Lastly, we focus briefly on the nonlinear case, where the BMSE generally lacks a closed form solution.
The average accuracy over individuals was assessed at time [mathematical expression not reproducible] by estimating the BMSE, as follows (cf.
The estimated BMSE of [mathematical expression not reproducible] when using only the primary data points was 0.
To set up the general procedure of improving prediction accuracy through Bayesian forecasting, we constructed the BMSE for a simple univariate random intercept model.
We applied the general procedure to a bivariate random intercept model and derived the BMSE of the primary response predictions for this model.
We found that the minimization of the BMSE with respect to the vector of times at which the data are collected can be divided into two subcases.
The BMSE of MMSE predictions for prediction BMSE in the univariate, linear, time-dependent model given by (58) is given by
Therefore, the BMSE of the estimated response is given by (A.
The BMSE of MMSE predictions for the univariate, linear, time-dependent model given by (58) is given by
Furthermore, the parameter BMSE matrix is given by (see Theorem A.
Unconstrained Minimization of the BMSE for the Univariate, Time-Dependent Linear Model
Evaluating the BMSE at this critical point, we find that