Figure 3

Illustration of mutual information between discrete and continuous variables. (a) The expression level of gene Y is modulated by a SNP X. The distribution of Y alone is a Gaussian with entropy H(Y)= 2.61. When conditional on SNP X, the gene Y is a bimodal Gaussian whose mutual information with SNP X is H(Y:X)=0.57. (b) The gene Y and SNP X are independent. Although gene Y follows a Gaussian distribution and its entropy is the same as the entropy in (a), its distribution conditional on SNP X remains a unimodal Gaussian and its mutual information with SNP X is H(Y:X)=0.