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Bayesian prediction for physical models with application to the optimization of the synthesis of pharmaceutical products using chemical kinetics

Bayesian prediction for physical models with application to the optimization of the synthesis of pharmaceutical products using chemical kinetics
Bayesian prediction for physical models with application to the optimization of the synthesis of pharmaceutical products using chemical kinetics
Quality control in industrial processes is increasingly making use of prior scientific knowledge, often encoded in physical models that require numerical approximation. Statistical prediction, and subsequent optimization, is key to ensuring the process output meets a specification target. However, the numerical expense of approximating the models poses computational challenges to the identification of combinations of the process factors where there is confidence in the quality of the response. Recent work in Bayesian computation and statistical approximation (emulation) of expensive computational models is exploited to develop a novel strategy for optimizing the posterior probability of a process meeting specification. The ensuing methodology is motivated by, and demonstrated on, a chemical synthesis process to manufacture a pharmaceutical product, within which an initial set of substances evolve according to chemical reactions, under certain process conditions, into a series of new substances. One of these substances is a target pharmaceutical product and two are unwanted by-products. The aim is to determine the combinations of process conditions and amounts of initial substances that maximize the probability of obtaining sufficient target pharmaceutical product whilst ensuring unwanted by-products do not exceed a given level. The relationship between the factors and amounts of substances of interest is theoretically described by the solution to a system of ordinary differential equations incorporating temperature dependence. Using data from a small experiment, it is shown how the methodology can approximate the multivariate posterior predictive distribution of the pharmaceutical target and by-products, and therefore identify suitable operating values.
0167-9473
126-142
Overstall, Antony
c1d6c8bd-1c5f-49ee-a845-ec9ec7b20910
Woods, David
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Martin, Kieran James
ebe4400b-e3c8-41ef-8986-7c47c8ba9294
Overstall, Antony
c1d6c8bd-1c5f-49ee-a845-ec9ec7b20910
Woods, David
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Martin, Kieran James
ebe4400b-e3c8-41ef-8986-7c47c8ba9294

Overstall, Antony, Woods, David and Martin, Kieran James (2019) Bayesian prediction for physical models with application to the optimization of the synthesis of pharmaceutical products using chemical kinetics. Computational Statistics and Data Analysis, 132, 126-142. (doi:10.1016/j.csda.2018.10.013).

Record type: Article

Abstract

Quality control in industrial processes is increasingly making use of prior scientific knowledge, often encoded in physical models that require numerical approximation. Statistical prediction, and subsequent optimization, is key to ensuring the process output meets a specification target. However, the numerical expense of approximating the models poses computational challenges to the identification of combinations of the process factors where there is confidence in the quality of the response. Recent work in Bayesian computation and statistical approximation (emulation) of expensive computational models is exploited to develop a novel strategy for optimizing the posterior probability of a process meeting specification. The ensuing methodology is motivated by, and demonstrated on, a chemical synthesis process to manufacture a pharmaceutical product, within which an initial set of substances evolve according to chemical reactions, under certain process conditions, into a series of new substances. One of these substances is a target pharmaceutical product and two are unwanted by-products. The aim is to determine the combinations of process conditions and amounts of initial substances that maximize the probability of obtaining sufficient target pharmaceutical product whilst ensuring unwanted by-products do not exceed a given level. The relationship between the factors and amounts of substances of interest is theoretically described by the solution to a system of ordinary differential equations incorporating temperature dependence. Using data from a small experiment, it is shown how the methodology can approximate the multivariate posterior predictive distribution of the pharmaceutical target and by-products, and therefore identify suitable operating values.

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Accepted/In Press date: 22 October 2018
e-pub ahead of print date: 2 November 2018
Published date: April 2019

Identifiers

Local EPrints ID: 425529
URI: http://eprints.soton.ac.uk/id/eprint/425529
ISSN: 0167-9473
PURE UUID: aed5c7ef-47a2-43b2-8afb-ecfc1c683f71
ORCID for Antony Overstall: ORCID iD orcid.org/0000-0003-0638-8635
ORCID for David Woods: ORCID iD orcid.org/0000-0001-7648-429X

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Date deposited: 23 Oct 2018 16:30
Last modified: 30 Jan 2020 05:03

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