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Weighted information and weighted entropy

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The talk will be about the weighted information (WI) and weighted entropy (WE) where outcomes of the same probability contribute according to their weight/utility. Think of two events: a tsunami somewhere far away and a cracking tree in a garden next door. Both are rare and hence quite informative (say they convey an equal amount of info). But they clearly are of different importance to us. The emerging concepts of WI/WE have some peculiar properties; this is what we try to explore. Math results include generalisations of Ky Fan and Hadamard inequalities and extensions of the Shannon-McMillan-Breiman theorem.

No preliminary knowledge of Probability/Info Theory will be assumed.

This talk is part of the Probability series.

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