Modeling Cognitive Performance under Sleep Restriction

Document Type

Presentation Abstract

Presentation Date

11-18-2013

Abstract

Mathematical modeling of performance impairment due to sleep restriction produces the results that can be used to optimize work scheduling which, e.g., involve night shifts, and which, in turn, can reduce the risk of automotive, flight, and other accidents. Models’ parameters may be estimated using the data related to driver centered metrics such as lane deviation and eye movement. The fitted models can be used to predict driving performance and make drivers aware of cognitive impairments. Population information for the models can be collected in laboratory based studies on high-fidelity driving simulators. This information may be employed to construct prior distributions for model parameters; it can also be combined with real time driving data to predict driving performance. Individual metrics differ with respect to cost, ease of implementation, correlations, and noise, and it is often of interest to determine the most cost effective combination of metrics. In the linear setting, we analytically determine a simple relationship between the improvement in prediction accuracy due to a secondary task and the sample size for that task.

In the nonlinear case, we may assess the improvement in prediction MSE using simulation; however, for models stated in the form of differential equations with no analytic solution, such repeated evaluation of the Bayesian minimum mean squared error estimator (MMSE) can be time consuming. An alternative estimator, the Bayesian maximum a posteriori (MAP), can reduce these computations by one or more orders of magnitude; however, it does not guarantee minimum mean squared error. Simulations show that in some important nonlinear cases there is virtually no difference in accuracy between these two estimators.

We hypothesize that the reduction in estimator accuracy (owing to the substitution of the MAP for the MMSE) can be approximated without the need for numerical integration. We begin by considering a limited class of nonlinear modeling scenarios, and analytically approximate the increase in MSE due to using the MAP estimator for this class. Our work builds a foundation for further construction of methodology to quickly determine modeling scenarios (i.e., model functions, covariate values and prior parameters) for which the MAP estimator will result in no significant loss of accuracy.

Additional Details

Monday, November 18 at 3:10 p.m. in Math 103

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