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**Modeling binary time series using Gaussian processes with application to predicting sleep states.**
*(English)*
Zbl 1422.62219

Summary: Motivated by the problem of predicting sleep states, we develop a mixed effects model for binary time series with a stochastic component represented by a Gaussian process. The fixed component captures the effects of covariates on the binary-valued response. The Gaussian process captures the residual variations in the binary response that are not explained by covariates and past realizations. We develop a frequentist modeling framework that provides efficient inference and more accurate predictions. Results demonstrate the advantages of improved prediction rates over existing approaches such as logistic 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 predictors for future sleep states. Simulation studies also show that our proposed method is promising and robust. To handle computational complexity, we utilize Laplace approximation, golden section search and successive parabolic interpolation. With this paper, we also submit an R-package (HIBITS) that implements the proposed procedure.

### MSC:

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

60G15 | Gaussian processes |

62M20 | Inference from stochastic processes and prediction |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

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