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

= January 19 =

Help identifying statistics(?) notation
I recently saw the equation fragment "\mathbf{x}_0)}\, D_{KL}[q(\mathbf{z}" 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? — crh 23   &thinsp;(Talk) 12:21, 19 January 2021 (UTC)


 * The hat generally indicates a statistical estimate of some population parameter or other population characteristic. 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 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. — crh 23   &thinsp;(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)