An Efficient Framework for Solving a Convex, State-Space Heartbeat Dynamics Model

The statistical study of interbeat intervals of the heart has been long investigated to track the cardiovascular and autonomic nervous systems. Typically used methods perform windowing and compute averages but do not capture the probabilistic nature of these intervals. More recent approaches capture the point process nature of interbeat intervals but result in a nonconvex model-fitting procedure, thus requiring delicate care with initialization and/ or approximations to compute reasonable estimates. Here, we consider a state-space point process model with a latent Gauss-Markov process and a gamma generalized linear model for interbeat intervals. We show that the maximum a posteriori (MAP) estimation problem is convex and describe an efficient, exact procedure to solve it with the alternating direction method of multipliers. Our method is applied to electrocardiogram recordings from a tilt table study. We demonstrate sensible goodness of fit with Kolmogorov-Smirnov plots. We additionally show that the estimated mean heart rate - a statistic of heartbeat dynamics - accurately reflects the dynamic postural changes in the tilt table study.