Mô hình Quasi-hóa học Ngẫu nhiên cho Sự Tăng trưởng của Vi khuẩn: Cập nhật Tham số Bayesian Biến thiên

Panagiotis Tsilifis1, William J. Browning2, Thomas E. Wood2, Paul K. Newton3, Roger G. Ghanem1
1Department of Civil Engineering, University of Southern California, Los Angeles, USA
2Applied Mathematics Inc., Gales Ferry, USA
3Department of Aerospace and Mechanical Engineering and Mathematics, University of Southern California, Los Angeles, USA

Tóm tắt

Chúng tôi phát triển các phương pháp Bayesian để xây dựng và ước lượng một mô hình quasi-hóa học ngẫu nhiên (QCM) cho sự tăng trưởng của vi khuẩn. QCM xác định rõ ràng, được mô tả như một hệ thống ODE phi tuyến, được xem như một hệ thống động lực học với các tham số ngẫu nhiên, và một cách tiếp cận biến thiên được sử dụng để xấp xỉ các phân phối xác suất của chúng và khám phá sự lan truyền của sự không chắc chắn qua mô hình. Cách tiếp cận này bao gồm việc xấp xỉ phân phối hậu nghiệm của các tham số bằng một phép đo xác suất được chọn từ một gia đình tham số, thông qua việc tối thiểu hóa sự phân kỳ Kullback–Leibler của chúng.

Từ khóa

#Mô hình Quasi-hóa học ngẫu nhiên #sự tăng trưởng của vi khuẩn #phương pháp Bayesian #sự không chắc chắn #phân phối xác suất.

Tài liệu tham khảo

Banks, H., Bihari, K.: Modelling and estimating uncertainty in parameter estimation. Inverse Prob. 17, 95 (2001)

Banks, H., Browning, W., Catenacci, J., Wood, T.: Analysis of a Quasi-chemical Kinetic Food Chemistry Model. Center for Research in Scientific Computation Technical Report CRSC-TR16-05. NC State University, Raleigh, NC (2016)

Baranyi, J., Roberts, T.: A dynamic approach to predicting bacterial growth in food. Int. J. Food Microbiol. 23, 277–294 (1994)

Baranyi, J., Roberts, T., McClure, P.: A non-autonomous differential equation to model bacterial growth. Food Microbiol. 10, 43–59 (1993)

Bickel, P., Doksum, K.: Mathematical Statistics: Basic Ideas and Selected Topics, vol. 2. CRC Press, Boca Raton (2015)

Bishop, C.: Pattern Recognition and Machine Learning, Information Science and Statistics. Springer, New York (2006)

Browning, W.J.: Near real-time quantification of stochastic model parameters. Tech. rep., prepared by Applied Mathematics Inc., Small Business Technology Transfer, Phase II Final Report, Army STTR Topic A13A-009 (28 September 2016)

Buchanan, R.: Predictive microbiology: Mathematical modeling of microbial growth in foods. In: ACS Symposium Series-American Chemical Society, (1992)

Buchanan, R., Whiting, R., Damert, W.: When is simple good enough: a comparison of the Gompertz. Baranyi, and three-phase linear models for fitting bacterial growth curves. Food Microbiol. 14, 313–326 (1997)

Byrd, R., Lu, P., Nocedal, J., Zhu, C.: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16, 1190–1208 (1995)

Chaloner, K., Verdinelli, I.: Bayesian experimental design: a review. Stat. Sci. 10(3), 273–304 (1995)

Chaspari, T., Tsiartas, A., Tsilifis, P., Narayanan, S.: Markov chain monte carlo inference of parametric dictionaries for sparse bayesian approximations. IEEE Trans. Signal Process. 64, 3077–3092 (2016)

Chen, P., Zabaras, N., Bilionis, I.: Uncertainty propagation using infinite mixture of gaussian processes and variational bayesian inference. J. Comput. Phys. 284, 291–333 (2015)

Doona, C., Feeherry, F., Ross, E.: A quasi-chemical model for the growth and death of microorganisms in foods by non-thermal and high-pressure processing. Int. J. Food Microbiol. 100, 21–32 (2005)

Doona, C., Feeherry, F., Ross, E., Kustin, K.: Inactivation kinetics of listeria monocytogenes by highpressure processing: pressure and temperature variation. J. Food Sci. 77, M458–M465 (2012)

Gershman, S., Hoffman, M., Blei, D.: Nonparametric variational inference. In: International Conference on Machine Learning (2012)

Goldbeter, A.: Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour. Cambridge University Press, Cambridge (1997)

Gompertz, B.: On the nature of the function expressive of the law of human mortality and on a new mode of determining the value of life contingencies. Philos. Trans. R. Soc. Lond. 115, 513–583 (1825)

Haario, H., Saksman, E., Tamminen, J.: An adaptive Metropolis algorithm. Bernoulli 7, 223–242 (2001)

Hastings, W.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97–109 (1970)

Huber, M., Bailey, T., Durrant-Whyte, H., Hanebeck, U.: On entropy approximation for Gaussian mixture random vectors, In: IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems, MFI 2008, (pp. 181–188). IEEE, (2008)

Kullback, S., Leibler, R.: On information and sufficiency. Ann. Math. Stat. 22, 79–86 (1951)

McMeekin, T., Brown, J., Krist, K., Miles, D., Neumeyer, K., Nichols, D., Olley, J., Presser, K., Ratkowsky, D., Ross, T., Salter, M.: Quantitative microbiology: a basis for food safety. Emerg. Infect. Dis. 3, 541 (1997)

Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., Teller, E.: Equations of state calculations by fast computing machines. J. Chem. Phys. 21, 1087–1091 (1953)

Pinski, F., Simpson, G., Stuart, A., Weber, H.: Algorithms for Kullback–Leibler approximation of probability measures in infinite dimensions. SIAM J. Sci. Comput. 37, A2733–A2757 (2015)

Ricker, W.: Growth rates and models. Fish Physiol. 8, 677–743 (1979)

Robert, C., Casella, G.: Monte Carlo Statistical Methods. Springer, Berlin (2013)

Roberts, G., Rosenthal, J.: Optimal scaling of discrete approximations to Langevin diffusions. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 60, 255–268 (1998)

Ross, E., Taub, I., Doona, C., Feeherry, F., Kustin, K.: The mathematical properties of the quasi-chemical model for microorganism growth-death kinetics in foods. Int. J. Food Microbiol. 99, 157–171 (2005)

Schnute, J.: A versatile growth model with statistically stable parameters. Can. J. Fish. Aquat. Sci. 38, 1128–1140 (1981)

Silverman, B.: Density estimation for statistics and data analysis, vol. 26. CRC Press, Boca Raton (1986)

Stuart, A.: Inverse problems: a bayesian perspective. Acta Numer. 19, 451–559 (2010)

Tarantola, A.: Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM, Philadelphia (2005)

Taub, I., Ross, E., Feeherry, F.: Model for predicting the growth and death of pathogenic organisms. In: Van Impe, J.F.M., Gernaerts, K. (eds.) Proceedings of the Third International Conference on Predictive Modeling in Foods (2000)

Taub, I., Feeherry, F., Ross, E., Kustin, K., Doona, C.: A quasi-chemical kinetics model for the growth and death of Staphylococcus aureus in intermediate moisture bread. J. Food Sci. 68, 2530–2537 (2003)

Tsilifis, P., Bilionis, I., Katsounaros, I., Zabaras, N.: Computationally efficient variational approximations for bayesian inverse problems. J. Verif. Valid. Uncertain. Quantif. 1, 031004 (2016)

Tsilifis, P., Ghanem, R., Hajali, P.: Efficient bayesian experimentation using an expected information gain lower bound. SIAM/ASA J. Uncertain. Quantif. 5, 30–62 (2017)

Vrettas, M., Cornford, D., Opper, M.: Estimating parameters in stochastic systems: a variational bayesian approach. Phys. D 240, 1877–1900 (2011)

Whiting, R.: Modeling bacterial survival in unfavorable environments. J. Ind. Microbiol. 12, 240–246 (1993)

Whiting, R., Sackitey, S., Calderone, S., Morely, K., Phillips, J.: Model for the survival of Staphylococcus aureus in nongrowth environments. Int. J. Food Microbiol. 31, 231–243 (1996)

Ye, J., Rey, D., Kadakia, N., Eldridge, M., Morone, U., Rozdeba, P., Abarbanel, H., Quinn, J.: Systematic variational method for statistical nonlinear state and parameter estimation. Phys. Rev. E 92, 052901 (2015)

Zwietering, M., Jongenburger, I., Rombouts, F., Van’t Riet, K.: Modeling of the bacterial growth curve. Appl. Environ. Microbiol. 56, 1875–1881 (1990)