Prediction Accuracy in Multivariate Repeated-Measures Bayesian Forecasting Models with Examples Drawn from Research on Sleep and Circadian Rhythms

Figure 6

Illustration of three types of absolute minima of the total cost of obtaining a fixed average prediction accuracy inside the region defined by (43). Each plot shows the total cost plotted against secondary response sample size . For given, the primary response sample size that obtains a fixed BMSE of in the expected primary response is computed using (38). The lower and upper boundaries of the region defined by (43) are shown with solid vertical lines. (a) shows an interior point minimum, obtained by letting . This type of solution occurs when the minimum of the unconstrained cost function lies within the region defined by (43). (b) shows a lower boundary solution, obtained by letting . This type of solution occurs when the minimum of the unconstrained cost function lies below the feasible region defined by (43). (c) shows an upper boundary solution, obtained by letting . This type of solution occurs when the minimum of the unconstrained cost function lies above the region defined by (43).

(a)

(b)

(c)