References
- Alspach, D. L. , and Sorenson, H. W. (1972), “Nonlinear Bayesian Estimation Using Gaussian Sum Approximations,” IEEE Transactions on Automatic Control , 17, 439–448. DOI: https://doi.org/10.1109/TAC.1972.1100034.
- Azzalini, A. (2011), “R Package sn: The Skew-Normal and Skew- t Distributions” (version 0.4-17), available at http://azzalini.stat.unipd.it/SN.
- ——— (2013), The Skew-Normal and Related Families , New York: Cambridge University Press.
- Bennett, C. H. (1976), “Efficient Estimation of Free Energy Differences From Monte Carlo Data,” Journal of Computational Physics , 22, 245–268. DOI: https://doi.org/10.1016/0021-9991(76)90078-4.
- Bornkamp, B. (2011), “Approximating Probability Densities by Iterated Laplace Approximations,” Journal of Computational and Graphical Statistics , 20, 656–669. DOI: https://doi.org/10.1198/jcgs.2011.10099.
- Bornn, L. , Jacob, P. E. , Del Moral, P. , and Doucet, A. (2013), “An Adaptive Interacting Wang–Landau Algorithm for Automatic Density Exploration,” Journal of Computational and Graphical Statistics , 22, 749–773. DOI: https://doi.org/10.1080/10618600.2012.723569.
- Ceperley, D. M. (1995), “Path Integrals in the Theory of Condensed Helium,” Reviews of Modern Physics , 67, 279–355. DOI: https://doi.org/10.1103/RevModPhys.67.279.
- Chen, J. , and Tan, X. (2009), “Inference for Multivariate Normal Mixtures,” Journal of Multivariate Analysis , 100, 1367–1383. DOI: https://doi.org/10.1016/j.jmva.2008.12.005.
- Chen, J. , Tan, X. , and Zhang, R. (2008), “Inference for Normal Mixtures in Mean and Variance,” Statistica Sinica , 18, 443–465.
- Chib, S. (1995), “Marginal Likelihood From the Gibbs Output,” Journal of the American Statistical Association , 90, 1313–1321. DOI: https://doi.org/10.1080/01621459.1995.10476635.
- Chib, S. , and Jeliazkov, I. (2001), “Marginal Likelihood From the Metropolis–Hastings Output,” Journal of the American Statistical Association , 96, 270–281. DOI: https://doi.org/10.1198/016214501750332848.
- Day, N. E. (1969), “Estimating the Components of a Mixture of Normal Distributions,” Biometrika , 56, 463–474. DOI: https://doi.org/10.1093/biomet/56.3.463.
- DiCiccio, T. J. , Kass, R. E. , Raftery, A. , and Wasserman, L. (1997), “Computing Bayes Factors by Combining Simulation and Asymptotic Approximations,” Journal of the American Statistical Association , 92, 903–915. DOI: https://doi.org/10.1080/01621459.1997.10474045.
- Elvira, V. , Martino, L. , Luengo, D. , and Bugallo, M. F. (2019), “Generalized Multiple Importance Sampling,” Statistical Science , 34, 129– 155. DOI: https://doi.org/10.1214/18-STS668.
- Gelman, A. , Carlin, J. B. , Stern, H. S. , Dunson, D. B. , Vehtari, A. , and Rubin, D. B. (2013), Bayesian Data Analysis , Boca Raton, FL: CRC Press.
- Gelman, A. , and Meng, X.-L. (1998), “Simulating Normalizing Constants: From Importance Sampling to Bridge Sampling to Path Sampling,” Statistical Science , 13, 163–185. DOI: https://doi.org/10.1214/ss/1028905934.
- Gronau, Q. F. , Sarafoglou, A. , Matzke, D. , Ly, A. , Boehm, U. , Marsman, M. , Leslie, D. S. , Forster, J. J. , Wagenmakers, E.-J. , and Steingroever, H. (2017), “A Tutorial on Bridge Sampling,” Journal of Mathematical Psychology , 81, 80–97. DOI: https://doi.org/10.1016/j.jmp.2017.09.005.
- Gronau, Q. F. , Singmann, H. , and Wagenmakers, E.-J. (2017), “Bridgesampling: An R Package for Estimating Normalizing Constants,” arXiv no. 1710.08162.
- Hesterberg, T. (1995), “Weighted Average Importance Sampling and Defensive Mixture Distributions,” Technometrics , 37, 185–194. DOI: https://doi.org/10.1080/00401706.1995.10484303.
- Jacob, P. E. , and Ryder, R. J. (2014), “The Wang–Landau Algorithm Reaches the Flat Histogram Criterion in Finite Time,” The Annals of Applied Probability , 24, 34–53. DOI: https://doi.org/10.1214/12-AAP913.
- Jones, D. E. (2015), “Likelihood Methods for Monte Carlo Estimation,” Ph.D. qualifying paper, Harvard University, Department of Statistics, pp. 1–30.
- Kass, R. E. , and Raftery, A. E. (1995), “Bayes Factors,” Journal of the American Statistical Association , 90, 773–795. DOI: https://doi.org/10.1080/01621459.1995.10476572.
- Kiefer, J. , and Wolfowitz, J. (1956), “Consistency of the Maximum Likelihood Estimator in the Presence of Infinitely Many Incidental Parameters,” The Annals of Mathematical Statistics , 27, 887–906. DOI: https://doi.org/10.1214/aoms/1177728066.
- Kong, A. , McCullagh, P. , Meng, X.-L. , and Nicolae, D. (2006), “Further Explorations of Likelihood Theory for Monte Carlo Integration,” in Advances in Statistical Modeling and Inference: Essays in Honor of Kjell A. Doksum , ed. V. Nair , Singapore: World Scientific Press, pp. 563–592.
- Kong, A. , McCullagh, P. , Meng, X.-L. , Nicolae, D. , and Tan, Z. (2003), “A Theory of Statistical Models for Monte Carlo Integration” (with discussions), Journal of the Royal Statistical Society, Series B, 65, 585–604. DOI: https://doi.org/10.1111/1467-9868.00404.
- Kou, S. , Zhou, Q. , and Wong, W. H. (2006), “Equi-Energy Sampler With Applications in Statistical Inference and Statistical Mechanics,” The Annals of Statistics , 34, 1581–1619. DOI: https://doi.org/10.1214/009053606000000515.
- Liang, F. (2005), “A Generalized Wang–Landau Algorithm for Monte Carlo Computation,” Journal of the American Statistical Association , 100, 1311–1327. DOI: https://doi.org/10.1198/016214505000000259.
- Liang, F. , Liu, C. , and Carroll, R. J. (2007), “Stochastic Approximation in Monte Carlo Computation,” Journal of the American Statistical Association , 102, 305–320. DOI: https://doi.org/10.1198/016214506000001202.
- Liu, J. S. , Liang, F. , and Wong, W. H. (2001), “A Theory for Dynamic Weighting in Monte Carlo Computation,” Journal of the American Statistical Association , 96, 561–573. DOI: https://doi.org/10.1198/016214501753168253.
- Martino, L. , Elvira, V. , Luengo, D. , and Corander, J. (2017), “Layered Adaptive Importance Sampling,” Statistics and Computing , 27, 599–623. DOI: https://doi.org/10.1007/s11222-016-9642-5.
- Meng, X.-L. (2005), “Comment: Computation, Survey and Inference,” Statistical Science , 20, 21–28.
- Meng, X.-L. , and Schilling, S. (2002), “Warp Bridge Sampling,” Journal of Computational and Graphical Statistics , 11, 552–586. DOI: https://doi.org/10.1198/106186002457.
- Meng, X.-L. , and Wong, W. H. (1996), “Simulating Ratios of Normalizing Constants via a Simple Identity: A Theoretical Exploration,” Statistica Sinica , 6, 831–860.
- Mira, A. , and Nicholls, G. (2004), “Bridge Estimation of the Probability Density at a Point,” Statistica Sinica , 14, 603–612.
- Owen, A. , and Zhou, Y. (2000), “Safe and Effective Importance Sampling,” Journal of the American Statistical Association , 95, 135–143. DOI: https://doi.org/10.1080/01621459.2000.10473909.
- Peel, D. , and McLachlan, G. J. (2000), “Robust Mixture Modelling Using the t-Distribution,” Statistics and Computing , 10, 339–348. DOI: https://doi.org/10.1023/A:1008981510081.
- Romero, M. (2003), “On Two Topics With No Bridge: Bridge Sampling With Dependent Draws and Bias of the Multiple Imputation Variance Estimator,” Ph.D. thesis, University of Chicago, Department of Statistics.
- Shao, Q.-M. , and Ibrahim, J. G. (2000), Monte Carlo Methods in Bayesian Computation , Springer Series in Statistics, New York: Springer.
- Tan, Z. (2004), “On a Likelihood Approach for Monte Carlo Integration,” Journal of the American Statistical Association , 99, 1027– 1036. DOI: https://doi.org/10.1198/016214504000001664.
- ——— (2013), “Calibrated Path Sampling and Stepwise Bridge Sampling,” Journal of Statistical Planning and Inference , 143, 675–690.
- Veach, E. , and Guibas, L. J. (1995), “Optimally Combining Sampling Techniques for Monte Carlo Rendering,” in Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, ACM, New York, NY, pp. 419–428. DOI: https://doi.org/10.1145/218380.218498.
- Villani, C. (2003), Topics in Optimal Transportation (Vol. 58), Providence, RI: American Mathematical Society.
- Voter, A. F. (1985), “A Monte Carlo Method for Determining Free-Energy Differences and Transition State Theory Rate Constants,” The Journal of Chemical Physics , 82, 1890–1899. DOI: https://doi.org/10.1063/1.448373.
- Voter, A. F. , and Doll, J. D. (1985), “Dynamical Corrections to Transition State Theory for Multistate Systems: Surface Self-Diffusion in the Rare-Event Regime,” The Journal of Chemical Physics , 82, 80– 92. DOI: https://doi.org/10.1063/1.448739.
- Wang, F. , and Landau, D. (2001), “Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States,” Physical Review Letters , 86, 2050–2053. DOI: https://doi.org/10.1103/PhysRevLett.86.2050.
- Wong, W. H. , and Liang, F. (1997), “Dynamic Weighting in Monte Carlo and Optimization,” Proceedings of the National Academy of Sciences of the United States of America , 94, 14220–14224. DOI: https://doi.org/10.1073/pnas.94.26.14220.