ABSTRACT
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.
Subject(s)
Algorithms , Bayes Theorem , Computer Simulation , Confidence IntervalsABSTRACT
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. We examine a specific case of this new model class, and demonstrate the existence of a bifurcation: for daily amounts of wakefulness less than a critical threshold, neurobehavioral performance is predicted to converge to an asymptotically stable state of equilibrium; whereas for daily wakefulness extended beyond the critical threshold, neurobehavioral performance is predicted to diverge from an unstable state of equilibrium. Comparison of model simulations to laboratory observations of lapses of attention on a psychomotor vigilance test (PVT), in experiments on the effects of chronic sleep restriction and acute total sleep deprivation, suggests that this bifurcation is an essential feature of performance impairment due to sleep loss. We present three new predictions that may be experimentally verified to validate the model. These predictions, if confirmed, challenge conventional notions about the effects of sleep and sleep loss on neurobehavioral performance. The new model class implicates a biological system analogous to two connected compartments containing interacting compounds with time-varying concentrations as being a key mechanism for the regulation of psychomotor vigilance as a function of sleep loss. We suggest that the adenosinergic neuromodulator/receptor system may provide the underlying neurobiology.
