Sequential Plans and Risk Evaluation

Introduced in 1990s, sequential plans generalize and optimize the classical sequential procedures allowing sampling in groups of variables sizes. Sequential plans are preferred to pure sequential procedures when the cost function is non-linear so that each observed group implies an additional fixed cost. Optimal plans minimize the risk, a weighted sum of the expected loss, cost of observations, and cost of groups. Although risk evaluation is a challenging problem in sequential planning, risk functions of sequentially planned probability ratio tests (SPPRT) can be obtained as roots of certain functional equations. Explicit solutions are derived for SPPRT on a lattice, allowing practitioners to compare exact risks and choose an optimal procedure.