Approximate Bayesian computational methods for the inference of unknown parameters. (English) Zbl 1419.65004
Wood, David R. (ed.) et al., 2017 MATRIX annals. Cham: Springer. MATRIX Book Ser. 2, 515-529 (2019).
Summary: Recent advances in biology, economics, engineering and physical sciences have generated a large number of mathematical models for describing the dynamics of complex systems. A key step in mathematical modelling is to estimate model parameters in order to realize experimental observations. However, it is difficult to derive the analytical density functions in the Bayesian methods for these mathematical models. During the last decade, approximate Bayesian computation (ABC) has been developed as a major method for the inference of parameters in mathematical models. A number of new methods have been designed to improve the efficiency and accuracy of ABC. Theoretical studies have also been conducted to investigate the convergence property of these methods. In addition, these methods have been applied to a wide range of deterministic and stochastic models. This chapter gives a brief review of the main ABC algorithms and various improvements.
For the entire collection see [Zbl 1411.37003].
For the entire collection see [Zbl 1411.37003].
MSC:
| 65C60 | Computational problems in statistics (MSC2010) |
| 62F15 | Bayesian inference |
References:
| [1] | Aeschbacher, S., Beaumont, M. A., Futschik, A.: A novel approach for choosing summary statistics in approximate Bayesian computation. Genetics 192, 1027-1047 (2012) |
| [2] | Barthelmé, S., Chopin, N.: Expectation propagation for likelihood-free inference. J. Am. Stat. Assoc. 109, 315-333 (2014) · Zbl 1367.62063 |
| [3] | Bazin, E., Dawson, K.J., Beaumont, M.A.: Likelihoodfree inference of population structure and local adaptation in a Bayesian hierarchical model. Genetics 185, 587-602 (2010) |
| [4] | Beaumont, M.A.: Adaptive approximate Bayesian computation. Biometrika 96, 983-990 (2009) · Zbl 1437.62393 |
| [5] | Beaumont, M.A.: Approximate Bayesian computation in evolution and ecology. Annu. Rev. Ecol. Evol. Syst. 41, 379-406 (2010) |
| [6] | Beaumont, M.A., Zhang, W., Balding, D.J.: Approximate Bayesian computation in population genetics. Genetics 162, 2025-2035 (2002) |
| [7] | Biau, G., Cérou, F., Guyader, A.: New insights into approximate Bayesian computation. Ann. I. H. Poincaré B 51, 376-403 (2015) · Zbl 1307.62012 |
| [8] | Blum, M.G.B.: Approximate Bayesian computation: a nonparametric perspective. J. Am. Stat. Assoc. 105, 1178-1187 (2010) · Zbl 1390.62052 |
| [9] | Blum, M.G.B.: Regression approaches for approximate Bayesian computation (2017). arXiv:1707.01254v1 |
| [10] | Blum, M.G.B., François, O.: Non-linear regression models for approximate Bayesian computation. Stat. Comput. 20, 63-73 (2010) |
| [11] | Blum, M.G.B., Nunes, M.A., Prangle, D., Sisson, S.A.: A comparative review of dimension reduction methods in approximate Bayesian computation. Stat. Sci. 28(2), 189-208 (2013) · Zbl 1331.62123 |
| [12] | Cappé, O., Guillin, A., Marin, J.-M., Robert, C.P.: Population Monte Carlo. J. Comput. Graph. Stat. 13(4), 907-929 (2004) |
| [13] | Christen, J.A., Fox, C.: Markov chain Monte Carlo using an approximation. J. Comput. Graph. Stat. 14, 795-810 (2005) |
| [14] | Csilléry, K., Blum, M.G.B., Gaggiotti, O., François, O.: Approximate Bayesian computation (ABC) in practice. Trends Ecol. Evol. 25(7), 410-418 (2010) |
| [15] | Del Moral, P., Doucet, A., Jasra, A.: Sequential Monte Carlo samplers. J. R. Stat. Soc. Ser. B 68, 411-436 (2006) · Zbl 1105.62034 |
| [16] | Del Moral, P., Doucet, A, Jasra, A.: An adaptive sequential Monte Carlo method for approximate Bayesian computation. Stat. Comput. 22(5), 1009-1020 (2012) · Zbl 1252.65025 |
| [17] | Deng, Z., Tian, T.: A continuous optimization approach for inferring parameters in mathematical models of regulatory networks. BMC Bioinform. 15, 256 (2014) |
| [18] | Drovandi, C.C., Pettitt, A.N.: Estimation of parameters for macroparasite population evolution using approximate Bayesian computation. Biometrics 67(1), 225-233 (2011) · Zbl 1217.62128 |
| [19] | Fearnhead, P., Prangle, D.: Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation. J. R. Stat. Soc. Ser. B 74, 419-474 (2012) · Zbl 1411.62057 |
| [20] | Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Chapman and Hall/CRC Press, London (2003) · Zbl 1279.62004 |
| [21] | Goel, G., Chou, I.C., Voit, E.O.: System estimation from metabolic time-series data. Bioinformatics 24(21), 2505-2511 (2008) |
| [22] | Green, P.J., Łatuszyński, K., Pereyra, M., Robert, C.P.: Bayesian computation: a summary of the current state, and samples backwards and forwards. Stat. Comput. 25, 835-862 (2015) · Zbl 1331.62017 |
| [23] | Johnson, R., Kirk, P., Stumpf, M.P.H.: SYSBIONS: nested sampling for systems biology. Bioinformatics 31(4), 604-605 (2015) |
| [24] | Joyce, P., Marjoram, P.: Approximately sufficient statistics and Bayesian computation. Stat. Appl. Genet. Mol. Biol. 7(1), Article 26 (2008) · Zbl 1276.62077 |
| [25] | Kousathanas, A., Leuenberger, C., Helfer, J., Quinodoz, M., Foll, M., Wegmann, D.: Likelihood-free inference in high-dimensional models. Genetics 203, 893-904 (2016) |
| [26] | Kypraios, T., Neal, P., Prangle, D.: A tutorial introduction to Bayesian inference for stochastic epidemic models using approximate Bayesian computation. Math. Biosci. 287, 42-53 (2016) · Zbl 1377.92091 |
| [27] | Lenormand, M., Jabot, F., Deffuant, G.: Adaptive approximate Bayesian computation for complex models. Comput Stat. 28(6), 2777-2796 (2013) · Zbl 1306.65088 |
| [28] | Li, J., Nott, D.J., Fan, Y., Sisson, S.A.: Extending approximate Bayesian computation methods to high dimensions via a Gaussian copula model. Comput. Stat. Data Anal. 106, 77-89 (2017) · Zbl 1466.62136 |
| [29] | Liepe, J., et al.: A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. Nat. Protoc. 9(2), 439-456 (2014) |
| [30] | Lillacci, G., Khammash, M.: Parameter estimation and model selection in computational biology. PLoS Comput. Biol. 6(3), e1000696 (2010) · Zbl 1258.93111 |
| [31] | Lintusaari, J., Gutmann, M., Dutta, R., Kaski, S., Corander, J.: Fundamentals and recent developments in approximate Bayesian computation. Syst. Biol. 66(1), e66-e82 (2017) |
| [32] | Marin, J.-M., Pudlo, P., Robert, C.P., Ryder, R.J.: Approximate Bayesian computational methods. Stat. Comput. 22, 1167-1180 (2012) · Zbl 1252.62022 |
| [33] | Marjoram, P., Molitor, J., Plagnol, V., Tavaré, S.: Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. U. S. A. 100(26), 15324-15328 (2003) |
| [34] | Nott, D.J., Fan, Y., Marshall, L., Sisson, S.A.: Approximate Bayesian computation and Bayes’s linear analysis: toward high-dimensional ABC. J. Comput. Graph. Stat. 23(1), 65-86 (2014) |
| [35] | Nunes, M.A., Balding, D.J.: On optimal selection of summary statistics for approximate Bayesian computation. Stat. Appl. Genet. Mol. Biol. 9, Article 34 (2010) · Zbl 1304.92047 |
| [36] | Nunes, M.A., Prangle, D.: abctools: an R package for tuning approximate Bayesian computation analyses. R J. 7(2), 189-205 (2015) |
| [37] | Picchini, U.: Inference for SDE models via approximate Bayesian computation. J. Comput. Graph. Stat. 23(4), 1080-1100 (2014) |
| [38] | Prangle, D.: Summary statistics in approximate Bayesian computation (2015). arXiv:1512.05633 · Zbl 1411.62057 |
| [39] | Prangle, D.: Lazy ABC. Stat. Comput. 26, 171-185 (2016) · Zbl 1342.62036 |
| [40] | Pritchard, J.K., Seielstad, M.T., Perez-Lezaun, A., Feldman, M.W.: Population growth of human Y chromosomes: a study of Y chromosome microsatellites. Mol. Biol. Evol. 16(12), 1791-1798 (1999) |
| [41] | Robert, C.P.: Approximate Bayesian Computation: A Survey on Recent Results. Monte Carlo and Quasi-Monte Carlo Methods, pp. 185-205. Springer, Cham (2016) · Zbl 1356.65031 |
| [42] | Robert, C.P., Casella, G.: Monte Carlo Statistical Methods. Springer, New York (2004) · Zbl 1096.62003 |
| [43] | Rubin, D.B.: Bayesianly justifiable and relevant frequency calculations for the applied statistics. Ann. Stat. 12(4), 1151-1172 (1984) · Zbl 0555.62010 |
| [44] | Sisson, S.A., Fan, Y.: Likelihood-Free MCMC. Handbook of Markov Chain Monte Carlo, pp. 313-335. CRC Press, Boca Raton (2011) · Zbl 1229.65035 |
| [45] | Sisson, S.A., Fan, Y., Tanaka, M.M.: Sequential Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. U. S. A. 104(6), 1760-1765 (2007) · Zbl 1160.65005 |
| [46] | Sisson, S.A., Fan, Y., Tanaka, M.M.: Sequential Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. U. S. A. 106(39), 16889 (2009) · Zbl 1160.65005 |
| [47] | Sunnaker, M., et al.: Approximate Bayesian computation. PLoS Comput. Biol. 9(1), e1002803 (2013) |
| [48] | Tavaré, S., Balding, D., Griffith, R., Donnelly, P.: Inferring coalescence times from DNA sequence data. Genetics 145, 505-518 (1997) |
| [49] | Tian, T., Smith-Miles, K.: Mathematical modeling of GATA-switching for regulating the differentiation of hematopoietic stem cell. BMC Syst. Biol. 8(Suppl 1), S8 (2014) |
| [50] | Toni, T., Welch, D., Strelkowa, N., Ipsen, A., Stumpf, M.P.H.: Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J. R. Soc. Interface 6, 187-202 (2009) |
| [51] | Turner, B.M., Van Zandt, T.: A tutorial on approximate Bayesian computation. J. Math. Psychol. 56(2), 69-85 (2012) · Zbl 1245.91084 |
| [52] | Vyshemirsky, V., Girolami, M.: BioBayes: a software package for Bayesian inference in systems biology. Bioinformatics 24(17), 1933-1934 (2008) |
| [53] | Wegmann, D., Leuenberger, C., Excoffier, L.: Efficient approximate Bayesian computation coupled with Markov chain Monte Carlo without likelihood. Genetics 182, 129-141 (2009) |
| [54] | Wilkinson, D.J.: Bayesian methods in bioinformatics and computational systems biology. Brief Bioinform. 8(2), 109-116 (2007) |
| [55] | Wu, Q., Smith-Miles, K., Tian, T.: Approximate Bayesian computation schemes for parameter inference of discrete stochastic models using simulated likelihood density. BMC Bioinform. 15, S3 (2014) |
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