To protect or not to protect: Bayes decisions with forecasts (Q912769)

For a detection problem, e.g. against adverse weather, a Bayes solution is given. The problem is modelled by a discrete-time, finite-horizon Markov decision process with 2 states (adverse weather or not), 2 actions (protect or not) and the total expected loss criterion. The state process, assumed to be an i.i.d. sequence, is not observable, only a one- period-ahead forecast is submitted. Two kinds of forecasts are treated separately: categorical and probabilistic. The solutions are analytically represented and structurally characterized. Especially it is worked out how the partial ordering of forecasts (according to a so-called sufficiency property) influences the optimal strategy. Proofs, comments and the relevant history of research are given in great detail.