Bayesian design for mathematical models of fruit growth based on misspecified prior information

TL;DR

This paper introduces a Bayesian design method for ODE-based models that incorporates spline terms to handle misspecified prior information, improving data collection efficiency in agricultural fruit growth studies.

Contribution

It proposes a flexible Bayesian design approach using spline-augmented ODEs to maintain efficiency despite prior misspecification.

Findings

Effective in modeling fruit growth with misspecified priors

Enhances data collection efficiency in agricultural studies

Flexible ODE models improve robustness to prior errors

Abstract

Bayesian design can be used for efficient data collection over time when the process can be described by the solution to an ordinary differential equation (ODE). Typically, Bayesian designs in such settings are obtained by maximising the expected value of a utility function that is derived from the joint probability distribution of the parameters and the response, given prior information about an appropriate ODE. However, in practice, appropriately defining such information \textit{a priori} can be difficult due to incomplete knowledge about the mechanisms that govern how the process evolves over time. In this paper, we propose a method for finding Bayesian designs based on a flexible class of ODEs. Specifically, we consider the inclusion of spline terms into ODEs to provide flexibility in modelling how the process changes over time. We then propose to leverage this flexibility to form designs that are efficient even when the prior information is misspecified. Our approach is motivated by a sampling problem in agriculture where the goal is to provide a better understanding of fruit growth where prior information is based on studies conducted overseas, and therefore is potentially misspecified.