Bayesian Computation with Intractable Likelihoods (original ) (raw )
P. Alquier, N. Friel, R. Everitt, A. Boland, Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels. Stat. Comput. 26 (1–2), 29–47 (2016). https://doi.org/10.1007/s11222-014-9521-x Article MathSciNet MATH Google Scholar
C. Andrieu, G.O. Roberts, The pseudo-marginal approach for efficient Monte Carlo computations. Ann. Statist. 37 (2), 697–725 (2009). https://doi.org/10.1214/07-AOS574 Article MathSciNet MATH Google Scholar
C. Andrieu, J. Thoms, A tutorial on adaptive MCMC. Stat. Comput. 18 (4), 343–373 (2008). https://doi.org/10.1007/s11222-008-9110-y Article MathSciNet Google Scholar
C. Andrieu, M. Vihola, Convergence properties of pseudo-marginal Markov chain Monte Carlo algorithms. Ann. Appl. Prob. 25 (2), 1030–1077, 04 (2015). https://doi.org/10.1214/14-AAP1022 Article MathSciNet MATH Google Scholar
C. Andrieu, A. Doucet, R. Holenstein, Particle Markov chain Monte Carlo methods. J. R. Stat. Soc. Ser. B 72 (3), 269–342 (2010). https://doi.org/10.1111/j.1467-9868.2009.00736.x Article MathSciNet MATH Google Scholar
M.A. Beaumont, Estimation of population growth or decline in genetically monitored populations. Genetics 164 (3), 1139–1160 (2003) Google Scholar
A. Boland, N. Friel, F. Maire, Efficient MCMC for Gibbs random fields using pre-computation. Electron. J. Statist. 12 (2), 4138–4179 (2018). https://doi.org/10.1214/18-EJS1504 .Article MathSciNet MATH Google Scholar
C.T. Butts, A perfect sampling method for exponential family random graph models. J. Math. Soc. 42 (1), 17–36 (2018). https://doi.org/10.1080/0022250X.2017.1396985 Article MathSciNet Google Scholar
A. Caimo, N. Friel, Bayesian inference for exponential random graph models. Soc. Networks 33 (1), 41–55 (2011). https://doi.org/10.1016/j.socnet.2010.09.004 Article Google Scholar
A. Caimo, N. Friel, Bergm: Bayesian exponential random graphs in R. J. Stat. Soft. 61 (2), 1–25 (2014). https://doi.org/10.18637/jss.v061.i02 Article Google Scholar
B. Calderhead, M. Girolami, Estimating Bayes factors via thermodynamic integration and population MCMC. Comput. Stat. Data Anal. 53 (12), 4028–4045 (2009). https://doi.org/10.1016/j.csda.2009.07.025 Article MathSciNet MATH Google Scholar
E. Cameron, A.N. Pettitt, Approximate Bayesian computation for astronomical model analysis: a case study in galaxy demographics and morphological transformation at high redshift. Mon. Not. R. Astron. Soc. 425 (1), 44–65 (2012). https://doi.org/10.1111/j.1365-2966.2012.21371.x Article Google Scholar
M.-H. Chen, Q.-M. Shao, J.G. Ibrahim, Monte Carlo Methods in Bayesian Computation . Springer Series in Statistics (Springer, New York, 2000)Book MATH Google Scholar
J.A. Christen, C. Fox, Markov chain Monte Carlo using an approximation. J. Comput. Graph. Stat. 14 (4), 795–810 (2005). https://doi.org/10.1198/106186005X76983 Article MathSciNet Google Scholar
L. Cucala, J.-M. Marin, C.P. Robert, D.M. Titterington, A Bayesian reassessment of nearest-neighbor classification. J. Am. Stat. Assoc. 104 (485), 263–273 (2009). https://doi.org/10.1198/jasa.2009.0125 Article MathSciNet MATH Google Scholar
P. Del Moral, A. Doucet, A. Jasra, An adaptive sequential Monte Carlo method for approximate Bayesian computation. Stat. Comput. 22 (5), 1009–20 (2012). https://doi.org/10.1007/s11222-011-9271-y Article MathSciNet MATH Google Scholar
A.P. Dempster, N.M. Laird, D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B 39 (1), 1–38 (1977).MathSciNet MATH Google Scholar
A. Doucet, M. Pitt, G. Deligiannidis, R. Kohn, Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator. Biometrika 102 (2), 295–313 (2015). https://doi.org/10.1093/biomet/asu075 Article MathSciNet MATH Google Scholar
C.C. Drovandi, A.N. Pettitt, Estimation of parameters for macroparasite population evolution using approximate Bayesian computation. Biometrics 67 (1), 225–233 (2011). https://doi.org/10.1111/j.1541-0420.2010.01410.x Article MathSciNet MATH Google Scholar
C.C. Drovandi, A.N. Pettitt, M.J. Faddy, Approximate Bayesian computation using indirect inference. J. R. Stat. Soc. Ser. C 60 (3), 317–337 (2011). https://doi.org/10.1111/j.1467-9876.2010.00747.x Article MathSciNet Google Scholar
C.C. Drovandi, A.N. Pettitt, A. Lee, Bayesian indirect inference using a parametric auxiliary model. Stat. Sci. 30 (1), 72–95 (2015). https://doi.org/10.1214/14-STS498 Article MathSciNet MATH Google Scholar
C.C. Drovandi, M.T. Moores, R.J. Boys, Accelerating pseudo-marginal MCMC using Gaussian processes. Comput. Stat. Data Anal. 118 , 1–17 (2018). https://doi.org/10.1016/j.csda.2017.09.002 Article MathSciNet MATH Google Scholar
P. Erdős, A. Rényi, On random graphs. Publ. Math. Debr. 6 , 290–297 (1959) Google Scholar
R.G. Everitt, Bayesian parameter estimation for latent Markov random fields and social networks. J. Comput. Graph. Stat. 21 (4), 940–960 (2012). https://doi.org/10.1080/10618600.2012.687493 Article MathSciNet Google Scholar
P. Fearnhead, V. Giagos, C. Sherlock, Inference for reaction networks using the linear noise approximation. Biometrics 70 (2), 457–466 (2014). https://doi.org/10.1111/biom.12152 Article MathSciNet MATH Google Scholar
O. Frank, D. Strauss, Markov graphs. J. Amer. Stat. Assoc. 81 (395), 832–842 (1986)Article MathSciNet MATH Google Scholar
N. Friel, Bayesian inference for Gibbs random fields using composite likelihoods, in ed. by C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, A.M. Uhrmacher, Proceedings of the 2012 Winter Simulation Conference (WSC) (2012), pp. 1–8. https://doi.org/10.1109/WSC.2012.6465236
N. Friel, A.N. Pettitt, Likelihood estimation and inference for the autologistic model. J. Comp. Graph. Stat. 13 (1), 232–246 (2004). https://doi.org/10.1198/1061860043029 Article MathSciNet Google Scholar
N. Friel, A.N. Pettitt, Marginal likelihood estimation via power posteriors. J. R. Stat. Soc. Ser. B 70 (3), 589–607 (2008). https://doi.org/10.1111/j.1467-9868.2007.00650.x Article MathSciNet MATH Google Scholar
N. Friel, A.N. Pettitt, R. Reeves, E. Wit, Bayesian inference in hidden Markov random fields for binary data defined on large lattices. J. Comp. Graph. Stat. 18 (2), 243–261 (2009). https://doi.org/10.1198/jcgs.2009.06148 Article MathSciNet Google Scholar
A. Gelman, X.-L. Meng, Simulating normalizing constants: from importance sampling to bridge sampling to path sampling. Statist. Sci. 13 (2), 163–185 (1998). https://doi.org/10.1214/ss/1028905934 Article MathSciNet MATH Google Scholar
C.J. Geyer, L. Johnson, potts: Markov Chain Monte Carlo for Potts Models . R package version 0.5-2 (2014). http://CRAN.R-project.org/package=potts
A. Golightly, D.A. Henderson, C. Sherlock, Delayed acceptance particle MCMC for exact inference in stochastic kinetic models. Stat. Comput. 25 (5), 1039–1055 (2015). https://doi.org/10.1007/s11222-014-9469-x Article MathSciNet MATH Google Scholar
A. Grelaud, C.P. Robert, J.-M. Marin, F. Rodolphe, J.-F. Taly, ABC likelihood-free methods for model choice in Gibbs random fields. Bayesian Anal. 4 (2), 317–336 (2009). https://doi.org/10.1214/09-BA412 Article MathSciNet MATH Google Scholar
M.L. Huber, A bounding chain for Swendsen-Wang. Random Struct. Algor. 22 (1), 43–59 (2003). https://doi.org/10.1002/rsa.10071 Article MathSciNet MATH Google Scholar
M.L. Huber, Perfect Simulation (Chapman & Hall/CRC Press, London/Boca Raton, 2016)Book MATH Google Scholar
P.E. Jacob, A.H. Thiery, On nonnegative unbiased estimators. Ann. Statist. 43 (2), 769–784 (2015). https://doi.org/10.1214/15-AOS1311 Article MathSciNet MATH Google Scholar
M. Järvenpää, M. Gutmann, A. Vehtari, P. Marttinen, Gaussian process modeling in approximate Bayesian computation to estimate horizontal gene transfer in bacteria. Ann. Appl. Stat. 12 (4), 2228–2251 (2018). https://doi.org/10.1214/18-AOAS1150 Article MathSciNet MATH Google Scholar
A. Lee, K. Łatuszyński, Variance bounding and geometric ergodicity of Markov chain Monte Carlo kernels for approximate Bayesian computation. Biometrika 101 (3), 655–671 (2014). https://doi.org/10.1093/biomet/asu027 Article MathSciNet MATH Google Scholar
A.-M. Lyne, M. Girolami, Y. Atchadé, H. Strathmann, D. Simpson, On Russian roulette estimates for Bayesian inference with doubly-intractable likelihoods. Statist. Sci. 30 (4), 443–467 (2015). https://doi.org/10.1214/15-STS523 Article MathSciNet MATH Google Scholar
F. Maire, R. Douc, J. Olsson, Comparison of asymptotic variances of inhomogeneous Markov chains with application to Markov chain Monte Carlo methods. Ann. Statist. 42 (4), 1483–1510, 08 (2014). https://doi.org/10.1214/14-AOS1209 Article MathSciNet MATH Google Scholar
J.-M. Marin, C.P. Robert, Bayesian Core: A Practical Approach to Computational Bayesian Statistics . Springer Texts in Statistics (Springer, New York, 2007) Google Scholar
P. Marjoram, J. Molitor, V. Plagnol, S. Tavaré, Markov chain Monte Carlo without likelihoods. Proc. Natl Acad. Sci. 100 (26), 15324–15328 (2003). https://doi.org/10.1073/pnas.0306899100 Article Google Scholar
C.A. McGrory, D.M. Titterington, R. Reeves, A.N. Pettitt, Variational Bayes for estimating the parameters of a hidden Potts model. Stat. Comput. 19 (3), 329–340 (2009). https://doi.org/10.1007/s11222-008-9095-6 Article MathSciNet Google Scholar
C.A. McGrory, A.N. Pettitt, R. Reeves, M. Griffin, M. Dwyer, Variational Bayes and the reduced dependence approximation for the autologistic model on an irregular grid with applications. J. Comput. Graph. Stat. 21 (3), 781–796 (2012). https://doi.org/10.1080/10618600.2012.632232 Article MathSciNet Google Scholar
T.J. McKinley, I. Vernon, I. Andrianakis, N. McCreesh, J.E. Oakley, R.N. Nsubuga, M. Goldstein, R.G. White, et al., Approximate Bayesian computation and simulation-based inference for complex stochastic epidemic models. Statist. Sci. 33 (1), 4–18 (2018). https://doi.org/10.1214/17-STS618 Article MathSciNet MATH Google Scholar
F.J. Medina-Aguayo, A. Lee, G.O. Roberts, Stability of noisy Metropolis-Hastings. Stat. Comput. 26 (6), 1187–1211 (2016). https://doi.org/10.1007/s11222-015-9604-3 Article MathSciNet MATH Google Scholar
E. Meeds, M. Welling, GPS-ABC: Gaussian process surrogate approximate Bayesian computation, in Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence , Quebec City, Canada (2014) Google Scholar
A. Mira, J. Møller, G.O. Roberts, Perfect slice samplers. J. R. Stat. Soc. Ser. B 63 (3), 593–606 (2001). https://doi.org/10.1111/1467-9868.00301 Article MathSciNet MATH Google Scholar
J. Møller, A.N. Pettitt, R. Reeves, K.K. Berthelsen, An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants. Biometrika 93 (2), 451–458 (2006). https://doi.org/10.1093/biomet/93.2.451 Article MathSciNet MATH Google Scholar
M.T. Moores, D. Feng, K. Mengersen, bayesImageS: Bayesian Methods for Image Segmentation Using a Potts Model . R package version 0.5-3 (2014). URL http://CRAN.R-project.org/package=bayesImageS
M.T. Moores, C.C. Drovandi, K. Mengersen, C.P. Robert, Pre-processing for approximate Bayesian computation in image analysis. Stat. Comput. 25 (1), 23–33 (2015). https://doi.org/10.1007/s11222-014-9525-6 Article MathSciNet MATH Google Scholar
M.T. Moores, G.K. Nicholls, A.N. Pettitt, K. Mengersen, Scalable Bayesian inference for the inverse temperature of a hidden Potts model. Bayesian Anal. 15 , 1–27 (2020). https://doi.org/10.1214/18-BA1130 .Article MathSciNet MATH Google Scholar
I. Murray, Z. Ghahramani, D.J.C. MacKay, MCMC for doubly-intractable distributions, in Proceedings of the 22nd Conference on Uncertainty in Artificial Intelligence , Arlington (AUAI Press, Tel Aviv-Yafo, 2006), pp. 359–366 Google Scholar
G.K. Nicholls, C. Fox, A. Muir Watt, Coupled MCMC with a randomized acceptance probability (2012).Preprint arXiv:1205.6857 [stat.CO]. https://arxiv.org/abs/1205.6857
C.J. Oates, T. Papamarkou, M. Girolami, The controlled thermodynamic integral for Bayesian model evidence evaluation. J. Am. Stat. Assoc. 111 (514), 634–645 (2016). https://doi.org/10.1080/01621459.2015.1021006 Article MathSciNet Google Scholar
H.E. Ogden, On asymptotic validity of naive inference with an approximate likelihood. Biometrika 104 (1), 153–164 (2017). https://doi.org/10.1093/biomet/asx002 Article MathSciNet MATH Google Scholar
S. Okabayashi, L. Johnson, C.J. Geyer, Extending pseudo-likelihood for Potts models. Statistica Sinica 21 , 331–347 (2011)MathSciNet MATH Google Scholar
E. Olbrich, T. Kahle, N. Bertschinger, N. Ay, J. Jost, Quantifying structure in networks. Eur. Phys. J. B 77 (2), 239–247 (2010). https://doi.org/10.1140/epjb/e2010-00209-0 Article Google Scholar
P.D. O’Neill, D.J. Balding, N.G. Becker, M. Eerola, D. Mollison, Analyses of infectious disease data from household outbreaks by Markov chain Monte Carlo methods. J. R. Stat. Soc. Ser. C 49 (4), 517–542 (2000). https://doi.org/10.1111/1467-9876.00210 Article MathSciNet MATH Google Scholar
A.N. Pettitt, N. Friel, R. Reeves, Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice. J. R. Stat. Soc. Ser. B 65 (1), 235–246 (2003). https://doi.org/10.1111/1467-9868.00383 Article MathSciNet MATH Google Scholar
M.K. Pitt, R. dos Santos Silva, P. Giordani, R. Kohn, On some properties of Markov chain Monte Carlo simulation methods based on the particle filter. J. Econometr. 171 (2), 134–151 (2012). https://doi.org/10.1016/j.jeconom.2012.06.004 Article MathSciNet MATH Google Scholar
D. Prangle, Lazy ABC. Stat. Comput. 26 (1), 171–185 (2016). https://doi.org/10.1007/s11222-014-9544-3 Article MathSciNet Google Scholar
J.K. Pritchard, M.T. Seielstad, A. Perez-Lezaun, M.W. Feldman, Population growth of human Y chromosomes: a study of Y chromosome microsatellites. Mol. Biol. Evol. 16 (12), 1791–1798 (1999). https://doi.org/10.1093/oxfordjournals.molbev.a026091 Article Google Scholar
J.G. Propp, D.B. Wilson, Exact sampling with coupled Markov chains and applications to statistical mechanics. Random Struct. Algor. 9 (1–2), 223–252 (1996). https://doi.org/10.1002/(SICI)1098-2418(199608/09)9:1/2<223::AID-RSA14>3.0.CO;2-O Article MathSciNet MATH Google Scholar
R. Reeves, A.N. Pettitt, Efficient recursions for general factorisable models. Biometrika 91 (3), 751–757 (2004). https://doi.org/10.1093/biomet/91.3.751 Article MathSciNet MATH Google Scholar
G.O. Roberts, J.S. Rosenthal, Examples of adaptive MCMC. J. Comput. Graph. Stat. 18 (2), 349–367 (2009). https://doi.org/10.1198/jcgs.2009.06134 Article MathSciNet Google Scholar
T. Rydén, D.M. Titterington, Computational Bayesian analysis of hidden Markov models. J. Comput. Graph. Stat. 7 (2), 194–211 (1998). https://doi.org/10.1080/10618600.1998.10474770 MathSciNet Google Scholar
C. Sherlock, A.H. Thiery, G.O. Roberts, J.S. Rosenthal, On the efficiency of pseudo-marginal random walk Metropolis algorithms. Ann. Statist. 43 (1), 238–275, 02 (2015). https://doi.org/10.1214/14-AOS1278 Article MathSciNet MATH Google Scholar
C. Sherlock, A. Golightly, D.A. Henderson, Adaptive, delayed-acceptance MCMC for targets with expensive likelihoods. J. Comput. Graph. Stat. 26 (2), 434–444 (2017). https://doi.org/10.1080/10618600.2016.1231064 Article MathSciNet Google Scholar
A.M. Stuart, A.L. Teckentrup, Posterior consistency for Gaussian process approximations of Bayesian posterior distributions. Math. Comp. 87 , 721–753 (2018). https://doi.org/10.1090/mcom/3244 Article MathSciNet MATH Google Scholar
R.H. Swendsen, J.-S. Wang, Nonuniversal critical dynamics in Monte Carlo simulations. Phys. Rev. Lett. 58 , 86–88 (1987). https://doi.org/10.1103/PhysRevLett.58.86 Article Google Scholar
M.A. Tanner, W.H. Wong, The calculation of posterior distributions by data augmentation. J. Am. Stat. Assoc. 82 (398), 528–40 (1987)Article MathSciNet MATH Google Scholar
C. Varin, N. Reid, D. Firth, An overview of composite likelihood methods. Statistica Sinica 21 , 5–42 (2011)MathSciNet MATH Google Scholar
R.D. Wilkinson, Accelerating ABC methods using Gaussian processes, in ed. by S. Kaski, J. Corander, Proceedings of the 17th International Conference on Artificial Intelligence and Statistics AISTATS (JMLR: Workshop and Conference Proceedings) , vol. 33 (2014), pp. 1015–1023 Google Scholar