Bayesian Analysis

Sequential Monte Carlo with Adaptive Weights for Approximate Bayesian Computation

Fernando V. Bonassi and Mike West

Full-text: Open access

Abstract

Methods of approximate Bayesian computation (ABC) are increasingly used for analysis of complex models. A major challenge for ABC is over-coming the often inherent problem of high rejection rates in the accept/reject methods based on prior:predictive sampling. A number of recent developments aim to address this with extensions based on sequential Monte Carlo (SMC) strategies. We build on this here, introducing an ABC SMC method that uses data-based adaptive weights. This easily implemented and computationally trivial extension of ABC SMC can very substantially improve acceptance rates, as is demonstrated in a series of examples with simulated and real data sets, including a currently topical example from dynamic modelling in systems biology applications.

Article information

Source
Bayesian Anal., Volume 10, Number 1 (2015), 171-187.

Dates
First available in Project Euclid: 28 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.ba/1422468427

Digital Object Identifier
doi:10.1214/14-BA891

Mathematical Reviews number (MathSciNet)
MR3420901

Zentralblatt MATH identifier
1335.62015

Keywords
complex modelling adaptive simulation dynamic bionetwork models importance sampling mixture model emulators

Citation

Bonassi, Fernando V.; West, Mike. Sequential Monte Carlo with Adaptive Weights for Approximate Bayesian Computation. Bayesian Anal. 10 (2015), no. 1, 171--187. doi:10.1214/14-BA891. https://projecteuclid.org/euclid.ba/1422468427


Export citation

References

  • Beaumont, M., Cornuet, J., Marin, J., and Robert, C. (2009). “Adaptive approximate Bayesian computation.” Biometrika, 96(4): 983–990.
  • Beaumont, M., Zhang, W., and Balding, D. (2002). “Approximate Bayesian computation in population genetics.” Genetics, 162(4): 2025.
  • Blum, M. G. B. and François, O. (2010). “Non-linear regression models for Approximate Bayesian Computation.” Statistics and Computing, 20: 63–73.
  • Bonassi, F. V., You, L., and West, M. (2011). “Bayesian learning from marginal data in bionetwork models.” Statistical Applications in Genetics & Molecular Biology, 10: Art 49.
  • Cameron, E. and Pettitt, A. (2012). “Approximate Bayesian Computation for astronomical model analysis: A case study in galaxy demographics and morphological transformation at high redshift.” Arxiv preprint arXiv:1202.1426.
  • Cornuet, J., Marin, J., Mira, A., and Robert, C. (2012). “Adaptive multiple importance sampling.” Scandinavian Journal of Statistics, 39(4): 798–812.
  • Cron, A. J. and West, M. (2011). “Efficient classification-based relabeling in mixture models.” The American Statistician, 65: 16–20.
  • Csilléry, K., Blum, M., Gaggiotti, O., and François, O. (2010). “Approximate Bayesian computation (ABC) in practice.” Trends in Ecology & Evolution, 25(7): 410–418.
  • Del Moral, P., Doucet, A., and Jasra, A. (2006). “Sequential Monte Carlo samplers.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68(3): 411–436.
  • — (2011). “An adaptive sequential Monte Carlo method for approximate Bayesian computation.” Statistics and Computing, 1–12.
  • Fearnhead, P. and Prangle, D. (2012). “Constructing summary statistics for approximate Bayesian computation: Semi-automatic approximate Bayesian computation (with discussion).” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 74(3): 419–474.
  • Filippi, S., Barnes, C. P., Cornebise, J., and Stumpf, M. P. (2013). “On optimality of kernels for approximate Bayesian computation using sequential Monte Carlo.” Statistical Applications in Genetics and Molecular Biology, 12(1): 87–107.
  • Fryer, M. (1977). “A review of some non-parametric methods of density estimation.” IMA Journal of Applied Mathematics, 20(3): 335–354.
  • Gardner, T. S., Cantor, C. R., and Collins, J. J. (2000). “Construction of a genetic toggle switch in Escherichia coli.” Nature, 403: 339–342.
  • Heggland, K. and Frigessi, A. (2004). “Estimating functions in indirect inference.” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66(2): 447–462.
  • Lenormand, M., Jabot, F., and Deffuant, G. (2013). “Adaptive approximate Bayesian computation for complex models.” Computational Statistics, 28(6): 2777–2796.
  • Liepe, J., Barnes, C., Cule, E., Erguler, K., Kirk, P., Toni, T., and Stumpf, M. P. (2010). “ABC-SysBio-approximate Bayesian computation in Python with GPU support.” Bioinformatics, 26(14): 1797–1799.
  • Liu, J. (2001). Monte Carlo Strategies in Scientific Computing. Springer-Verlag.
  • Liu, J. and West, M. (2001). “Combined parameter and state estimation in simulation-based filtering.” In Doucet, A., Freitas, J. D., and Gordon, N. (eds.), Sequential Monte Carlo Methods in Practice, 197–217. New York: Springer-Verlag.
  • Marjoram, P., Molitor, J., Plagnol, V., and Tavaré, S. (2003). “Markov chain Monte Carlo without likelihoods.” Proceedings of the National Academy of Sciences USA, 100: 15324–15328.
  • McKinley, T., Cook, A., and Deardon, R. (2009). “Inference in epidemic models without likelihoods.” The International Journal of Biostatistics, 5(1).
  • Pritchard, J., Seielstad, M., Perez-Lezaun, A., and Feldman, M. (1999). “Population growth of human Y chromosomes: a study of Y chromosome microsatellites.” Molecular Biology and Evolution, 16(12): 1791.
  • Scott, D. and Sain, S. (2005). “Multidimensional density estimation.” Handbook of Statistics, 24: 229–261.
  • Scott, D. W. (1992). Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley Series in Probability and Mathematical Statistics.
  • Silk, D., Filippi, S., and Stumpf, M. P. (2013). “Optimizing threshold-schedules for sequential approximate Bayesian computation: applications to molecular systems.” Statistical applications in genetics and molecular biology, 12(5): 603–618.
  • Silverman, B. (1986). Density estimation for statistics and data analysis, volume 26. Chapman & Hall/CRC.
  • Sisson, S. A., Fan, Y., and Tanaka, M. M. (2007). “Sequential Monte Carlo without likelihoods.” Proceedings of the National Academy of Sciences USA, 104: 1760–1765.
  • — (2009). “Correction for Sisson et al., Sequential Monte Carlo without likelihoods.” Proceedings of the National Academy of Sciences, 106(39): 16889.
  • Suchard, M. A., Wang, Q., Chan, C., Frelinger, J., Cron, A. J., and West, M. (2010). “Understanding GPU programming for statistical computation: Studies in massively parallel massive mixtures.” Journal of Computational and Graphical Statistics, 19: 419–438.
  • Toni, T. and Stumpf, M. P. H. (2010). “Simulation-based model selection for dynamical systems in systems and population biology.” Bioinformatics, 26: 104–110.
  • Toni, T., Welch, D., Strelkowa, N., Ipsen, A., and Stumpf, M. (2009). “Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems.” Journal of the Royal Society Interface, 6(31): 187–202.
  • Turner, B. M. and Van Zandt, T. (2012). “A tutorial on approximate Bayesian computation.” Journal of Mathematical Psychology, 56(2): 69–85.
  • West, M. (1992). “Modelling with mixtures (with discussion).” In Bernardo, J. M., Berger, J. O., Dawid, A. P., and Smith, A. F. M. (eds.), Bayesian Statistics 4, 503–524. Oxford University Press.
  • — (1993a). “Approximating posterior distributions by mixtures.” Journal of the Royal Statistical Society: Series B (Statistical Methology), 54: 553–568.
  • — (1993b). “Mixture models, Monte Carlo, Bayesian updating and dynamic models.” Computing Science and Statistics, 24: 325–333.