Boundary-mode approximations for posterior expectations

Journal of Statistical Planning and Inference

Volumn 58, Issue 2, 1997, Pages 217-239

  Erkanli, Alaattin ^a  

^a DUKE UNIVERSITY MEDICAL CENTER   (United States)

Author keywords

Asymptotics; Bayesian inference; Laplace's method; Tierney Kadane approximation

Indexed keywords

EID: 0031498171     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(96)00089-4     Document Type: Article

References (18)

1. Bleistein, N. and J. Handelsman (1986). Asymptotic Expansions of Integrals. Holt, Rinehart and Winston, New York.
2. Box, E.P. and G.C. Tiao (1973). Bayesian Inference in Statistical Analysis. Addison-Wisley, Reading, MA.
3. Erkanli, A. (1991). Laplace approximations for posterior expectations when the mode occurs at the boundary of the parameter space. Technical Report # 522, Department of Statistics, Carnegie Mellon University.
4. Erkanli, A. (1994). Laplace approximations for posterior expectations when the mode occurs at the boundary of the parameter space. J. Amer. Statist. Assoc. 89, 250-258.
5. Gelfand, A.E. and A.F.M. Smith (1990). Sampling Based Approximations to Calculating Marginal Densities. J. Amer. Statist. Assoc. 85, 972-985.
6. Jones, D.S. (1980). The Theory of Generalized Functions. Cambridge University Press, Cambridge.
7. Kass, R.E. (1988). Comment on 'Approximating posterior distributions and posterior moments' by C.N. Morris, In: J.M. Bernardo, M.H. DeGroot, D.V. Lindley and A.F.M. Smith, Eds., Bayesian Statistics 3. Oxford Press, New York, 327-344.
8. Kass, R.E. and J.C. Fu (1987). Posterior large deviations. Technical Report # 405, Department of Statistics, Carnegie Mellon University.
9. Kass, R.E., L. Tierney and J.B. Kadane (1990). The validity of posterior expansions based on Laplace's method. In: S. Geisser, J.S. Hodges, S.J. Press and A. Zellner, Eds., Essays in Honor of George Barnard. North-Holland. Amsterdam, 473-488.
10. Lewis, S.M. and A.E. Raftery (1994). Estimating Bayes factors via posterior simulation with the Laplace-Metropolis estimator. Manuscript, University of Washington.
11. Lindley, D.V. (1980). Approximate Bayesian methods. In: J.M. Bernardo, M.H. DeGroot, D.V. Lindley and A.F.M. Smith, Eds., Bayesian Statistics. University Press, Valencia, 223-245.
12. Moran, P.A.P. (1971). Maximum-likelihood estimation in non-standard conditions. Proc. Cambridge Philos. Soc. 70, 441-450.
13. Morris, C.N. (1988). Approximating posterior distributions and posterior moments. In: J.M. Bernardo, M.H. DeGroot, D.V. Lindley and A.F.M. Smith. Eds., Bayesian Statistics 3. Oxford Press, New York, 327-344.
14. Mosteller, F. and D.L. Wallace (1964). Inference and Disputed Authorship: The Federalist Papers. Addison-Wesley, Reading, MA.
15. Pei, G. (1980). Asymptotic distributions of M-estimators in non-standard cases. Ph.D. Thesis, Carnegie Mellon University.
16. Tierney, L. and J.B. Kadane (1986). Accurate approximations for posterior moments and marginal densities. J. Amer. Statist. Assoc. 81, 82-86.
17. Tierney, L., R.E. Kass and J.B. Kadane (1989a). Approximate marginal densities of nonlinear functions. Biometrika 76, 425-433.
18. Tierney, L., R.E. Kass and J.B. Kadane (1989b). Fully exponential Laplace approximations to expectations and variances of nonpositive functions. J. Amer. Statist. Assoc. 84, 710-716.