Efficient estimation of temporal Gaussian processes models for physical activity level on a large scale population study

Rapid developments in streaming data technologies are continuing to generate increased interest in monitoring human activity. Wearable devices, such as wrist-worn sensors that monitor gross motor activity (actigraphy), have become prevalent. An Actigraph unit continually records the activity level of an individual, producing a very large amount of data at a high-resolution that can be immediately downloaded and analyzed. While this kind of big data includes both spatial and temporal information, the variation in such data seems to be more appropriately modeled by considering stochastic evolution through time while accounting for spatial information separately. We propose a comprehensive Bayesian hierarchical modeling and inferential framework for actigraphy data reckoning with the massive sizes of such databases while attempting to offer full inference. Building upon recent developments in this field, we construct Nearest Neighbour Gaussian Processes(NNGPs) for actigraphy data to compute at large temporal scales. More specifically, we construct a temporal NNGP and we focus on the optimized implementation of the collapsed algorithm in this specific context. This approach permits improved model scaling while also offering full inference. We test and validate our methods on simulated data and subsequently apply and verify their predictive ability on an original data-set concerning a health study conducted by the Fielding School of Public Health of the University of California Los Angeles.