where is the mutual information between two random variables and H(•) is the entropy of a probability distribution p(•). The mutual information is the reduction in the entropy of the probability density function of the location of the optimum NPM, x * , as a result of observing the property x n+1 if the acquisition strategy were purely exploration and purely exploitation. Pure exploration dictates x n+1 = arg max σ(x), but this NPM has a poor property. Pure exploitation dictates x n+1 = arg max ŷ (x), but this NPM is too close to an existing observation. EI balances the trade-off by picking an NPM with both a high uncertainty and high predicted property.