Summary
The elimination of nuisance parameters has classically been tackled by variousad hoc devices, and has led to a number of attempts to define partial sufficiency and ancillarity. The Bayesian approach is clearly defined. This paper examines some classical procedures in order to see when they can be given a Bayesian justification.
Similar content being viewed by others
References
Barnard, G.A. (1963). Some logical aspects of the fiducial argument.J. Roy. Statist. Soc., B. 25, 111–114.
Barndorff-Nielsen, O. (1965). Identifiability of mixtures of exponential families.J. Math. Anal. Appl.,12, 115–21.
— (1976). Nonformation.Biometrika 63, 567–571.
— (1978).Information and Exponential Families in Statistical Theory. Wiley: Chichester-New York-Brisbane.
Basu, D. (1977). On the elimination of nuisance parameters.J. Amer. Statist. Ass. 72, 355–366.
— (1978). On partial sufficiency: a review.J. Stat. Plann. Inference,2, 1–13.
Chandra, S. (1977). On the mixtures of probability distributions.Scand. J. Statist. 4, 105–112.
Dawid, A.P. (1975). On the concepts of sufficiency and ancillarity in the presence of nuisance parameters.J. Roy. Statist. Soc. B. 37, 248–258.
— (1975). On the concepts of sufficiency and ancillarity in the presence of nuisance parameters.J. Roy. Statist. Soc. B. 37, 248–258.
— (1977). Invariant distributions and analysis of variance models.Biometrika 64, 291–7.
— (1979a). Conditional independence in statistical theory (with Discussion).J. Roy. Statist. Soc. B 41, 1–31.
— (1979b). Some misleading arguments involving conditional independence.J. Roy. Statist. Soc. B 41, 249–252.
— (1980). Conditional independence for statistical operations.Ann. Statist. 8, 598–617.
Dawid, A.P. & Dickey, J.M. (1977). Problems with nuisance parameters-traditional and Bayesian concepts.Tech. Report., University College London.
Dawid, A.P., Stone, M. &Zidek, J.V. (1973) Marginalization paradoxes in Bayesian and structural inference (with Discussion).J. Roy. Statist. Soc. B,35, 189–233.
Hájek, J. (1965). On basic concepts of statistics.Fifth Berkeley Symposium on Mathematical Statistic and Probability 1, 139–162.
Jaynes, E.T. (1980). Marginalization and prior probabilities.Bayesian Analysis in Econometrics and Statistics: Essays in Honor of Harold Jeffreys, (A. Zellner, ed.) Amsterdam: North Holland.
Koehn, U. &Thomas, D.L. (1975). On statistics independent of a sufficient statistic: Basu’s lemma.American Statistician 29, 40–42.
Lehmann, E.L. (1959).Testing Statistical Hypotheses. New York: Wiley.
Lindley, D.V. (1965).Introduction to Probability and Statistics from a Bayesian Viewpoint. Part 2: Inference. Cambridge: University Press.
Martin, F., Petit, J.L. &Littaye, M. (1973) Indépendance conditionelle dans le modèle statistique bayésien.Ann. Inst. Henri Poincaré, B,9, 19–40.
Raiffa, H.A., &Schlaifer, R.S. (1961).Applied Statistical Decision Theory. Boston: Harvard University.
Schou, G. (1978). Estimation of the concentration parameter in von Mises-Fisher distributions.Biometrika 65, 369–377.
Stone, M. &Springer, B.G.F. (1965). A paradox involving quasi prior distributions.Biometrika 52, 623–627.
Sudgen, R.A. (1978).Exchangeability and the foundations of survey sampling. Ph. D. Thesis, University of Southampton.
Teicher, H. (1960). On the mixture of distributions.Ann. Math. Statist. 31, 55–73.
— (1961). Identifiability of mixtures.Ann. Math. Statist. 32, 244–248.
— (1967). Identifiability of mixtures of product measures.Ann. Math. Statist. 38, 1300–2.
References in the Discussion
Akaike, H. (1974). A new look at the statistical model identification.IEEE Transactions on Automatic Control 19, 716–722.
— (1976). Canonical correlation analysis of time series and the use of information criterion. InSystem Identification: Advances and Case Studies. (Mehra and Lainiotis eds.) New York: Academic Press.
— (1978). On the likelihood of a time series model.The Statistician,27, 217–235.
Akaike, H. (1979). Smoothness priors and the distributed lag estimator.Tech. Report No. 40, Stanford University.
Bartlett, M.S. (1978).An introduction to Stochastic Processes. Cambridge: University Press.
Box, G.E.P. andJenkins, G.M. (1970).Time Series Analysis, Forecasting and Control. New York: Holden-Day.
Box, G.E.P. andTiao, G.C. (1973).Bayesian Inference in Statistical Analysis. New York: Addison Wesley.
Box, G.E.P., Hillmer, G.C. andTiao, G.C. (1976). Analysis and modelling of seasonal Time Series. Presented atNBER/Bureau of the Census Conference on Seasonal Analysis of Economic Time Series. Washington, D.C.
Good, I.J. (1979). Book review ofLogic, Law and Life: Some Philosophical Complications, (R.G. Colodomy ed.)J. Amer. Statist. Assoc. 74, 501–502.
Kalbfleisch, J.D. andSprott, D.A. (1970). Application of likelihood method to models involving large numbers of parameters (with discussion).J. Roy. Statist. Soc. B. 32, 175–208.
Lindley, D.V. andSmith A.F.M. (1972). Bayes estimates for the linear model (with discussion).J. Roy Statist. Soc. B. 34, 1–41.
Nelder, J.A. (1977). A reformulation of linear models (with discussion).J. Roy. Statist. Soc. A 140, 48–77.
O’Hagan, A. (1976). On posterior joint and marginal modes.Biometrika 63, 329–333.
Popper, K.R. (1965).Conjectures and Refutations: The Growth of Scientific Knowledge. New York: Basic Books. Also in Harper and Row, (1968) New York.
Raiffa, H. (1968).Decision Analysis. New York: Addison-Wesley.
Shakespeare, W. (1598).The Second Part of the History of Henry the Fourth, I. 3, 35–36. London: Wise and Aspley.
Shibata, R. (1976). Selection of the order of an autoregressive model by Akaike’s information criterion.Biometrika 63, 117–126.
— (1980). Asymptotically efficient selection of the order of the model for estimating parameters of a linear process.Ann. Statist. 8, 147–164.
Young, A.S. (1977). A Bayesian approach to prediction using polynomials.Biometrika 64, 309–317.
Zellner, A. (1977). Maximal data information prior distributions. InNew Developments in the Applications of Bayesian Methods. (A. Aykas & C. Brumat eds.) Amsterdam: North-Holland.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dawid, A.P. A Bayesian look at nuisance parameters. Trabajos de Estadistica Y de Investigacion Operativa 31, 167–203 (1980). https://doi.org/10.1007/BF02888351
Issue Date:
DOI: https://doi.org/10.1007/BF02888351