fdesigns: Bayesian Optimal Designs of Experiments for Functional Models in R

TL;DR

The paper introduces the R package fdesigns, which implements Bayesian optimal design methods for experiments involving functional models with dynamic, infinite-dimensional factors, using basis function dimension reduction.

Contribution

It presents a novel methodology and software implementation for designing experiments with functional factors, addressing challenges of infinite-dimensional models.

Findings

Effective dimension reduction via B-spline basis functions.

Successful application to functional linear and generalized linear models.

Demonstrated efficiency in designing experiments with profile and scalar factors.

Abstract

This paper describes the R package fdesigns that implements a methodology for identifying Bayesian optimal experimental designs for models whose factor settings are functions, known as profile factors. This type of experiments which involve factors that vary dynamically over time, presenting unique challenges in both estimation and design due to the infinite-dimensional nature of functions. The package fdesigns implements a dimension reduction method leveraging basis functions of the B-spline basis system. The package fdesigns contains functions that effectively reduce the design problem to the optimisation of basis coefficients for functional linear functional generalised linear models, and it accommodates various options. Applications of the fdesigns package are demonstrated through a series of examples that showcase its capabilities in identifying optimal designs for functional linear and generalised linear models. The examples highlight how the package's functions can be used to efficiently design experiments involving both profile and scalar factors, including interactions and polynomial effects.