Bayesian inference of Stochastic reaction networks using Multifidelity Sequential Tempered Markov Chain Monte Carlo

Catanach, Thomas A.; Vo, Huy D.; Munsky, Brian

doi:10.1615/int.j.uncertaintyquantification.2020033241

Bayesian inference of Stochastic reaction networks using Multifidelity Sequential Tempered Markov Chain Monte Carlo

Journal Article · Mon Jun 01 00:00:00 EDT 2020 · International Journal for Uncertainty Quantification

DOI:https://doi.org/10.1615/int.j.uncertaintyquantification.2020033241· OSTI ID:1670752

Catanach, Thomas A. ^[1]; Vo, Huy D. ^[2]; Munsky, Brian ^[2]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Colorado State Univ., Fort Collins, CO (United States)

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells.These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not directly measurable and must be inferred from experimental data. Bayesian inference provides a rigorous probabilistic frame-work for identifying these parameters by finding a posterior parameter distribution that captures their uncertainty.Traditional computational methods for solving inference problems such as Markov Chain Monte Carlo methods based on classical Metropolis-Hastings algorithm involve numerous serial evaluations of the likelihood function, which in turn requires expensive forward solutions of the chemical master equation (CME). We propose an alternate approach based on a multifidelity extension of the Sequential Tempered Markov Chain Monte Carlo (ST-MCMC) sampler. This algorithm is built upon Sequential Monte Carlo and solves the Bayesian inference problem by decomposing it into a sequence of efficiently solved subproblems that gradually increase both model fidelity and the influence of the observed data. We reformulate the finite state projection (FSP) algorithm, a well-known method for solving the CME, to produce a hierarchy of surrogate master equations to be used in this multifidelity scheme. To determine the appropriate fidelity, we introduce a novel information-theoretic criteria that seeks to extract the most information about the ultimate Bayesian posterior from each model in the hierarchy without inducing significant bias. This novel sampling scheme is tested with high performance computing resources using biologically relevant problems.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000; 89233218CNA000001; NA0003525

OSTI ID:: 1670752

Alternate ID(s):: OSTI ID: 1822774

Report Number(s):: SAND2020--7898J; SAND2019--15382J; 687782

Journal Information:: International Journal for Uncertainty Quantification, Journal Name: International Journal for Uncertainty Quantification Journal Issue: 6 Vol. 10; ISSN 2152-5080

Publisher:: Begell HouseCopyright Statement

Country of Publication:: United States

Language:: English

References (26)

New Rosenbrock W-Methods of Order 3 for Partial Differential Algebraic Equations of Index 1 Rang, J.; Angermann, L. BIT Numerical Mathematics, Vol. 45, Issue 4 https://doi.org/10.1007/s10543-005-0035-y	journal	December 2005
State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation Cao, Youfang; Terebus, Anna; Liang, Jie Bulletin of Mathematical Biology, Vol. 78, Issue 4 https://doi.org/10.1007/s11538-016-0149-1	journal	April 2016
Estimating Bayes factors via thermodynamic integration and population MCMC Calderhead, Ben; Girolami, Mark Computational Statistics & Data Analysis, Vol. 53, Issue 12 https://doi.org/10.1016/j.csda.2009.07.025	journal	October 2009
A multiple time interval finite state projection algorithm for the solution to the chemical master equation Munsky, Brian; Khammash, Mustafa Journal of Computational Physics, Vol. 226, Issue 1 https://doi.org/10.1016/j.jcp.2007.05.016	journal	September 2007
A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters Koutsourelakis, P. S. Journal of Computational Physics, Vol. 228, Issue 17 https://doi.org/10.1016/j.jcp.2009.05.016	journal	September 2009
KIOPS: A fast adaptive Krylov subspace solver for exponential integrators Gaudreault, Stéphane; Rainwater, Greg; Tokman, Mayya Journal of Computational Physics, Vol. 372 https://doi.org/10.1016/j.jcp.2018.06.026	journal	November 2018
Listening to the noise: random fluctuations reveal gene network parameters Munsky, Brian; Trinh, Brooke; Khammash, Mustafa Molecular Systems Biology, Vol. 5, Issue 1 https://doi.org/10.1038/msb.2009.75	journal	January 2009
Multiplex RNA single molecule FISH of inducible mRNAs in single yeast cells Li, Guoliang; Neuert, Gregor Scientific Data, Vol. 6, Issue 1 https://doi.org/10.1038/s41597-019-0106-6	journal	June 2019
Transient analysis of stochastic switches and trajectories with applications to gene regulatory networks Munsky, B.; Khammash, M. IET Systems Biology, Vol. 2, Issue 5 https://doi.org/10.1049/iet-syb:20070082	journal	September 2008
Regularity and approximability of the solutions to the chemical master equation Gauckler, Ludwig; Yserentant, Harry ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 48, Issue 6 https://doi.org/10.1051/m2an/2014018	journal	October 2014
The finite state projection algorithm for the solution of the chemical master equation Munsky, Brian; Khammash, Mustafa The Journal of Chemical Physics, Vol. 124, Issue 4 https://doi.org/10.1063/1.2145882	journal	January 2006
Finite state projection based bounds to compare chemical master equation models using single-cell data Fox, Zachary; Neuert, Gregor; Munsky, Brian The Journal of Chemical Physics, Vol. 145, Issue 7 https://doi.org/10.1063/1.4960505	journal	August 2016
An adaptive solution to the chemical master equation using tensors Vo, Huy D.; Sidje, Roger B. The Journal of Chemical Physics, Vol. 147, Issue 4 https://doi.org/10.1063/1.4994917	journal	July 2017
Distribution shapes govern the discovery of predictive models for gene regulation Munsky, Brian; Li, Guoliang; Fox, Zachary R. Proceedings of the National Academy of Sciences, Vol. 115, Issue 29 https://doi.org/10.1073/pnas.1804060115	journal	June 2018
Rapid Bayesian Inference for Expensive Stochastic Models Warne, David J.; Baker, Ruth E.; Simpson, Matthew J. Journal of Computational and Graphical Statistics, Vol. 31, Issue 2 https://doi.org/10.1080/10618600.2021.2000419	journal	December 2021
Bayesian inference on stochastic gene transcription from flow cytometry data Tiberi, Simone; Walsh, Mark; Cavallaro, Massimo Bioinformatics, Vol. 34, Issue 17 https://doi.org/10.1093/bioinformatics/bty568	journal	September 2018
Systematic Identification of Signal-Activated Stochastic Gene Regulation Neuert, Gregor; Munsky, Brian; Tan, Rui Zhen Science, Vol. 339, Issue 6119 https://doi.org/10.1126/science.1231456	journal	January 2013
Tensor Approximation of Stationary Distributions of Chemical Reaction Networks Kazeev, Vladimir; Schwab, Christoph SIAM Journal on Matrix Analysis and Applications, Vol. 36, Issue 3 https://doi.org/10.1137/130927218	journal	January 2015
Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions Dolgov, Sergey V.; Savostyanov, Dmitry V. SIAM Journal on Scientific Computing, Vol. 36, Issue 5 https://doi.org/10.1137/140953289	journal	January 2014
The Zoltan and Isorropia Parallel Toolkits for Combinatorial Scientific Computing: Partitioning, Ordering and Coloring Boman, Erik G.; Çatalyürek, Ümit V.; Chevalier, Cédric Scientific Programming, Vol. 20, Issue 2 https://doi.org/10.1155/2012/713587	journal	January 2012
Generalizing Information to the Evolution of Rational Belief Duersch, Jed A.; Catanach, Thomas A. Entropy, Vol. 22, Issue 1 https://doi.org/10.3390/e22010108	journal	January 2020
Near-optimal experimental design for model selection in systems biology Busetto, Alberto Giovanni; Hauser, Alain; Krummenacher, Gabriel ETH Zurich https://doi.org/10.3929/ethz-b-000073427	text	January 2013
A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow Dodwell, T. J.; Ketelsen, C.; Scheichl, R. arXiv https://doi.org/10.48550/arxiv.1303.7343	preprint	January 2013
Designing Experiments to Understand the Variability in Biochemical Reaction Networks Ruess, Jakob; Milias-Argeitis, Andreas; Lygeros, John arXiv https://doi.org/10.48550/arxiv.1304.1455	text	January 2013
Bayesian Updating and Uncertainty Quantification using Sequential Tempered MCMC with the Rank-One Modified Metropolis Algorithm Catanach, Thomas A.; Beck, James L. arXiv https://doi.org/10.48550/arxiv.1804.08738	preprint	January 2018
BayFish: Bayesian inference of transcription dynamics from population snapshots of single-molecule RNA FISH in single cells Gรณmez-Schiavon, Mariana; Chen, Liang-Fu; West, Anne E. Figshare https://doi.org/10.6084/m9.figshare.c.3870658	collection	January 2017

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