# Bayesian fractional posteriors

@article{Bhattacharya2019BayesianFP, title={Bayesian fractional posteriors}, author={Anirban Bhattacharya and Debdeep Pati and Yun Yang}, journal={The Annals of Statistics}, year={2019} }

We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the contraction property of the fractional posterior in a general misspecified framework. Our contraction results only require a prior mass condition on certain Kullback-Leibler (KL) neighborhood of the true parameter (or the KL divergence minimizer in the…

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