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Mathematically, given a sequence of observed variables xt and hidden states zt, at time t=1,...,T, the joint distribution for this model can be specified as follows:
Overview of the hidden Markov model (HMM) approach showing the main processing and modeling steps involved in the method. (A) The Behapp app was installed and collected data passively. (B) These data were processed into activity bins. (C) The HMM was trained on the binned hourly time series.
J Med Internet Res 2025;27:e64007
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Longitudinal plot of a representative 3-week interval of minute-level metabolic equivalent of task (MET) data (left) from (A) 1 female individual (F, blue) and (B) 1 male individual (M, red), with the histogram of the MET values for each separated by awake (light) and asleep (dark) values (right). MET values were examined at minute-level resolution.
J Med Internet Res 2025;27:e66231
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In a robust version of this hierarchical model, we specified the true study effects as arising from a t-distribution (with estimated df) to increase robustness against potential outliers. We chose vaguely informative default priors for all model parameters and conducted prior sensitivity analyses. Multimedia Appendix 4 [20] provides more details. All models were estimated using Hamiltonian Monte Carlo sampling [30].
J Med Internet Res 2025;27:e63111
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A Social Media Study of Portrayals of Bipolar Disorders on YouTube: Content and Thematic Analyses
J Med Internet Res 2025;27:e67129
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