Regularized Differentiation for Bioburden Density Estimation in Planetary Protection

Conference · Thu Jun 27 00:00:00 EDT 2024

OSTI ID:3020589

Gribok, Andrei Vasilyevich ^[1]; DiNicola, Michael ^[2]; Guan, Lisa ^[2]

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1. Idaho National Laboratory
2. California Institute of Technology, Jet Propulsion Laboratory

In this paper, we propose and investigate the performance of two novel shrinkage estimators for bioburden density estimation in planetary protection. The estimators are based on the regularized differentiation of a cumulative count of colony forming units collected throughout the data collecting session or the life cycle of the entire mission. The regularized differentiation recasts the problem of bioburden density estimation as a linear least squares problem. The least squares problem is then solved through regularization techniques, such as truncated singular value decomposition and penalized least squares. The regularization is necessary to avoid noise amplification during the differentiation of noisy data. The two regularization estimators are compared with four other commonly used estimators to simultaneously evaluate the means of multivariable independent Poisson distributions: the maximum likelihood, noninformative Bayes estimator with Jeffreys prior, Empirical Bayes using conjugate gamma-Poisson model with gamma parameters selected by method of moments, and the Clevenson-Zidek estimator. It is shown through computer-simulated data that the regularized differentiation based on ridge regression has the smallest mean-squared error among all estimators. The analysis of shrinkage mechanism implemented by regularized differentiation is performed, and it is shown that the regularized differentiation amounts to performing a weighted averaging of all the samples. The weights are determined by the regularization parameter automatically selected by the L-curve technique. Since the method of least squares makes no distributional assumptions about the data, it presents an attractive technique for bioburden density estimation when there are concerns about the misspecification of the distributional model. The paper concludes with the analysis of the bioburden data collected during InSight mission and directions for future work.

• Research Organization: Idaho National Laboratory (INL), Idaho Falls, ID (United States)
• Sponsoring Organization: USDOE Office of Nuclear Energy (NE); USDOE Office of Nuclear Energy (NE)
• DOE Contract Number: AC07-05ID14517
• OSTI ID: 3020589
• Report Number(s): INL/CON-24-78570
• Resource Type: Conference proceedings
• Conference Information: The 34-th European Safety and Reliability Conference-ESREL2024, Jagiellonian University, Cracow, Poland, 06/23/2024 - 06/27/2024
• Country of Publication: United States
• Language: English

Related Subjects

97 - MATHEMATICS AND COMPUTING
Bioburden density
ill-posed problems
least squares
Planetary protection
Regularization