Wikipedia:Reference desk/Archives/Mathematics/2021 January 19

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January 19

Help identifying statistics(?) notation

I recently saw the equation fragment

${\hat {R}}(i,\mathbf {x} _{0})=\mathbb {E} _{\mathbf {x} _{i}\sim {\hat {p}}(\mathbf {x} _{i}|\mathbf {x} _{0})}\,D_{KL}[q(\mathbf {z} |\mathbf {x} _{i},\mathbf {x} _{0})||q(\mathbf {z} |\mathbf {x} _{0})]-$

and I feel like I recognise it from my previous statistics education, but I can't quite place it — does anyone know what ${\hat {R}}(i,\mathbf {x} _{0})$ refers to in this context? — crh23 (Talk) 12:21, 19 January 2021 (UTC)

The hat generally indicates a statistical estimate of some population parameter or other population characteristic.^[1][2] So this denotes an estimate of $R(i,\mathbf {x} _{0}),$ but what the latter stands for, I cannot tell. It might help if you revealed the source – presumably not a napkin.  --Lambiam 15:08, 19 January 2021 (UTC)

This is actually mentioned in our article Estimator: "An estimator of $\theta$ is usually denoted by the symbol ${\widehat {\theta }}$." And Hat operator § Estimated value has: "In statistics, the hat is used to denote an estimator or an estimated value."  --Lambiam 01:37, 20 January 2021 (UTC)

The blackboard bold "E" usually means expectation and the subscript tells you the distribution over which one takes the expectation. Robinh (talk) 19:15, 20 January 2021 (UTC)

Thanks to all for the replies, I realise I phrased my question poorly: I am aware of the notation (hat-notation for an estimator, expectation over a distribution, K-L divergence), but I am trying to figure out where that (partial) equation comes from, i.e. what $R$ actually is that an estimator of it could take that form. — crh23 (Talk) 22:34, 26 January 2021 (UTC)

Have a look at equation (9) of the paper "EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE".  --Lambiam 00:45, 27 January 2021 (UTC)