  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.
