A Response Model with a Fixed Probability Boundary

Abstract

The optimal policy for either problem TDC or DC prescribes a decision rule that is deterministic in the probability boundaries ϒ* or ϒ*, respectively. Given the problem parameters α, f_j(x), w, and F, the value of ϒ* (or ϒ*) may be obtained numerically together with the minimum expected loss R(P) (or R(P)). The optimal policy may then be tested with data collected in detection of change experiments, as done in Chapter 8. If the major purpose of such an investigation is to assess the DM’s efficiency in detecting a change, then the actual loss he incurs may be compared to the appropriate minimum loss expected in employing the optimal policy. As shown in Chapter 6, however, such an investigation may not be very informative because of the flatness of the expected loss functions at the minima. A psychologically more valuable prediction concerns the actual decision rule employed by the DM, According to the optimal policy, the decision rule should be stated only in terms of P_n-1 = P, the probability of change prior to stage n, as compared to the appropriate probability boundary. P may be estimated directly, by employing one of the many procedures for assessing subjective probabilities (see Slovic and Lichtenstein, 1971, for a review of these procedures), or indirectly, by assuming a model for revision of probabilities, Bayesian or not, which predicts the stage-to-stage changes in P Note also that adherence to the optimal policy implies ratio scale utilities of the delay and error costs, both of which should be specified in the task instructions.