Nested sampling approach to set-membership estimation

This paper is concerned with set-membership estimation in nonlinear dynamic systems. The problem entails characterizing the set of all possible parameter values such that given predicted outputs match their corresponding measurements within prescribed error bounds. Most existing methods to tackle this problem rely on outer-approximation techniques, which perform poorly when the parameter host set is large due to the curse of dimensionality. An adaptation of nested sampling—a Monte Carlo technique introduced to compute Bayesian evidence—is presented herein. The nested sampling algorithm leverages efficient strategies from Bayesian statistics for generating an inner-approximation of the desired parameter set. Several case studies are presented to demonstrate the approach

Bayesian approach to probabilistic design space characterization: a nested sampling strategy

Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space characterization, which determine a feasibility probability that can be used as a measure of reliability and risk by the practitioner. An adaptation of nested sampling—a Monte Carlo technique introduced to compute Bayesian evidence—is presented. The nested sampling algorithm maintains a given set of live points through regions with increasing probability feasibility until reaching a desired reliability level. It furthermore leverages efficient strategies from Bayesian statistics for generating replacement proposals during the search. Features and advantages of this algorithm are demonstrated by means of a simple numerical example and two industrial case studies. It is shown that nested sampling can outperform conventional Monte Carlo sampling and be competitive with flexibility-based optimization techniques in low-dimensional design space problems. Practical aspects of exploiting the sampled design space to reconstruct a feasibility probability map using machine learning techniques are also discussed and illustrated. Finally, the effectiveness of nested sampling is demonstrated on a higher-dimensional problem, in the presence of a complex dynamic model and significant model uncertainty

Critical assessment of parameter estimation methods in models of biological oscillators

Many biological systems exhibit oscillations in relation to key physiological or cellular functions, such as circadian rhythms, mitosis and DNA synthesis. Mathematical modelling provides a powerful approach to analysing these biosystems. Applying parameter estimation methods to calibrate these models can prove a very challenging task in practice, due to the presence of local solutions, lack of identifiability, and risk of overfitting. This paper presents a comparison of three state-of-the-art methods: frequentist, Bayesian and set-membership estimation. We use the Fitzhugh-Nagumo model with synthetic data as a case study. The computational performance and robustness of these methods is discussed, with a particular focus on their predictive capability using cross-validation