Abstract
This paper defines structural probability and develops its interpretation through the introduction of an error variable. The formulation of the observed data as having been generated by a combination of an error variable and an unknown parameter has come to be called the structural model, and inference based on this model structural inference.
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References
Barndorff-Nielsen, O.E. (1980). Conditionality resolutions, Biometrika, 67, 293–311.
Barndorff-Nielsen, O.E. (1988). Parametric Statistical Models and Likelihood. Lecture Notes in Statistics, Vol. 50, Springer-Verlag, New York.
Bartlett, M.S. (1965). R.A. Fisher and the last fifty years of statistical methodology, J. Amer. Statist. Assoc, 60, 395–409.
Berger, J.O., and Wolpert, R.L. (1984). The Likelihood Principle. I.M.S. Lecture Notes Series, Vol. 6. Institute of Mathematical Statistics, Hayward, California.
Birnbaum, A. (1962). On the foundations of statistical inference, J. Amer. Statist. Assoc, 57, 269–326.
Cox, D.R. (1958). Some problems connected with statistical inference, Ann. Math. Statist., 29, 357–372.
Cox, D.R. (1980). Local ancillarity, Biometrika, 67, 279–286.
Dawid, A.P., and Stone, M. (1982). The functional model basis of fiducial inference (with discussion), Ann. Statist., 10, 1054–1074.
DiCiccio, T.J. (1988). Likelihood inference for linear regression models, Biometrika, 75, 29–34.
DiCiccio, T.J., Field, C.A., and Fraser, D.A.S. (1990). Approximations of marginal tail probabilities and inference for scalar parameters, Biometrika, 77, 77–95.
Durbin, J. (1980a). Approximations for densities of sufficient estimators, Biometrika, 67, 311–335.
Durbin, J. (1980b). The approximate distribution of partial serial correlation coefficients calculated from residuals from regression on Fourier series, Biometrika, 67, 335–350.
Efron, B. (1978). Controversies in the foundations of statistics, Amer. Math. Monthly, 85, 231–246.
Fienberg, S.E., and Hinkley, D.V. (1980). R.A. Fisher: An Appreciation. Springer Verlag, New York.
Fisher, R.A. (1962). Bayes’ method of determination of probabilities, J. Roy. Statist. Soc., Ser.B, 24, 118–124.
Fraser, D.A.S. (1961). The fiducial method and invariance, Biometrika, 48, 261–280.
Fraser, D.A.S. (1962). On the consistency of the fiducial method, J. Roy. Statist. Soc., Ser. B, 24, 425–434.
Fraser, D.A.S. (1963a). On the sufficiency and likelihood principles, J. Amer. Statist. Assoc, 58, 641–647.
Fraser, D.A.S. (1963b). On the definition of fiducial probability, Bull. Internat. Statist. lnst., 40, 842–856.
Fraser, D.A.S. (1964a). Local conditional sufficiency, J. Roy. Statist. Soc., Ser. B, 26, 52–62.
Fraser, D.A.S. (1964b). On local inference and information, J. Roy. Statist. Soc., Ser. B, 26, 253–260.
Fraser, D.A.S. (1968). The Structure of Inference. Wiley, New York.
Fraser, D.A.S. (1979). Inference and Linear Models. McGraw-Hill, New York.
Fraser, D.A.S. (1988). Structural inference, structural models, structural prediction, structural probability, in Encyclopedia of Statistical Sciences (S. Kutz, N.L. Johnson, and C.B. Read, eds.). Wiley, New York.
Fraser, D.A.S., Lee, H.-S., and Reid, N. (1990). Nonnormal linear regression; an example of significance levels in high dimensions, Biometrika, 11, 333–341.
Fraser, D.A.S., Reid, N., and Wong, A. (1991). Exponential linear models: A two-pass procedure for saddlepoint approximation, J. Roy. Statist. Soc., Ser. B, 53, 483–492.
Fisher, R.A. (1962). Bayes’ method of determination of probabilities, J. Roy. Statist. Soc., Ser. B, 24, 118–124.
Hinkley, D.V. (1980). Likelihood as approximate pivotal distribution, Biometrika, 67, 287–292.
Lawless, J.F. (1982). Statistical Models and Methods for Lifetime Data. Wiley, New York.
Lindley, D.V. (1958). Fiducial distributions and Bayes’ theorem, J. Roy. Statist. Soc., Ser. B, 20, 102–107.
Sprott, D.A. (1960). Necessary restrictions for distributions a posteriori, J. Roy. Statist. Soc.,Ser.B, 22, 312–318.
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Reid, N. (1992). Introduction to Fraser (1966) Structural Probability and a Generalization. In: Kotz, S., Johnson, N.L. (eds) Breakthroughs in Statistics. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0919-5_35
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DOI: https://doi.org/10.1007/978-1-4612-0919-5_35
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