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).

A new mathematical model for the homeostatic effects of sleep loss on neurobehavioral performance.

The two-process model of sleep regulation makes accurate predictions of sleep timing and duration for a variety of experimental sleep deprivation and nap sleep scenarios. Upon extending its application to waking neurobehavioral performance, however, the model fails to predict the effects of chronic sleep restriction. Here we show that the two-process model belongs to a broader class of models formulated in terms of coupled non-homogeneous first-order ordinary differential equations, which have a dynamic repertoire capturing waking neurobehavioral functions across a wide range of wake/sleep schedules.