Bayesian Inference in Models with Euclidean Structures

References

• Bayes , T. 1764 . An Essay Towards Solving a Problem in the Doctrine of Chances . Philosophical Transactions of the Royal Society of London , 53 : 370 – 418 .
   Google Scholar
• Bourbaki , N. 1974 . Algebra I , Reading , MA : Addison-Wesley .
   Google Scholar
• Chang , T. and Villegas , C. 1986 . On a Theorem of Stein Relating Bayesian and Classical Inferences in Group Models . The Canadian Journal of Statistics , 14 : 289 – 296 .
   Google Scholar
• Dawid , A. P. 1983 . “ Invariant Prior Distributions ” . In Encyclopedia of Statistical Sciences , Edited by: Kotz , S. and Johnson , N. L. vol. 4 , 228 – 236 . New York : John Wiley .
   Google Scholar
• Dempster , A. P. 1971 . “ Model Searching and Estimation in the Logic of Inference ” . In Foundations of Statistical Inference , Edited by: Godambe , V. P. and Sprott , D. A. 56 – 81 . Toronto : Holt, Rinehart & Winston .
   Google Scholar
• Durbin , J. 1987 . Statistics and Statistical Science . Journal of the Royal Statistical Society , : 177 – 191 . Ser. A
   Google Scholar
• Edgeworth , F. Y. 1885 . Observations and Statistics: An Essay on the Theory of Errors of Observation and the First Principles of Statistics . Transactions of the Cambridge Philosophical Society , 14 : 138 – 169 . Corrigendum in Proceedings of the Cambridge Philosophical Society, 6, 101–102
   Google Scholar
• Fisher , R. A. 1922 . On the Mathematical Foundations of Theoretical Statistics . Philosophical Transactions of the Royal Society of London , 222 : 309 – 368 . Ser. A
   Google Scholar
• Fraser , D. A. S. 1961 . The Fiducial Method and Invariance . Biometrika , 48 : 261 – 280 .
   Web of Science ®Google Scholar
• Fraser , D. A. S. 1968 . The Structure of Inference, , 2nd ed. , Toronto : DAI, University of Toronto Textbook Store .
   Google Scholar
• Fraser , D. A. S. 1988a . “ Structural Inference ” . In Encyclopedia of Statistical Sciences , Edited by: Kotz , S. and Johnson , N. L. vol. 9 , 20 – 27 . New York : John Wiley .
   Google Scholar
• Fraser , D. A. S. 1988b . “ Structural Models ” . In Encyclopedia of Statistical Sciences , Edited by: Kotz , S. and Johnson , N. L. vol. 9 , 27 – 32 . New York : John Wiley .
   Google Scholar
• Geisser , S. 1984 . On Prior Distributions for Binary Trials . The American Statistician , 38 : 244 – 251 .
   Web of Science ®Google Scholar
• Haldane , J. B. S. 1932 . A Note on Inverse Probability . Proceedings of the Cambridge Philosophical Society , 28 : 55 – 61 .
   Google Scholar
• Haldane , J. B. S. 1948 . The Precision of Observed Values of Small Frequencies . Biometrika , 35 : 297 – 300 .
   Web of Science ®Google Scholar
• Hartigan , J. 1964 . Invariant Prior Distributions . Annals of Mathematical Statistics , 35 : 836 – 845 .
   Google Scholar
• Jaynes , E. T. 1968 . Prior Probabilities . IEEE Transactions on Systems Science and Cybernetics , SSC-4 : 227 – 241 .
   Web of Science ®Google Scholar
• Jeffreys , H. 1946 . An Invariant Form for the Prior Probability in Estimation Problems . Proceedings of the Royal Society of London , 186 : 453 – 461 . Ser. A
   Google Scholar
• Kass , R. 1980 . The Riemannian Structures of Model Spaces: A Geometric Approach to Inference , University of Chicago, Dept. of Statistics . unpublished Ph.D. thesis
   Google Scholar
• Kass , R. 1989 . The Geometry of Asymptotic Inference . Statistical Science , 4 : 188 – 219 .
   Google Scholar
• Krantz , D. H. , Luce , R. D. , Suppes , P. and Tversky , A. 1971 . Foundations of Measurement , New York : Academic Press .
   Google Scholar
• Lane , D. A. 1980 . “ Fisher, Jeffreys, and the Nature of Probability ” . In R. A. Fisher: An Appreciation , Edited by: Fienberg , S. E. and Hinkley , D. V. 148 – 160 . New York : Springer-Verlag .
   Google Scholar
• Laplace , P. S. 1812 . Théorie Analytique des Probabilités , Paris : Courcier .
   Google Scholar
• Lhoste , E. 1923 . Le Calcul des Probabilités Appliqué à l'Artillerie . Revue d'Artillerie , 91 : 405 – 423 . 516 – 532 . 92 58 – 82 . 152 – 179 .
   Google Scholar
• Lindley , D. V. 1965 . Introduction to Probability and Statistics, Part II, Inference , Cambridge , , UK : Cambridge University Press .
   Google Scholar
• Little , R. J. A. 1989 . Testing the Equality of Two Independent Binomial Proportions . The American Statistician , 43 : 283 – 288 .
   Web of Science ®Google Scholar
• Millman , R. S. 1977 . Kleinian Transformation Geometry . American Mathematical Monthly , 84 : 338 – 349 .
   Google Scholar
• Nachbin , L. 1965 . The Haar Integral , Princeton , NJ : Van Nostrand . (reprinted, 1976, New York: Robert E. Krieger)
   Google Scholar
• O'Reilly , F. J. and Villegas , C. 1987 . Conditional and Predictive Probability Integral Transforms . The Canadian Journal of Statistics , 15 : 151 – 158 .
   Google Scholar
• Pratt , J. W. 1965 . Bayesian Interpretation of Standard Inference Statements . Journal of the Royal Statistical Society , 2 : 169 – 203 . (with discussion), Ser. B
   Google Scholar
• Santaló , L A. 1976 . Integral and Geometric Probability , Reading , MA : Addison-Wesley .
   Google Scholar
• Snapper , E. and Troyer , R. J. 1971 . Metric Affine Geometry , New York : Academic Press .
   Google Scholar
• Stigler , S. M. 1986 . The History of Statistics , Cambridge , MA : Harvard University Press .
   Google Scholar
• Stuart , A. and Ord , J. K. 1987 . Kendall's Advanced Theory of Statistics , vol. 1 , London : Charles W. Griffin .
   Google Scholar
• Swartz , T. and Villegas , C. 1990 . Posterior Probability and Conditional Coverage unpublished paper
   Google Scholar
• Tuller , A. 1967 . A Modern Introduction to Geometries , New York : Van Nostrand .
   Google Scholar
• Villegas , C. 1967 . On Qualitative Probability . American Mathematical Monthly , 74 : 661 – 669 .
   Web of Science ®Google Scholar
• Villegas , C. 1977a . Inner Statistical Inference . Journal of the American Statistical Association , 72 : 453 – 458 .
   Web of Science ®Google Scholar
• Villegas , C. 1977b . On the Representation of Ignorance . Journal of the American Statistical Association , 72 : 651 – 654 .
   Web of Science ®Google Scholar
• Villegas , C. 1981 . Inner Statistical Inference II . The Annals of Statistics , 9 : 768 – 776 .
   Web of Science ®Google Scholar
• Villegas , C. 1983 . “ Inner Inference ” . In Encyclopedia of Statistical Sciences , Edited by: Kotz , S. , Johnson , N. L. and Read , C. B. vol. 4 , 141 – 143 . New York : John Wiley .
   Google Scholar