The Raven's Hat: Fallen Pictures, Rising Sequences, and Other Mathematical Games by Jonas Peters & Nicolai Meinshausen

Author:Jonas Peters & Nicolai Meinshausen [Peters, Jonas & Meinshausen, Nicolai]
Language: eng
Format: epub
ISBN: 9780262044516
Google: bykWEAAAQBAJ
Publisher: MIT Press
Published: 2021-02-02T00:33:03.128013+00:00

Information Content and Selecting Hypotheses

Information content is closely related to the ability to identify the true hypothesis among a set of possible hypotheses. This set is often written as Ω. Let us start again with the number guessing game described near the start of this section. There, Ω = {0, 1, 2, …, 15}.

We now describe any strategy as a map to help us navigate from the set of possible hypotheses to a set of possible answers. Let ω* ∈ Ω denote the secret number that your friend thinks about but that is unknown to us. Asking a yes/no question now corresponds to constructing a function (“O” for outcome),

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