Here, we extend the case in Equation ( ) to case where one or more of the scoring components are random variables, i.e., the values of each scoring component are distributed according to some probability distribution 𝑠 𝑖 (𝑥)~𝑝 𝑖 (𝑠|𝑥). We indicate realized samples of scoring component 𝑖 with a second index and no parenthesis 𝑠 𝑖,𝑗|𝑥 .We assume that different scoring components are independent, conditioned on the compound in question, which implies that the MPO score is distributed according to a transformed distribution of all of these components 𝑀𝑃𝑂(𝑥)~𝑝 𝑀𝑃𝑂 (𝑀𝑃𝑂|𝑥