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Conditional Independence in Statistical Theory

Dawid, A. P.·1979·Journal of the Royal Statistical Society Series B: Statistical Methodology

Abstract

Summary: Some simple heuristic properties of conditional independence are shown to form a conceptual framework for much of the theory of statistical inference. This framework is illustrated by an examination of the rôle of conditional independence in several diverse areas of the field of statistics. Topics covered include sufficiency and ancillarity, parameter identification, causal inference, prediction sufficiency, data selection mechanisms, invariant statistical models and a subjectivist approach to model-building.

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Crossref · 10.1111/j.2517-6161.1979.tb01052.x

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Citations

Cites

Research works printed but not linked: 39

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  2. Barankin, 1961, Sufficient parameters: solution of the minimal dimensionality problem, Ann. Inst. Statist. Math., 12, 91, 10.1007/BF01733119 · DOI
  3. Basu, 1970, On sufficiency and invariance, 61
  4. Bickel, 1977, Sex bias in graduate admissions: data from Berkeley, 113
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  6. Cole, 1973, Bias in selection, J. Educ. Meas., 10, 237, 10.1111/j.1745-3984.1973.tb00802.x · DOI
  7. Dawid, 1975, On the concepts of sufficiency and ancillarity in the presence of nuisance parameters, J. R. Statist. Soc. B, 37, 248, 10.1111/j.2517-6161.1975.tb01540.x · DOI
  8. Dawid, 1976, Properties of diagnostic data distributions, Biometrics, 32, 647, 10.2307/2529753 · DOI
  9. Dawid, 1977, Invariant distributions and analysis of variance models, Biometrika, 64, 291, 10.1093/biomet/64.2.291 · DOI
  10. Dawid, 1977, Spherical matrix distributions and a multivariate model, J. R. Statist. Soc. B, 39, 254, 10.1111/j.2517-6161.1977.tb01623.x · DOI
  11. Dawid, 1980, Conditional independence for statistical operations, 10.1214/aos/1176345011 · DOI
  12. Dawid, 1977, Likelihood and Bayesian inference from selectively reported data, J. Amer. Statist. Ass., 72, 845
  13. Dawid, 1973, Marginalization paradoxes in Bayesian and structural inference (with Discussion), J. R. Statist. Soc. B, 35, 189, 10.1111/j.2517-6161.1973.tb00952.x · DOI · Paper page
  14. De Finetti, 1937, Foresight: Its logical laws, its subjective sources (in French), 93
  15. De Finetti, 1975, Theory of Probability (English translation)
  16. Dempster, 1961, Elements of Continuous Multivariate Analysis.
  17. Drèze, 1974, Bayesian theory of identification in simultaneous equations models
  18. Farrell, 1962, Representation of invariant measures, Illinois J. Math., 6, 447, 10.1215/ijm/1255632504 · DOI
  19. Florens, 1977, Reduction of Bayesian experiments
  20. Fraser, 1966, On sufficiency and conditional sufficiency, Sankhyā A, 28, 145
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  22. Kadane, 1974, The role of identification in Bayesian theory
  23. Kemperman, 1961, The Passage Problem for a Stationary Markov Chain., 10.1063/1.3057754 · DOI
  24. Kendall, 1967, On finite and infinite sequences of exchangeable events, Studia Sci. Math. Hungar., 2, 319
  25. Kudō, 1967, On partial prior information and the property of parametric sufficiency, Proc. Fifth Berk. Symp., I, 251
  26. Lauritzen, 1974, Sufficiency, prediction and extreme models, Scand. J. Statist., 1, 128
  27. Lehmann, 1959, Testing Statistical Hypotheses.
  28. Lindley, 1979, The role of exchangeability in inference
  29. Padmanabhan, 1972, Local efficiency, efficiency, adequacy, ancillarity and truncation, Sankhyā A., 34, 145
  30. Picci, 1977, Some connections between the theory of sufficient statistics and the identifiability problem, SIAM J. Appl. Math., 33, 383, 10.1137/0133025 · DOI
  31. Pitman, 1973, A note on random times, Stoch. Procs and their Applns, 1, 369, 10.1016/0304-4149(73)90017-3 · DOI
  32. Reiersøl, 1950, Identifiability of a linear relationship between variables which are subject to error, Econometrica, 18, 375, 10.2307/1907835 · DOI · Paper page
  33. Rubin, 1976, Inference and missing data, Biometrika, 63, 581, 10.1093/biomet/63.3.581 · DOI · Paper page
  34. Rubin, 1978, Bayesian inference for causal effects: the role of randomization, Ann. Statist., 6, 34, 10.1214/aos/1176344064 · DOI · Paper page
  35. Siegmund, 1967, Some problems in the theory of optimal stopping, Ann. Math. Statist., 38, 1627, 10.1214/aoms/1177698596 · DOI
  36. Skibinsky, 1967, Adequate subfields and sufficiency, Ann. Math. Statist., 38, 155, 10.1214/aoms/1177699065 · DOI
  37. Takeuchi, 1975, Characterizations of prediction sufficiency (adequacy) in terms of risk functions, Ann. Statist., 3, 1018, 10.1214/aos/1176343206 · DOI
  38. Torgersen, 1977, Prediction sufficiency when the loss function does not depend on the unknown parameter, Ann. Statist., 5, 155, 10.1214/aos/1176343748 · DOI
  39. Tukey, 1949, Sufficiency, truncation and selection, Ann. Math. Statist., 20, 309, 10.1214/aoms/1177730042 · DOI

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Metadata

Authors
Dawid, A. P.
Venue
Journal of the Royal Statistical Society Series B: Statistical Methodology
Published
1979-09-01
Volume
41
Issue
1
Pages
1-15
ISSN
  • 1369-7412 (ISSN-L)
  • 1467-9868
OpenAlex
W30853191
Cited by
1,501
References
3
FWCI
3.92
Type
journal article
Language
en
Open access
closed

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