Figure 1
From: Quantification of expected information gain in visual acuity and contrast sensitivity tests
(a) Probability distribution of a quantity \(x\) occurring in population \(X, P\left(x\right)\). (b) Probability distribution of obtaining measurement \(y\) given \(x\) is the true value being measured: \(P\left(y|x\right)\). (c) Probability distribution of obtaining a measurement \(y\) from all potential measurement outcomes \(Y\) regardless of the underlying true value, \(P(y)\). (d) Posterior distribution of \(X, P\left(x|y\right),\) following a measurement outcome \(y\). (e) Expected information gain \(IG(X|Y)\) is the difference between \(H\left(X\right)\) and the expected posterior entropy \(H\left(X|Y\right)\). Expected information gain \(IG\left(Y|X\right)\) is the difference between \(H\left(Y\right)\) and the expected residual entropy \(H\left(Y|X\right)\). \(IG\left(X|Y\right)=IG(Y|X)\).
