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A coherent framework for learning spatiotemporal piecewise-geodesic trajectories from longitudinal manifold-valued data. (English) Zbl 1474.62463

Summary: This paper provides a coherent framework for studying longitudinal manifold-valued data for which the dynamic changes over time. We introduce a Bayesian mixed-effects model that allows estimating both a group-representative piecewise-geodesic trajectory in the Riemannian space of shape and interindividual variability. We prove the existence of the maximum a posteriori estimate and its asymptotic consistency under reasonable assumptions. Due to the nonlinearity of the proposed model, we use a stochastic version of the expectation-maximization algorithm to estimate the model parameters. Our simulations show that our model is not noise-sensitive and succeeds in explaining various paths of progression.

MSC:

62R30 Statistics on manifolds
62F12 Asymptotic properties of parametric estimators
62F15 Bayesian inference
62J05 Linear regression; mixed models
62P10 Applications of statistics to biology and medical sciences; meta analysis

Software:

Monolix
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