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In this paper, we introduce a model for multivariate, spatio-temporalfunctional data. Specifically, this work proposes a mixture model that is usedto perform spatio-temporal prediction (cokriging) when both the response andthe additional covariates are functional data. The estimation of such models inthe context of expansive data poses many methodological and computationalchallenges. We propose a new Monte Carlo Expectation Maximization algorithmbased on importance sampling to estimate model parameters. We validate ourmethodology using simulation studies and provide a comparison to previouslyproposed functional clustering methodologies. To tackle computationalchallenges, we describe a variety of advances that enable application on largespatio-temporal datasets. The methodology is applied on Argo oceanographic datain the Southern Ocean to predict oxygen concentration, which is critical toocean biodiversity and reflects fundamental aspects of the carbon cycle. Ourmodel and implementation comprehensively provide oxygen predictions and theirestimated uncertainty as well as recover established oceanographic fronts.

A multivariate functional-data mixture model for spatio-temporal data: inference and cokriging