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Generalized Bayes posterior distributions are formed by putting a fractional power on the likelihood before combining with the prior via Bayes's formula.
Limiting behavior of posterior distributions when the model is incorrect
Berk, R. H. (1966) · 1966
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The behavior of maximum likelihood estimates under nonstandard conditions
Huber, P. J. (1967) · 1967
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Approximate Bayesian inference with the weighted likelihood bootstrap
Newton, M. A. and Raftery, A. E. (1994) · 1994
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Asymptotic behavior of Bayes estimates under possibly incorrect models
Bunke, O. and Milhaud, X. (1998) · 1998
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The consistency of posterior distributions in nonparametric problems
Barron, A., Schervish, M. J., and Wasserman, L. (1999) · 1999
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Posterior consistency of Dirichlet mixtures in density estimation
Ghosal, S., Ghosh, J. K., and Ramamoorthi, R. V. (1999) · 1999
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Convergence rates of posterior distributions
Ghosal, S., Ghosh, J. K., and van der Vaart, A. W. (2000) · 2000
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Asymptotic Statistics
van der Vaart, A. W. (2000) · 2000
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Walker, S. and Hjort, N. (2001) · 2001
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Gibbs posterior inference on multivariate quantiles
Bhattacharya, I. and Martin, R. (2020) · 2002
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Monte Carlo Statistical Methods
Robert, C. and Casella, G. (2004) · 2004
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Data tracking and the understanding of Bayesian consistency
Walker, S. G., Lijoi, A., and Prünster, I. (2005) · 2005
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Misspecification in infinite-dimensional bayesian statistics
Kleijn, B. J. K. and van der Vaart, A. (2006) · 2006
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From ϵ \epsilon -entropy to KL-entropy: analysis of minimum information complexity density estimation
Zhang, T. (2006) · 2006
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Is Bayes posterior just quick and dirty confidence?
Fraser, D. A. S. (2011) · 2011
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The safe Bayesian: learning the learning rate via the mixability gap
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Gibbs posterior concentration rates under sub-exponential type losses
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Bayesian asymptotics with misspecified models
De Blasi, P. and Walker, S. G. (2013) · 2013
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Bayesian inference for logistic models using Pólya-Gamma latent variables
Polson, N. G., Scott, J. G., and Windle, J. (2013) · 2013
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Safe probability
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A Bayesian genomic regression model with skew normal random errors
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Bayesian fractional posteriors
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General Bayesian updating and the loss-likelihood bootstrap
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False confidence, non-additive beliefs, and valid statistical inference
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Minimum clinically important difference in medical studies
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On posterior concentration in misspecified models
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A general framework for updating belief distributions
Bissiri, P. G., Holmes, C. C., and Walker, S. G. (2016) · 2016
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Fundamentals of Nonparametric Bayesian Inference
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Inconsistency of Bayesian inference for misspecified linear models, and a proposal for repairing it
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Data-dependent priors and their posterior concentration rates
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Robust Bayesian inference via coarsening
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Calibrating general posterior credible regions
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Fast rates for general unbounded loss functions: from ERM to generalized Bayes
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Empirical priors for prediction in sparse high-dimensional linear regression
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