Bayesian Sequential Batch Design in Functional Data
Keywords: Sequential Batch Design, Bayesian Hierarchical Model, Gaussian Process, Functional Data, Simulated Annealing
Abstract: Many longitudinal studies are hindered by noisy observations sampled at irregular and sparse time points. In handling such data and optimizing the design of a study, most of the existing functional data analysis focuses on the frequentist approach that bears the uncertainty of model parameter estimation. While the Bayesian approach as an alternative takes into account the uncertainty, little attention has been given to sequential batch designs that enable information update and cost efficiency. To fill the gap, we propose a Bayesian hierarchical model with Gaussian processes which allows us to propose a new form of the utility function based on the Shannon information between posterior predictive distributions. The proposed procedure sequentially identifies optimal designs for new subject batches, opening a new way for incorporating the Bayesian approach in finding the optimal design and enhancing model estimation and the quality of analysis with sparse data.
Submission Number: 59
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