Theory and Methods

Bayesian Asymptotics

Clarke, B. and Sun, D. (1999). "Asymptotics of the Expected Posterior". Annals of the Institute of Statistical Mathematics, Vol. 51, No. 1, 163-185.

Yuan, A. and Clarke, B. (2004). “Asymptotic Normality of the Posterior Given a Statistic”. Canadian Journal of Statistics, Vol. 32, No. 2, 119-137.

Prior Selection

Clarke, B. and Wasserman, L. (1993). "Non Informative Priors and Nuisance Parameters."Journal of the American Statistical Association, 88, 1427-1432.

Clarke, B. and Barron, A. (1994). "Jeffreys' Prior is Asymptotically Least Favourable Under Entropy Risk." The Journal of Statistical Planning and Inference, 41, 37-60.

Clarke, B. and Wasserman, L.A. (1995). "Information Tradeoff". TEST, 4-1, 19-38.

Clarke, B. and Sun, D. (1997). "Reference Priors Under the x2 Distance". Sankhya Series A, Vol. 59, Part II, 215-231

Clarke, B. and Yuan, A. (2004). “Partial Information Reference Priors: Derivation and Interpretations”. Journal of Statistical Planning and Inference, Vol. 123, No. 2, 313-345.

Analyzing the Bayesian Model more Broadly
From an information/sample size, model selection or robustness standpoint

Clarke, B. (1996). "Implications of Reference Priors for Prior Information and Sample Size." Journal of the American Statistical Association, 91, 173-184.

Clarke, B. and Gustafson, P. (1998). "On the overall sensitivity of the posterior distribution to its inputs. Journal of Statistical Planning and Inference, 71: 137-150.

Yuan, A. and Clarke, B. (1999). A Minimally Informative Likelihood for Decision Analysis: Illustration and Robustness. Canadian Journal of Statistics, Vol. 27, No. 3, 649-665.

Yuan, A. and Clarke, B. (1999). An Information Criterion for Likelihood Selection. IEEE Transactions on Information Theory. Vol. 45, No. 2, 562-571.

Gustafson, P. and Clarke, B. (2004). A Decomposition for the Posterior Variance. Journal of Statistical Planning and Inference, Vol. 119, No. 2, 311-327.

Clarke, B. and Yuan, A. (2006). Closed Form Expressions for Bayesian Sample Sizes. Annals of Statistics, Vol. 34, No. 3, 1293-1330.

Lin, X., Pittman, J. and Clarke, B. (2007). Information Conversion, Effective Samples & Parametric Size. Information Theory Transactions. Vol. 53, No. 12, 4438-4456.

Datta, G., Bhattacharya, A. and Clarke, B. (2008) “Bayesian Tests for the Zero Inflated Piosson Model. In: Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of P. K. Sen, Balakrishnan, A., Pena, E, and Silvapulle, M. Eds. p. 89-104.

Other stuff

Yuan, A. and Clarke, B. (2001). Manifest Characterization and Testing for Two Latent Traits. Annals of Statistics., Vol. 29, No. 3, 876-898.

Clarke, B. and Song, X. (2004). Approximating the Dependence Structure of Discrete and Continuous Stochastic Processes. Sankhya A Vol. 66, No. 3, 536-547.

And here’s some work on median methods in statistics:

Yu, C-W and Clarke, B. Asymptotics of Bayesian Median Loss Estimation. Submitted October 2008

Yu, C-W and Clarke, B. Cube Root Asymptotics of the Least Quantile of Squares Estimator in Nonlinear Regression Models. ”. Submitted October 2008.

Yu, C-W and Clarke, B. Median Based Cross-Validation for Model Selection. Submitted March 2009

Yu, C-W and Clarke, B. Median Loss Decision Theory. Submitted June 2009.

And some more Reference prior stuff:

Clarke, B. and Ghosal, S. Reference Priors in the Limit of Increasing Parameters. Basic theorem understood; verification of details nearly complete.