Transitions between sleep stages are described in the article “Multinomial Logistic Estimation of…
Transitions between sleep stages are described in the article “Multinomial Logistic Estimation of Markov-Chain Models for Modeling Sleep Architecture in Primary Insomnia Patients” (J. Pharmacokinet. Pharmacodyn., 2010:137–155). The following one-step transition probabilities for the five stages awake (AW), stage 1 sleep (ST1), stage 2 sleep (ST2), slowwave sleep (SWS), and rapid-eye movement sleep (REM) were obtained from a graph in the article: The time index of the Markov chain corresponds to half-hour intervals (i.e., n = 1 is 30 min after the beginning of the study, n = 2 is 60 min in, etc.). Initially, all patients in the study were awake. (a) Let v0 denote the probability vector for X0, the initial state of a patient in the sleep study. Determine v0. (b) Without performing any matrix computations, determine the distribution of patients’ sleep states 30 min (one time interval) into the study. (c) Determine the distribution of patients’ sleep states 4 h into the study. [Hint: What time index corresponds to the 4-h mark?] Apr 08 2022 03:25 PM
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