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- Article] A LOGIC OF PROBABILITY, WITH APPLICATION TO THE FOUNDATIONS OF STATISTICS
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DocNo of ILP: 8308
Doc. Type: Article
Title: A LOGIC OF PROBABILITY, WITH APPLICATION TO THE FOUNDATIONS OF STATISTICS
Authors: VOVK, VG
Full Name of Authors: VOVK, VG
Keywords by Author: BAYES FACTORS; CENTRAL LIMIT THEOREM; FREQUENTIAL FRAMEWORK; PRINCIPLE OF EXCLUDED GAMBLING STRATEGY; P-VALUES; STRONG LAW OF LARGE NUMBERS
Keywords Plus:
Abstract: A simple example shows that the classical theory of probability implies more than one can deduce via Kolmogorov's calculus of probability. Developing Dawid's ideas I propose a new calculus of probability which is free from this drawback. This calculus naturally leads to a new interpretation of probability. I argue that attempts to create a general empirical theory of probability should be abandoned and we should content ourselves with the logic of probability establishing relations between probabilistic theories and observations. My approach to the logic of probability is based on a variant of Ville's principle of the excluded gambling strategy. In addition to the classical theory of probability this approach is applied to the probabilistic theories provided by the problem of testing validity of probability forecasts and by statistical models.
Cate of OECD: Mathematics
Year of Publication: 1993
Business Area: gamble
Detail Business: gamble
Country: England
Study Area: regulation, law, invest, value, statistics, statistics, software, application
Name of Journal: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL
Language: English
Country of Authors:
Press Adress: VOVK, VG (reprint author), RES COUNCIL CYBERNET MOSCOW,9-3-451 ULITSA RAMENKI,MOSCOW 117607,RUSSIA.
Email Address:
Citaion:
Funding:
Lists of Citation: Bertsekas D. P., 1978, STOCHASTIC OPTIMAL C; BRAITHWAITE RB, 1953, SCI EXPLANATION, P154; Church A, 1940, B AM MATH SOC, V46, P130, DOI 10.1090/S0002-9904-1940-07154-X; DAWID AP, 1985, ANN STAT, V13, P1251, DOI 10.1214/aos/1176349736; DAWID AP, 1984, J ROY STAT SOC A STA, V147, P278, DOI 10.2307/2981683; de Finetti B, 1993, FUND MATH, P291; de Finetti B., 1949, ANN U TRIESTE, V19, P3; Dubins L., 1965, GAMBLE YOU MUST INEQ; Durrett R., 1991, PROBABILITY THEORY E; Fleming W.H., 1975, DETERMINISTIC STOCHA; HOLZER S, 1985, B UNIONE MAT ITAL, V4C, P441; HOWARD JV, 1975, Z MATH LOGIK, V21, P215; Karatzas I., 1987, BROWNIAN MOTION STOC; Kolmogorov A. N., 1942, IZV AKAD NAUK USSR M, V6, P3; KOLMOGOROV A.N., 1933, GRUNDBEGRIFFE WAHRSC; KOOPMAN BO, 1941, ANN MATH, V41, P269; Lindley DV, 1965, INTRO PROBABILITY ST; LOVELAND D, 1966, Z MATH LOGIK, V12, P279, DOI 10.1002/malq.19660120124; MARTINLO.P, 1966, INFORM CONTROL, V9, P602, DOI 10.1016/S0019-9958(66)80018-9; Neveu J., 1975, DISCRETE PARAMETER M; PAPAMARCOU A, 1991, ANN PROBAB, V19, P893, DOI 10.1214/aop/1176990457; PIERCE DA, 1973, ANN STAT, V1, P241, DOI 10.1214/aos/1176342362; Raiffa H, 1968, DECISION ANAL; Ramsey F., 1931, FDN MATH OTHER LOGIC, P156; Rao C. R., 1992, STAT SCI, V7, P34, DOI 10.1214/ss/1177011442; REGAZZINI E, 1991, ATT CONV SVIL MET NE, V2, P101; REGAZZINI E, 1987, ANN STAT, V15, P845, DOI 10.1214/aos/1176350379; Russell B., 1948, HUMAN KNOWLEDGE ITS; SAVAGE LJ, 1954, F STATISTICS; SAVAGE LJ, 1971, J AM STAT ASSOC, V66, P783, DOI 10.2307/2284229; SCHERVISH MJ, 1985, ANN STAT, V13, P1251; SCOZZAFAVA R, 1984, STATISTICA, V44, P21; Shafer G., 1976, MATH THEORY EVIDENCE; SHAFER G, 1992, HDB DATA ANAL BEHAV, P165; von Mises R, 1939, PROBABILITY STATISTI; VOVK VG, 1993, J ROY STAT SOC B MET, V55, P253; VOVK VG, 1993, IN PRESS J R STATI B; Walley P., 1991, STATISTICAL REASONIN; Williams D., 1991, PROBABILITY MARTINGA
Number of Citaion: 39
Publication: BLACKWELL PUBL LTD
City of Publication: OXFORD
Address of Publication: 108 COWLEY RD, OXFORD, OXON, ENGLAND OX4 1JF
ISSN: 0035-9246
29-Character Source Abbreviation: J ROY STAT SOC B MET
ISO Source Abbreviation: J. R. Stat. Soc. Ser. B-Methodol.
Volume: 55
Version: 2
Start of File: 317
End of File: 351
DOI:
Number of Pages: 35
Web of Science Category: Statistics & Probability
Subject Category: Mathematics
Document Delivery Number: KW965
Unique Article Identifier: WOS:A1993KW96500001
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