,et al.  THE ESTIMATION OF MANY PARAMETERS , 1970 .

[28]  Paul Slovic,et al.  Comparison of Bayesian and Regression Approaches to the Study of Information Processing in Judgment. , 1971 .

[29]  R. Dawes.  A case study of graduate admissions: Application of three principles of human decision making. , 1971 .

[30]  I. Good.  Nonparametric roughness penalties for probability densities , 1971 .

[31]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[32]  Donald B. Rubin,et al.  Max-imum Likelihood from Incomplete Data , 1972 .

[33]  Tom Leonard,et al.  A Bayesian method for histograms , 1973 .

[34]  J. F. Crook,et al.  The Bayes/Non-Bayes Compromise and the Multinomial Distribution , 1974 .

[35]  M. Stone.  Cross-validation and multinomial prediction , 1974 .

[36]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[37]  I. Good.  The Bayes Factor Against Equiprobability of a Multinomial Population Assuming a Symmetric Dirichlet Prior , 1975 .

[38]  Seymour Geisser,et al.  The Predictive Sample Reuse Method with Applications , 1975 .

[39]  Tom Leonard,et al.  Bayesian Estimation Methods for Two‐Way Contingency Tables , 1975 .

[40]  I. Good.  On the Application of Symmetric Dirichlet Distributions and their Mixtures to Contingency Tables , 1976 .

[41]  A. O'Hagan,et al.  Bayes estimation subject to uncertainty about parameter constraints , 1976 .

[42]  I. Good.  The Bayesian Influence, or How to Sweep Subjectivism under the Carpet , 1976 .

[43]  P. Holland,et al.  Discrete Multivariate Analysis. , 1976 .

[44]  W. Pelz.  Topics on the estimation of small probabilities. , 1977 .

[45]  I. J. Good,et al.  The enumeration of arrays and a generalization related to contingency tables , 1977, Discret. Math..

[46]  Tom Leonard,et al.  A Bayesian Approach to Some Multinomial Estimation and Pretesting Problems , 1977 .

[47]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[48]  J. Reeds,et al.  Compound Multinomial Likelihood Functions are Unimodal: Proof of a Conjecture of I. J. Good , 1977 .

[49]  Tom Leonard.  Density Estimation, Stochastic Processes and Prior Information , 1978 .

[50]  C50. Predictive sample re-use and the estimation of probabilities , 1979 .

[52]  Wayne S. Smith,et al.  Interactive Elicitation of Opinion for a Normal Linear Model , 1980 .

[53]  I. Good,et al.  Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data , 1980 .

[54]  M. Degroot,et al.  Information about Hyperparameters in Hierarchical Models , 1981 .