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Motivated by the problem of predicting sleep states, we develop a mixedeffects model for binary time series with a stochastic component represented bya Gaussian process. The fixed component captures the effects of covariates onthe binary-valued response. The Gaussian process captures the residualvariations in the binary response that are not explained by covariates and pastrealizations. We develop a frequentist modeling framework that providesefficient inference and more accurate predictions. Results demonstrate theadvantages of improved prediction rates over existing approaches such aslogistic regression, generalized additive mixed model, models for ordinal data,gradient boosting, decision tree and random forest. Using our proposed model,we show that previous sleep state and heart rates are significant predictorsfor future sleep states. Simulation studies also show that our proposed methodis promising and robust. To handle computational complexity, we utilize Laplaceapproximation, golden section search and successive parabolic interpolation.With this paper, we also submit an R-package (HIBITS) that implements theproposed procedure.

Modeling Binary Time Series Using Gaussian Processes with Application to Predicting Sleep States