Discrimination analysis when the variates are grouped and observed in sequential order

Suppose that measurements Math', i = l,....,k, are consecutively taken on an individual at the prescribed costs C_i, i = l,....,k. the individual comes from one of the two populations H₁ and H₂, and it is desired to detect which population the individual belongs to. Given the loss incurreed in selecting population H_r when in fact it belongs to H_s, the prior probability P_r of H_r (r = 1,2), and assuming that H_r has the normal distribution N(µ_r, V), r = 1,2, we derive the sequential Bayesian solution of the discrimination problem when µ₁, µ₂ and V are known. When µ_r, V are unknown and must be estimated, we propose a solution which is asymptotic Bayesian with exponential convergence rate.