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I am currently working on my bachelor thesis and I came across a sufficient statistic,

φ : X × Y → H of y | x

where X is a candidate set in this case strings, Y is a binary property space: {-1,1}, H is a Hilbert Space.

I understand that φ is sufficient if it does not depend on y | x but I just can’t grasp how a sufficient statistic could be constructed here. Any help would be appreciated!

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    Perhaps you were looking for stats.stackexchange.com? – theHigherGeometer Oct 25 '23 at 20:02
  • $\varphi$ is a sufficient statistic for a specified family of probability distributions on the space $X\times Y$ if the conditional distribution of the random variable taking values in $X\times Y$ given the value of $\varphi$ is the same for all probability distributions in that family. And you haven't told us which family of distributions that is. You have to understand what this definition says before you'll get anywhere with this. – Michael Hardy Oct 25 '23 at 21:02

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