×

Approximate Bayesian inference in semi-mechanistic models. (English) Zbl 1384.62075

Summary: Inference of interaction networks represented by systems of differential equations is a challenging problem in many scientific disciplines. In the present article, we follow a semi-mechanistic modelling approach based on gradient matching. We investigate the extent to which key factors, including the kinetic model, statistical formulation and numerical methods, impact upon performance at network reconstruction. We emphasize general lessons for computational statisticians when faced with the challenge of model selection, and we assess the accuracy of various alternative paradigms, including recent widely applicable information criteria and different numerical procedures for approximating Bayes factors. We conduct the comparative evaluation with a novel inferential pipeline that systematically disambiguates confounding factors via an ANOVA scheme.

MSC:

62F15 Bayesian inference
62J10 Analysis of variance and covariance (ANOVA)
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C42 Systems biology, networks
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Aderhold, A., Husmeier, D., Grzegorczyk, M.: Statistical inference of regulatory networks for circadian regulation. Stat. Appl. Genet. Mol. Biol. 13(3), 227-273 (2014) · Zbl 1296.92011
[2] Babtie, A.C., Kirk, P., Stumpf, M.P.H.: Topological sensitivity analysis for systems biology. PNAS 111(51), 18,507-18,512 (2014) · Zbl 1355.92039 · doi:10.1073/pnas.1414026112
[3] Barenco, M., Tomescu, D., Brewer, D., Callard, R., Stark, J., Hubank, M.: Ranked prediction of p53 targets using hidden variable dynamic modeling. Genome Biol. 7(3), r25 (2006) · doi:10.1186/gb-2006-7-3-r25
[4] Brandt, S.: Data Analysis: Statistical and Computational Methods for Scientists and Engineers. Springer, New York (1999) · Zbl 0983.62001 · doi:10.1007/978-1-4612-1446-5
[5] Chatfield, C.: The Analysis of Time Series. Chapman & Hall, Boca Raton (1989). iSBN 0-412-31820-2 · Zbl 0732.62088
[6] Chib, S., Jeliazkov, I.: Marginal likelihood from the Metropolis-Hastings output. J. Am. Stat. Assoc. 96(453), 270-281 (2001) · Zbl 1015.62020 · doi:10.1198/016214501750332848
[7] Ciocchetta, F., Hillston, J.: Bio-PEPA: a framework for the modelling and analysis of biological systems. Theor. Comput. Sci. 410(33), 3065-3084 (2009) · Zbl 1173.68041 · doi:10.1016/j.tcs.2009.02.037
[8] Davis, J., Goadrich, M.: The relationship between precision-recall and ROC curves. In: Proceedings of the 23rd International Conference on Machine Learning (ICML), ACM, pp. 233-240 (2006)
[9] De Jong, H.: Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol. 9(1), 67-103 (2002) · doi:10.1089/10665270252833208
[10] Drezner, Z., Weslowsky, G.: On the computation of the bivariate normal integral. J. Stat. Comput. Simul. 35, 101-107 (1989) · doi:10.1080/00949659008811236
[11] Flis, A., Fernández, A.P., Zielinski, T., Mengin, V., Sulpice, R., Stratford, K., Hume, A., Pokhilko, A., Southern, M.M., Seaton, D.D., et al.: Defining the robust behaviour of the plant clock gene circuit with absolute rna timeseries and open infrastructure. Open Biol. 5(10), 150,042 (2015) · doi:10.1098/rsob.150042
[12] Fogelmark, K., Troein, C.: Rethinking transcriptional activation in the arabidopsis circadian clock. PLoS Comput. Biol. 10(7), e1003,705 (2014) · doi:10.1371/journal.pcbi.1003705
[13] Friel, N., Pettitt, A.: Marginal likelihood estimation via power posteriors. J. R. Stat. Soc.: Ser. B (Stat. Methodol.) 70, 589-607 (2008) · Zbl 05563360 · doi:10.1111/j.1467-9868.2007.00650.x
[14] Friel, N., Hurn, M., Wyse, J.: Improving power posterior estimation of statistical evidence. Stati. Comput. 24(5), 709-723 (2013) · Zbl 1322.62098
[15] Gelfand, A.E., Dey, D.K., Chang, H.: Model determination using predictive distributions with implementation via sampling-based methods. Bayesian Stat. 4, 147-167 (1992)
[16] Gelman, A., Rubin, D.B.: Inference from iterative simulation using multiple sequences. Stat. Sci. 1, 457-472 (1992) · Zbl 1386.65060 · doi:10.1214/ss/1177011136
[17] Gelman, A., Carling, J.B., Stern, H., Dunson, D.B., Vehtari, A., Rubin, D.: Bayesian Data Analysis, 3rd edn. Chapman & Hall, Boca Raton (2014a) · Zbl 1279.62004
[18] Gelman, A., Hwang, J., Vehtari, A.: Understanding predictive information criteria for Bayesian models. Stat. Comput. 24(6), 997-1016 (2014b) · Zbl 1332.62090 · doi:10.1007/s11222-013-9416-2
[19] Genz, A.: Numerical computation of rectangular bivariate and trivariate normal and t probabilities. Stat. Comput. 14(3), 251-260 (2004) · doi:10.1023/B:STCO.0000035304.20635.31
[20] Genz, A., Bretz, F.: Numerical computation of multivariate t probabilities with application to power calculation of multiple contrasts. J. Stat. Comput. Simul. 63, 361-378 (1999) · Zbl 0934.62020 · doi:10.1080/00949659908811962
[21] Genz, A., Bretz, F.: Comparison of methods for the computation of multivariate t probabilities. J. Comput. Graph. Stat. 11(4), 950-971 (2002) · doi:10.1198/106186002394
[22] Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340-2361 (1977) · doi:10.1021/j100540a008
[23] Grzegorczyk, M., Aderhold, A., Husmeier, D.: Inferring bi-directional interactions between circadian clock genes and metabolism with model ensembles. Stat. Appl. Genet. Mol. Biol. 14(2), 143-167 (2015) · Zbl 1311.92082
[24] Guerriero, M.L., Pokhilko, A., Fernández, A.P., Halliday, K.J., Millar, A.J., Hillston, J.: Stochastic properties of the plant circadian clock. J. R. Soc. Interface 9(69), 744-756 (2012) · doi:10.1098/rsif.2011.0378
[25] Hanley, J.A., McNeil, B.J.: The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143(1), 29-36 (1982) · doi:10.1148/radiology.143.1.7063747
[26] Holsclaw, T., Sansó, B., Lee, H.K., Heitmann, K., Habib, S., Higdon, D., Alam, U.: Gaussian process modeling of derivative curves. Technometrics 55(1), 57-67 (2013) · doi:10.1080/00401706.2012.723918
[27] Lawrence, N.D., Girolami, M., Rattray, M., Sanguinetti, G.: Learning and Inference in Computational Systems Biology. Computational Molecular Biology. MIT Press, Cambridge (2010) · Zbl 1196.92018
[28] Lindley, D.V.: A statistical paradox. Biometrika 1, 187-192 (1957) · Zbl 0080.12801 · doi:10.1093/biomet/44.1-2.187
[29] Lunn, D., Jackson, C., Best, N., Thomas, A., Spiegelhalter, D.: The BUGS Book: A Practical Introduction to Bayesian Analysis. Chapman & Hall, Boca Raton (2012) · Zbl 1281.62009
[30] Marbach, D., Costello, J.C., Küffner, R., Vega, N.M., Prill, R.J., Camacho, D.M., Allison, K.R., Kellis, M., Collins, J.J., Stolovitzky, G., et al.: Wisdom of crowds for robust gene network inference. Nat. Methods 9(8), 796-804 (2012) · doi:10.1038/nmeth.2016
[31] Marin, J.M., Robert, C.P.: Bayesian Core: A Practical Approach to Computational Bayesian Statistics. Springer, New York (2007) · Zbl 1137.62013
[32] Mockler, T., Michael, T., Priest, H., Shen, R., Sullivan, C., Givan, S., McEntee, C., Kay, S., Chory, J.: The DIURNAL project: DIURNAL and circadian expression profiling, model-based pattern matching, and promoter analysis. In: Cold Spring Harbor Symposia on Quantitative Biology, Cold Spring Harbor Laboratory Press, vol. 72, pp. 353-363 (2007) · Zbl 1296.92011
[33] Murphy, K.: Machine Learning: A Probabilistic Perspective. MIT Press, Cambridge (2012) · Zbl 1295.68003
[34] Oates, C.J., Dondelinger, F., Bayani, N., Korkola, J., Gray, J.W., Mukherjee, S.: Causal network inference using biochemical kinetics. Bioinformatics 30(17), i468-i474 (2014) · doi:10.1093/bioinformatics/btu452
[35] Oates, C.J., Papamarkou, T., Girolami, M.: The controlled thermodynamic integral for Bayesian model evidence evaluation. J. Am. Stat. Assoc. (2016). doi:10.1080/01621459.2015.1021006 · doi:10.1080/01621459.2015.1021006
[36] Ota, K., Yamada, T., Yamanishi, Y., Goto, S., Kanehisa, M.: Comprehensive analysis of delay in transcriptional regulation using expression profiles. Genome Inform. 14, 302-303 (2003)
[37] Pokhilko, A., Hodge, S., Stratford, K., Knox, K., Edwards, K., Thomson, A., Mizuno, T., Millar, A.: Data assimilation constrains new connections and components in a complex, eukaryotic circadian clock model. Mol. Syst. Biol. 6(1), 416 (2010)
[38] Pokhilko, A., Fernández, A., Edwards, K., Southern, M., Halliday, K., Millar, A.: The clock gene circuit in Arabidopsis includes a repressilator with additional feedback loops. Mol. Syst. Biol. 8, 574 (2012) · doi:10.1038/msb.2012.6
[39] Pokhilko, A., Mas, P., Millar, A.: Modelling the widespread effects of TOC1 signalling on the plant circadian clock and its outputs. BMC Syst. Biol. 7(1), 1-12 (2013) · doi:10.1186/1752-0509-7-23
[40] Ramsay, J., Hooker, G., Campbell, D., Cao, J.: Parameter estimation for differential equations: a generalized smoothing approach. J. R. Stat. Soc.: Ser. B 69(5), 741-796 (2007) · Zbl 07555374
[41] Rasmussen, C.E.: Evaluation of Gaussian processes and other methods for non-linear regression. PhD thesis, University of Toronto, Dept. of Computer Science (1996)
[42] Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006) · Zbl 1177.68165
[43] Rasmussen CE, Neal RM, Hinton GE, van Camp D, Revow M, Ghahramani Z, Kustra R, Tibshirani R (1996) The DELVE manual. http://www.cs.toronto.edu/ delve · Zbl 1320.62058
[44] Smolen, P., Baxter, D.A., Byrne, J.H.: Modeling transcriptional control in gene networks—methods, recent results, and future directions. Bull. Math. Biol. 62(2), 247-292 (2000) · Zbl 1323.92088 · doi:10.1006/bulm.1999.0155
[45] Solak E, Murray-Smith R, Leithead WE, Leith DJ, Rasmussen CE (2002) Derivative observations in Gaussian process models of dynamic systems. In: Proceedings of Advances in Neural Information Processing Systems (NIPS), MIT Press, Cambridge (2002)
[46] Spiegelhalter, D.J., Best, N.G., Carlin, B.P., Van Der Linde, A.: Bayesian measures of model complexity and fit. J. R. Stat. Soc.: Ser. B (Stat. Methodol.) 64(4), 583-639 (2002) · Zbl 1067.62010 · doi:10.1111/1467-9868.00353
[47] Toni, T., Welch, D., Strelkowa, N., Ipsen, A., Stumpf, M.P.: Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface 6(31), 187-202 (2009) · doi:10.1098/rsif.2008.0172
[48] Vanhatalo, J., Riihimäki, J., Hartikainen, J., Jylänki, P., Tolvanen, V., Vehtari, A.: GPstuff: Bayesian modeling with Gaussian processes. J. Mach. Learn. Res. 14(1), 1175-1179 (2013) · Zbl 1320.62010
[49] Vyshemirsky, V., Girolami, M.A.: Bayesian ranking of biochemical system models. Bioinformatics 24(6), 833-839 (2008) · doi:10.1093/bioinformatics/btm607
[50] Watanabe, S.: Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory. J. Mach. Learn. Res. 11, 3571-3594 (2010) · Zbl 1242.62024
[51] Watanabe, S.: A widely applicable Bayesian information criterion. J. Mach. Learn. Res. 14, 867-897 (2013) · Zbl 1320.62058
[52] Yang, Z.: Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: approximate methods. J. Mol. Evol. 39, 306-314 (1994) · doi:10.1007/BF00160154
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.