# An inverse Sanov theorem for curved exponential families

@inproceedings{Macci2021AnIS, title={An inverse Sanov theorem for curved exponential families}, author={Claudio Macci and Mauro Piccioni}, year={2021} }

We prove the large deviation principle (LDP) for posterior distributions arising from curved exponential families in a parametric setting, allowing misspecification of the model. Moreover, motivated by the so called inverse Sanov Theorem, obtained in a nonparametric setting by Ganesh and O’Connell (1999 and 2000), we study the relationship between the rate function for the LDP studied in this paper, and the one for the LDP for the corresponding maximum likelihood estimators. In our setting…

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