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Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.

3 votes
1 answer
477 views

Strictly Proper Scoring Rules and f-Divergences

Let $S$ be a scoring rule for probability functions. Define $EXP_{S}(Q|P) = \sum \limits_{w} P(w)S(Q, w)$. Say that $S$ is striclty proper if and only if $P$ always minimises $EXP_{S}(Q|P)$ as a fu …
3 votes
1 answer
358 views

Minimising the f-divergence to a conditional probability constraint

Let $P$ be a probability distribution and let $A$ and $B$ be some events, and suppose that we want to minimise an $f$-divergence between $P$ and the set of all distributions $Q$ that satisfy that cons …