The Bayes/Non-Bayes Compromise: A Brief Review

Abstract Various compromises that have occurred between Bayesian and non-Bayesian methods are reviewed. (A citation is provided that discusses the inevitability of compromises within the Bayesian approach.) One example deals with the masses of elementary particles, but no knowledge of physics will be assumed.

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

[2]  S. Ramanujan,et al.  Highly Composite Numbers , 1915 .

[3]  Arthur Eddington.  The mathematical theory of relativity , 1923 .

[4]  E. S. Pearson,et al.  ON THE USE AND INTERPRETATION OF CERTAIN TEST CRITERIA FOR PURPOSES OF STATISTICAL INFERENCE PART I , 1928 .

[5]  E. S. Pearson,et al.  On the Problem of the Most Efficient Tests of Statistical Hypotheses , 1933 .

[6]  E. S. Pearson,et al.  On the Problem of the Most Efficient Tests of Statistical Hypotheses , 1933 .

[7]  S. S. Wilks.  The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses , 1938 .

[8]  E. S. Pearson.  WILLIAM SEALY GOSSET, 1876-1937(2) “STUDENT” AS STATISTICIAN , 1939 .

[9]  E. S. Pearson.  "Student" as Statistician , 1939 .

[10]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[11]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

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

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

[14]  D. Lindley.  A STATISTICAL PARADOX , 1957 .

[15]  R. A. Fisher,et al.  Statistical methods and scientific inference. , 1957 .

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

[17]  J. Polkinghorne,et al.  The Development and Meaning of Eddington's Fundamental Theory , 1958 .

[18]  I. Good.  Significance Tests in Parallel and in Series , 1958 .

[19]  Leonard J. Savage,et al.  The Foundations of Statistics Reconsidered , 1961 .

[20]  L. J. Savage.  The Foundations of Statistical Inference. , 1963 .

[21]  Ward Edwards,et al.  Bayesian statistical inference for psychological research. , 1963 .

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

[23]  A. R. Thatcher,et al.  Relationships between Bayesian and Confidence Limits for Predictions , 1964 .

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

[25]  John W. Pratt,et al.  Bayesian Interpretation of Standard Inference Statements , 1965 .

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

[27]  C. Kilmister,et al.  Men of Physics: Sir Arthur Eddington , 1968 .

[28]  P. Rowlatt,et al.  Group theory and elementary particles , 1968 .

[29]  I. J. Good,et al.  The proton and neutron masses and a conjecture for the gravitational constant , 1970 .

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

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

[32]  Oscar Kempthorne,et al.  A comparison of the chi2 and likelihood ratio tests for composite alternatives1 , 1972 .

[33]  Rory A. Fisher,et al.  Statistical methods and scientific inference. , 1957 .

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

[35]  Hayes,et al.  Review of particle properties. , 1978, Physical review. D, Particles and fields.

[36]  D. Haar,et al.  Men of physics , 1974 .

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

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

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

[40]  R. Tapia,et al.  Nonparametric Probability Density Estimation , 1978 .

[41]  D. Cheng,et al.  Elementary Particle Physics: An Introduction , 1979 .

[42]  I. Good.  Some history of the hierarchical Bayesian methodology , 1980 .

[43]  I. Good.  C67. Another relationship between weight of evidence and errors of the first and second kinds , 1980 .

[44]  G. Box.  Sampling inference, Bayes’ inference, and robustness in the advancement of learning , 1980 .

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

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

[47]  J. F. Crook,et al.  The Powers and Strengths of Tests for Multinomials and Contingency Tables , 1982 .

[48]  G. Shafer.  Lindley's Paradox , 1982 .

[49]  I. Good.  C176. The bayes/non-bayes compromise or synthesis and box′ current philosophy (see the first paragraph of c74.) , 1983 .

[50]  I. Good.  C148. Probability estimation by maximum penalized likelhood for large contingency tables and for other categorical data , 1983 .

[51]  I. J. Good,et al.  The Robustness of a Hierarchical Model for Multinomials and Contingency Tables , 1983 .

[52]  I. Good.  Good Thinking: The Foundations of Probability and Its Applications , 1983 .

[53]  I. Good.  C175. Hierarchical bayes, mixed dirichlet priors, penalized likelihood, etc. (see the first paragraph of C174.) [this note was my response to comments by tom leonard.] , 1983 .

[54]  Irving John Good,et al.  C191. How should tail-area probabilities be standardized for sample size in unpaired comparisons? , 1984 .

[55]  Irving John Good,et al.  C213. A sharpening of the harmonic-mean rule of thumb for combining tests ”in parallel“ , 1984 .

[56]  Irving John Good,et al.  C214. The harmonic-mean rule of thumb: some classes of applications , 1984 .

[57]  I. Good.  C192. One tail versus two-tails, and the harmonic-mean rule of thumb , 1984 .

[58]  J. Schwarz.  Superstrings: The First 15 years of Superstring TheoryReprints + Commentary — In 2 Volumes , 1985 .

[59]  C. Quigg.  Elementary Particles and Forces. , 1985 .

[60]  Michael B. Green,et al.  Anomaly-free chiral theories in six dimensions , 1985 .

[61]  J. Berger,et al.  Testing a Point Null Hypothesis: The Irreconcilability of P Values and Evidence , 1987 .

[62]  J. F. Crook,et al.  The Robustness and Sensitivity of the Mixed-Dirichlet Bayesian Test for "Independence" in Contingency Tables , 1987 .

[63]  I. Good.  What are the masses of elementary particles? , 1988, Nature.

[64]  R. L. Crawford,et al.  Review of Particle Properties, 1988-1989 , 1988 .

[65]  Irving John Good,et al.  The Interface Between Statistics and Philosophy of Science , 1988 .

[66]  N. J. A. Sloane,et al.  Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.

[67]  I. Good.  C319. Weight of evidence and a compelling metaprinciple , 1989 .

[68]  D. Lovett,et al.  Tensor Properties of Crystals , 1989 .

[69]  I. Good.  C312. Yet another argument for the explicatum of weight of evidence , 1989 .

[70]  I. Good.  C317. The theorem of corroboration and undermining, and popper's demarcation rule , 1989 .

[71]  I. Good.  C378. Comments concerning the hadron quantal hypothesis , 1990 .

[72]  I. Good.  Speculations concerning the future of statistics , 1990 .

[73]  G. A. Barnard,et al.  Student: A Statistical Biography of William Sealy Gosset , 1990 .

[74]  I. Good.  C370. A compromise between credibility and subjective probability , 1990 .

[75]  W. Mccrea,et al.  Arthur Stanley Eddington , 1945 .

[76]  I. Good.  C383. A comment concerning optional stopping , 1991 .