Abstract

Approximate Bayesian computation (ABC) has become a standard tool

to conduct Bayesian inference for models with intractable likelihoods. However,

most existing ABC methods suffer from the curse of dimensionality when the

number of parameters is large.

To solve this problem, we introduce a Gibbs

Sequential Monte Carlo (SMC) method that utilizes a Gibbs kernel to update

parameters within the SMC framework and approximate the conditional distribution of the parameters using a variety of regression adjustment methods. We

discuss the computational advantage of our method over existing approaches and

establish the theoretical property of the Gibbs kernel. We further demonstrate

the superior numerical performance of our method using simulation studies and

an application to cell motility example.

Information

Preprint No.SS-2023-0332
Manuscript IDSS-2023-0332
Complete AuthorsWeixuan Zhu, Wei Li, Weining Shen
Corresponding AuthorsWeining Shen
Emailsweinings@uci.edu

References

  1. Beaumont, M. A., W. Zhang, and D. J. Balding (2002). Approximate bayesian computation in population genetics. Genetics 162(4), 2025–2035.
  2. Bernton, E., P. E. Jacob, M. Gerber, and C. P. Robert (2019). Approximate bayesian computation with the wasserstein distance. Journal of the Royal Statistical Society Series B: Statistical Methodology 81(2), 235–269.
  3. Bi, J., W. Shen, and W. Zhu (2022). Random forest adjustment for approximate bayesian computation. Journal of Computational and Graphical Statistics 31(1), 64–73.
  4. Blum, M. G. and O. Fran¸cois (2010). Non-linear regression models for approximate bayesian computation. Statistics and computing 20, 63–73.
  5. Blum, M. G. and V. C. Tran (2010). Hiv with contact tracing: a case study in approximate bayesian computation. Biostatistics 11(4), 644–660.
  6. Clart´e, G., C. P. Robert, R. J. Ryder, and J. Stoehr (2021). Componentwise approximate bayesian computation via gibbs-like steps. Biometrika 108(3), 591–607.
  7. Del Moral, P., A. Doucet, and A. Jasra (2006). Sequential monte carlo samplers. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 68(3), 411–436.
  8. Del Moral, P., A. Doucet, and A. Jasra (2012). An adaptive sequential monte carlo method for approximate bayesian computation. Statistics and computing 22, 1009–1020.
  9. Doucet, A., S. Godsill, and C. Andrieu (2000). On sequential monte carlo sampling methods for bayesian filtering. Statistics and computing 10, 197–208.
  10. Filippi, S., C. P. Barnes, J. Cornebise, and M. P. Stumpf (2013). On optimality of kernels for approximate bayesian computation using sequential monte carlo. Statistical applications in genetics and molecular biology 12(1), 87–107.
  11. Fran¸cois, O., M. G. Blum, M. Jakobsson, and N. A. Rosenberg (2008). Demographic history of european populations of arabidopsis thaliana. PLoS genetics 4(5), e1000075.
  12. Fronza, M., B. Heinzmann, M. Hamburger, S. Laufer, and I. Merfort (2009). Determination of the wound healing effect of calendula extracts using the scratch assay with 3t3 fibroblasts. Journal of ethnopharmacology 126(3), 463–467.
  13. Haario, H., E. Saksman, and J. Tamminen (1999). Adaptive proposal distribution for random walk metropolis algorithm. Computational statistics 14, 375–395.
  14. Johnston, S. T., M. J. Simpson, D. S. McElwain, B. J. Binder, and J. V. Ross (2014). Interpreting scratch assays using pair density dynamics and approximate bayesian computation. Open biology 4(9), 140097.
  15. Kousathanas, A., C. Leuenberger, J. Helfer, M. Quinodoz, M. Foll, and D. Wegmann (2016). Likelihood-free inference in high-dimensional models. Genetics 203(2), 893–904.
  16. Lee, A. (2012). On the choice of mcmc kernels for approximate bayesian computation with smc samplers. In Proceedings of the 2012 Winter simulation conference (WSC), pp. 1–12. IEEE.
  17. Li, J., D. J. Nott, Y. Fan, and S. A. Sisson (2017). Extending approximate bayesian computation methods to high dimensions via a gaussian copula model. Computational Statistics & Data Analysis 106, 77–89.
  18. Liu, J. S. and R. Chen (1995). Blind deconvolution via sequential imputations. Journal of the american statistical association 90(430), 567–576.
  19. Marin, J.-M., P. Pudlo, C. P. Robert, and R. J. Ryder (2012). Approximate bayesian computational methods. Statistics and computing 22(6), 1167–1180.
  20. Marjoram, P., J. Molitor, V. Plagnol, and S. Tavar´e (2003). Markov chain monte carlo without likelihoods. Proceedings of the National Academy of Sciences 100(26), 15324–15328.
  21. Nott, D. J., Y. Fan, L. Marshall, and S. Sisson (2014). Approximate bayesian computation and bayes’ linear analysis: toward high-dimensional abc. Journal of Computational and Graphical Statistics 23(1), 65–86.
  22. Picchini, U. and M. Tamborrino (2022). Guided sequential schemes for intractable Bayesian models. arXiv preprint arXiv:2206.12235.
  23. Price, L. F., C. C. Drovandi, A. Lee, and D. J. Nott (2018). Bayesian synthetic likelihood. Journal of Computational and Graphical Statistics 27(1), 1–11.
  24. Pritchard, J. K., M. T. Seielstad, A. Perez-Lezaun, and M. W. Feldman (1999). Population growth of human y chromosomes: a study of y chromosome microsatellites. Molecular biology and evolution 16(12), 1791–1798.
  25. Ravandi, M. and P. Hajizadeh (2022). Application of approximate bayesian computation for estimation of modified weibull distribution parameters for natural fiber strength with high uncertainty. Journal of Materials Science 57(4), 2731–2743.
  26. Rodrigues, G., D. J. Nott, and S. A. Sisson (2020). Likelihood-free approximate gibbs sampling. Statistics and computing 30, 1057–1073.
  27. Rubin, D. B. (1984). Bayesianly justifiable and relevant frequency calculations for the applied statistician. The Annals of Statistics, 1151–1172.
  28. Simpson, M. J., K. K. Treloar, B. J. Binder, P. Haridas, K. J. Manton, D. I. Leavesley, D. S.
  29. McElwain, and R. E. Baker (2013). Quantifying the roles of cell motility and cell proliferation in a circular barrier assay. Journal of the Royal Society Interface 10(82), 20130007.
  30. Sisson, S. A., Y. Fan, and M. M. Tanaka (2007). Sequential monte carlo without likelihoods. Proceedings of the National Academy of Sciences 104(6), 1760–1765.
  31. Swanson, K. R., C. Bridge, J. Murray, and E. C. Alvord Jr (2003). Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. Journal of the neurological sciences 216(1), 1–10.
  32. Tavar´e, S., D. J. Balding, R. C. Griffiths, and P. Donnelly (1997). Inferring coalescence times from dna sequence data. Genetics 145(2), 505–518.
  33. Toni, T., D. Welch, N. Strelkowa, A. Ipsen, and M. P. Stumpf (2009). Approximate bayesian computation scheme for parameter inference and model selection in dynamical systems. Journal of the Royal Society Interface 6(31), 187–202.
  34. Vo, B. N., C. C. Drovandi, A. N. Pettitt, and G. J. Pettet (2015). Melanoma cell colony expansion parameters revealed by approximate bayesian computation. PLOS computational biology 11(12), e1004635.
  35. Zahm, J.-M., H. Kaplan, A.-L. H´erard, F. Doriot, D. Pierrot, P. Somelette, and E. Puchelle
  36. (1997). Cell migration and proliferation during the in vitro wound repair of the respiratory epithelium. Cell motility and the cytoskeleton 37(1), 33–43.
  37. Zhu, W., T. Zuo, and C. Wang (2023). Approximate bayesian computation with semiparametric density ratio model. Journal of Nonparametric Statistics, 1–16.

Acknowledgments

W. Zhu is supported by grants from Humanities and Social Sciences

Foundation of the Ministry of Education of China (Grant No. 24YJC910014)

and the National Natural Science Foundation of China (Grant No. 72033002).