Information-theoretic analysis of multivariate single-cell signaling responses
Fig 1
Probabilities of correct discrimination between two inputs, xi and xj.
The input distribution, P(X) = (1/2, 1/2), visualized in (A), and the conditional output probabilities P(Y|X), presented in (B), can be translated, via the Bayes formula, into conditional input distributions, P(X|Y), visualized in (C). The conditional input distribution, P(X|Y), serves to calculate the probability of correct discrimination of the observation y, as shown in (D). Precisely, for any fixed output, y, vertical line in (B), the conditional input probability, in (C), P(X|Y = y), quantifies how likely it is that y was generated by each of the inputs. The probability of correct discrimination of the observation, y is given as the maximum of P(xi|Y = y) and P(xj|Y = y). Completely overlapping conditional output probabilities P(Y|X), left column, yield random discrimination as opposed to non-overlapping distributions yielding perfect discrimination, right column. The use of the conditional input distribution, P(X|Y), enables quantification of intermediate scenarios, middle column.