Abstract
A geometrical interpretation of independence and exchangeability leads to understanding the failure of de Finetti's theorem for a finite exchangeable sequence. In particular an exchangeable sequence of length r which can be extended to an exchangeable sequence of length k is almost a mixture of independent experiments, the error going to zero like 1/k.
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References
Crisma, L.: 1971, ‘Sulla proseguibilità di processi scambiabili,’ Rend. Matem. Trieste 3, 96–124.
Ericson, W. A.: 1973, ‘A Bayesian Approach to 2-Stage Sampling,’ Technical Report No. 26, Department of Statistics, University of Michigan, Ann Arbor.
Fienberg, S. E.: 1968, ‘The Geometry of an r × c Contingency Table,’ Ann. Math. Stat. 39, 1186–90.
Fienberg, S. E. and Gilbert, J. P.: 1970, ‘The Geometry of a Two by Two Contingency Table,’ Jour. Amer. Stat. Assoc. 65, 695–701.
de Finetti, B.: 1964, ‘Foresight: Its Logical Laws, Its Subjective Sources,’ in Kyburg, H. E. and Smokler, H. E. (eds.), Studies in Subjective Probability, Wiley, New York.
de Finetti, B.: 1969, ‘Sulla proseguibilità di processi aleatori scambiabili,’ Rend. Matem. Trieste 1, 53–67.
de Finetti, B.: 1972, Probability Induction and Statistics, Wiley, New York.
Hewitt, E. and Savage, L. J.: 1955, ‘Symmetric Measures on Cartesian Products,’ Trans. Amer. Math. Soc. 80, 470–501.
Kendall, D. G.: 1967, ‘On Finite and Infinite Sequences of Exchangeable Events,’ Studia Sci. Math. Hung. 2, 319–327.
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Diaconis, P. Finite forms of de Finetti's theorem on exchangeability. Synthese 36, 271–281 (1977). https://doi.org/10.1007/BF00486116
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DOI: https://doi.org/10.1007/BF00486116
Keywords
- Independent Experiment
- Geometrical Interpretation
- Finite Form
- Exchangeable Sequence
- Finite Exchangeable Sequence