Efficient computation of confidence intervals for Bayesian model predictions based on multidimensional parameter space.

A new algorithm is introduced to efficiently estimate confidence intervals for Bayesian model predictions based on multidimensional parameter space. The algorithm locates the boundary of the smallest confidence region in the multidimensional probability density function (pdf) for the model predictions by approximating a one-dimensional slice through the mode of the pdf with splines made of pieces of normal curve with continuous z values. This computationally efficient process (of order N) reduces estimation of the lower and upper bounds of the confidence interval to a multidimensional constrained nonlinear optimization problem, which can be solved with standard numerical procedures (of order N(2) or less). Application of the new algorithm is illustrated with a five-dimensional example involving the computation of 95% confidence intervals for predictions made with a Bayesian forecasting model for cognitive performance deficits of sleep-deprived individuals.