Publication

Bayesian Sequential Batch Design in Functional Data

Authors: Ping-Han Huang, Shuang Zhou, Ming-Hung Kao

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.

Optimal Next-stage Designs for Sparse Functional/Longitudinal Data

Authors: Ming-Hung Kao, Alejandro Vidales Aller, Ping-Han Huang

Selecting the best time points to collect informative observations for precisely predicting individual curves is an important optimal design issue for studies involving sparse longitudinal/functional data. Tackling this issue requires knowledge of unknown model parameters, and the previous works primarily yield locally optimal designs by replacing these parameters with their estimates from the prior stage. However, except for the parameter estimates, the data collected at the prior stage and the design used to collect them are discarded at the next stage. To avoid this waste of resources, a multi-stage design approach is proposed in this work. The primary design goal is to develop optimal designs for future subjects in the next stage, by adapting to the prior-stage design and by considering the trajectory recovery of all the curves in both the prior and next stages. An optimlaity criterion, relevant theoretical results, and an efficient computational approach are developed for finding such an optimal next-stage design. Numerical studies, including a real case, are conducted to compare the obtained design with other designs.

New Pilot-Study Design in Functional Data Analysis

Authors: Ping-Han Huang and Ming-Hung Kao

A primary focus on design problems in sparse functional data has revolved around finding the best time points to collect observations from subjects. Previous work has yielded locally optimal designs that rely on the estimation of unknown parameters from pilot studies. In contrast to the existing work, our study focuses on formulating a good pilot-study design to facilitate identifying optimal designs for subjects in the next study as well as recovering trajectories for subjects in the pilot study. A search algorithm is developed to generate such highquality pilot-study designs. We further demonstrate the usefulness of our designs by comparing with balanced incomplete block designs and random designs. Our simulation studies and real data application show that our designs yield better performance than the competing designs.

Optimal Designs for Functional Principal and Empirical Component Scores

Authors: Ming-Hung Kao and Ping-Han Huang

Sparse functional data analysis (FDA) is powerful for making inference on the underlying random function when noisy observations are collected at sparse time points. To have a precise inference, knowledge on optimal designs that allow the experimenters to collect informative functional data is crucial. Here, we propose a framework for selecting optimal designs to precisely predict functional principal and empirical component scores. Our work gives a relevant generalization of previous results on the design for predicting individual response curves. We obtain optimal designs, and evaluate the performance of commonly used designs. We demonstrate that without a judiciously selected design, there can be a great loss in statistical efficiency.

APA Citation: Kao, M.-H. & Huang, P.-H. (in press). Optimal Designs for Functional Principal and Empirical Component Scores. Statistica Sinica. https://doi.org/10.5705/ss.202023.0051

Hybrid Exact-approximate Design Approach for Sparse Functional Data

Authors: Ming-Hung Kao and Ping-Han Huang

Optimal designs for sparse functional data under the functional empirical component (FEC) settings are studied. This design issue has some unique features, making it different from classical design problems. To efficiently obtain optimal exact and approximate designs, new computational methods and useful theoretical results are developed, and a hybrid exact-approximate design approach is proposed. The proposed methods are demonstrated to be efficient via simulation studies and a real example.

APA Citation: Kao, M.-H., & Huang, P.-H. (2024). Hybrid Exact-approximate Design Approach for Sparse Functional Data. Computational Statistics & Data Analysis, 190, 107850. https://doi.org/10.1016/j.csda.2023.107850

• Ping-Han.Huang@asu.edu
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