We obtain the likelihood of the control data based on the assumptions that they correspond to extreme responses and that measurement error has a similar structure to the curve. The bottom control data D b include the observations r b,j for j = 1, . . . , N b and are considered as measurements in which x is extremely large, such that x → ∞. In this limit, the Hill equation yields R b and measured responses are r b,j = R b + b,j where b,j 's are the measurement errors. Because the controls may be measurements of solutions containing different substances than the curve, we cautiously assume that the measurement errors follow different normal distributions for the control and curve data. Specifically, b,j 's independently and identically follow the normal distribution N (0, σ 2 b ), where σ 2 b is a constant, the variance of the measurement error. Like σ 2 c , σ 2 b is an unknown nuisance parameter. At the other extreme, the top control data D t include the observations r t,j for j = 1, . . . , N t and correspond to x → -∞. Based on the Hill equation in this limit, r t,j = R t + t,j