Smith, J. Q., 1953- and Rigat, Fabio, 1975- (2007) Isoseparation and robustness in finite parameter Bayesian inference. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers, Vol.2007).

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Abstract

Under a new family of separations the distance between two posterior densities is the same as the distance between their prior densities whatever the observed likelihood when that likelihood is strictly positive. Local versions of such separations form the basis of a weak topology having close links to the Euclidean metric on the natural parameters of two exponential family densities. Using these local separation measures it is shown that when the tails of the approximating density have appropriate properties, the variation distance between an approximating posterior density to a genuine density can be bounded explicitly. These bounds apply irrespective of whether the prior densities are grossly misspecified with respect to variation distance and irrespective of the form or the validity of the observed likelihood.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Mathematical statistics
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2007
Volume:	Vol.2007
Number:	No.22
Number of Pages:	23
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
References:	[1] Andrade, J. A. A. and O’Hagan, A. (2006). “Bayesian robustness mod- elling using regularly varying distributions”. Bayesian Analysis 1, 169- 188. [2] Berger, J. (1992) in discussion of Wasserman, L.(1992b) ”Recent methodological advances in robust Bayesian inference (with discus- sion)”, in Bayesian Statistics 4 J.M. Bernado et al (eds) 495 - 496 Oxford University Press. [3] Bernardo, J.M. and Smith, A.F.M.(1996) ”Bayesian Theory”, Wiley Chichester [4] Daneseshkhah,A (2004) ”Estimation in Causal Graphical Models”, PhD Thesis University of Warwick. [5] Dawid, A.P. (1973) ”Posterior expectations for large observations”, Biometrika, 60, 664-667. [6] DeRobertis, L. (1978) ”The use of partial prior knowledge in Bayesian inference”, Ph.D. dissertation, Yale University. [7] Gustafson, P. and Wasserman, L. (1995) ”Local sensitivity diagnostics for Bayesian inference”, Annals of Statistics , 23, 2153-2167. [8] Ghosh, J.K. and Ramamoorthi, R.V.(2003) ”Bayesian Nonparametrics”, Springer. [9] West, M. and Harrison, P.J.(1997) ”Bayesian Forecasting and Dynamic Models”, Springer. [10] Marshall, A.W. and Olkin, (1979) ”Inequalities: Theory of Majorisation and its Applications”, Academic Press. [11] Monhor, D. (2007) ”A Chebyshev Inequality for Multivariate Normal Distribution”, Probability in the Engineering And Informational Sci- ences, 21-2, 289-300. [12] Moran, P.A.P.(1968) ”An Introduction to Probability Theory”, Oxford University Press. [13] O’Hagan, A.(1979) “On outlier rejection phenomena in Bayesian infer- ence”, Journal of the Royal Statistical Society B 41, 358-367. [14] O’Hagan, A and Forster, J. (2004) ”Bayesian Inference”, Kendall’s Ad- vanced Theory of Statistics, Arnold. [15] Peterka, V. (1981) ”Bayesian system identification”. In: Trends and Progress in System Identification, P. Eykhoff, Ed., p. 239-304. Pergamon Press, Oxford. [16] Schervish, M.J. (1995) ”The Theory of Statistics”, Springer Verlag New York. [17] Smith, J.Q.(1979) ”A generalisation of the Bayesian steady forecasting model”, Journal of the Royal Statistical Society B 41, 375-87. [18] Smith, J.Q. ”Local Robustness of Bayesian Parametric Inference and Observed Likelihoods”, CRiSM Research Report 07-09. [19] Tong, Y.L.(1980) ”Probability Inequalities in Multivariate Distribu- tions” Academic Press New York. [20] Wasserman, L.(1992a) ”Invariance properties of density ratio priors” Annals of Statistics, 20, 2177-2182. [21] Poole, A. and Raftery, A.(2000) “Inference for Deterministic Simulation Models: The Bayesian Melding Approach” Journal of the American Statistical Association, 95, 1244-1255.
URI:	http://wrap.warwick.ac.uk/id/eprint/35555

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