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Abstract:
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Bayesian Melding (BM) and downscaling are two Bayesian approaches used to combine data from different sources to make statistical inferences. We propose a general framework based on these two approaches to obtain the path of moving objectives, where accurate but sparse direct observations of location must be combined with simulated observations from a high-resolution but biased model. Use of this framework is illustrated by a case study of tracking marine mammals. To enable fast calculation for the high dimensional (big) data encountered by the BM approach, we exploit the properties of the processes along with approximations to the likelihood to break the high dimensional problem into a series of lower dimensional problems. The alternative downscaling approach, that connects the two sources of observations via a linear mixed effect model, is implemented with R-INLA. The two approaches are compared by cross-validation and they achieve similar results: both provide accurate, high-resolution estimates of the animal's path along with Bayesian credible intervals to characterize the uncertainty about the estimated path. We further extend the BM with stochastic differential equations.
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