Bayesian Sequential Batch Design in Functional Data

Ping-Han Huang, Shuang Zhou, Ming-Hung Kao
Arizona State University

Many longitudinal studies are hindered by noisy observations sampled at irregularand sparse time points. In handling such data and optimizing the design of a study,most of existing functional data analysis literature 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 enhance cost efficiency. To fill the gap, we propose a Bayesian hierarchical model with Gaussian processes, leading to a new form of the utility function based on the Shannon information between posterior predictive distributions. The proposed utility function has a closed form that improves the computation efficiency by avoiding the evaluation of intractable marginal likelihood, which has been a common problem in Bayesian optimal designs. We further implement a simulated annealing algorithm to find the optimal design, and sequentially identify optimal designs for new subject batches. Our procedure opens 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.