### Abstract

Minimization of the expectation EP(X) of a random variable X over a family Γ of plausible prior distributions P is addressed, when Γ is a level set of some convex integral functional. As typical cases, Γ may be an I-divergence ball or some other f-divergence ball or Bregman distance ball. Regarding localization of the infimum we show that whether or not the minimum of EP(X) subject to P∈ Γ is attained, the densities of the almost minimizing distributions cluster around an explicitly specified function that may have integral less than 1 if the minimum is not attained. If Γ is an f-divergence ball of radius k, the minimum is either attained for any choice of k, or it is/is not attained when k is less/larger than a critical value. A conjecture is formulated about extending this result beyond f-divergence balls.

Original language | English |
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Journal | IEEE Transactions on Information Theory |

DOIs | |

Publication status | Accepted/In press - ápr. 19 2018 |

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences