Bayesian Approach to Probabilistic Design Space Characterization: A Nested Sampling Strategy

TL;DR

This paper introduces a Bayesian nested sampling method for probabilistic design space characterization in pharmaceutical manufacturing, providing a reliable measure of feasibility and risk with demonstrated advantages over traditional sampling techniques.

Contribution

It adapts nested sampling for design space analysis, enabling efficient probability estimation and risk assessment in complex, low-dimensional, and high-dimensional problems.

Findings

Nested sampling outperforms conventional Monte Carlo methods.

The approach is effective in low-dimensional and high-dimensional problems.

Feasibility probability maps can be reconstructed using machine learning.

Abstract

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.