where m(x S+1 ), s 2 (x S+1 ) are the GP's mean and variance respectively and σ(x) is the observational noise from Equation . In reality an estimate from Equation 6 is used as a proxy for existing observations and an estimate based on the current GP fit is calculated for future observations. This is discussed in detail in Section 4.1.1. The choice of β tunes the level of reliability wanted on the final result, setting β = 0.5 means that the algorithm will compare design points based on the GP model's mean only in Equation 8 and uncertainty from Equation . With a higher β, EQI penalizes designs with high uncertainty and becomes more conservative. It should be noticed that, to calculate EQI using Equation , future noise σ 2 (x S+1 ) is required at any x S+1 as σ 2 (x S+1 ) also influence the performance of EQI.