Approximate Expectation Propagation for Bayesian Inference on Large-scale Problems
where k indexes experimental replicates, i indexes the probe positions, j indexes the binding positions, andN ( jPj aji jjsjbj; i) represents the probability density function of a Gaussian distribution with mean Pj aji jjsjbj and variance i. We assign prior distributions on the binding event bj and the binding strength sj: p(bjj j) = bj j (1 j)1 bj (3) p0(sj) = Gamma(sjjc0; d0) (4) where Gamma( jc0; d0) stands for the probability density functions of Gamma distributions with hyperparameters c0 and d0. We assign a hyperprior distribution on the binding probability j as: p0( j) = Beta( jj 0; 0) (5)