Chapter 15 References
Altekar, Gautam, Sandhya Dwarkadas, John P. Huelsenbeck, and Fredrik Ronquist. 2004. “Parallel Metropolis Coupled Markov Chain Monte Carlo for Bayesian Phylogenetic Inference.” Bioinformatics 20 (3): 407–15. https://doi.org/10.1093/bioinformatics/btg427.
Baydin, Atilim Gunes, Barak A. Pearlmutter, Alexey Andreyevich Radul, and Jeffrey Mark Siskind. 2018. “Automatic Differentiation in Machine Learning: A Survey.” Journal of Machine Learning Research 18 (153): 1–43. http://jmlr.org/papers/v18/17-468.html.
Bernardo, José M, and Adrian FM Smith. 2001. Bayesian Theory. IOP Publishing.
Betancourt, Michael. 2017. “A Conceptual Introduction to Hamiltonian Monte Carlo,” January. http://arxiv.org/abs/1701.02434.
Gelman, Andrew, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin. 2013. Bayesian Data Analysis. 3rd ed. Boca Raton, FL: Chapman & Hall/CRC.
Gelman, Andrew, and Donald B. Rubin. 1992. “Inference from Iterative Simulation Using Multiple Sequences.” Statistical Science 7 (4): 457–72. https://doi.org/10.1214/ss/1177011136.
Gelman, Andrew, and Kenneth Shirley. 2011. “Inference and Monitoring Convergence.” In Handbook of Markov Chain Monte Carlo, edited by Steve Brooks, Andrew Gelman, Galin Jones, and Xiao-Li Meng. Chapman & Hall/CRC. http://www.mcmchandbook.net/HandbookChapter6.pdf.
Gentle, James E. 2009. Computational Statistics. 1st ed. New York, NY: Springer.
Geyer, Charles J. 1992. “Practical Markov Chain Monte Carlo.” Statistical Science 7 (4): 473–83. https://doi.org/10.1214/ss/1177011137.
Givens, Geof H., and Jennefer A. Hoeting. 2013. Computational Statistics. 2nd ed. Hoboken, NJ: Wiley.
Hoffman, Matthew D., and Andrew Gelman. 2014. “The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo.” J. Mach. Learn. Res. 15 (1): 1593–1623. http://www.jmlr.org/papers/volume15/hoffman14a/hoffman14a.pdf.
Kass, R. E., and A. E. Raftery. 1995. “Bayes Factors.” Journal of the American Statistical Association 90: 773–95. https://doi.org/10.1080/01621459.1995.10476572.
Koistinen, Petri. 2013. “Computational Statistics.”
Kucukelbir, Alp, Dustin Tran, Rajesh Ranganath, Andrew Gelman, and David M. Blei. 2017. “Automatic Differentiation Variational Inference.” Journal of Machine Learning Research 18: 14:1–14:45. http://jmlr.org/papers/v18/16-107.html.
Lartillot, Nicolas, and Hervé Philippe. 2006. “Computing Bayes Factors Using Thermodynamic Integration.” Systematic Biology 55 (2): 195–207. https://doi.org/10.1080/10635150500433722.
Neal, Radford M. 2011. “MCMC Using Hamiltonian Dynamics.” In Handbook of Markov Chain Monte Carlo, edited by Steve Brooks, Andrew Gelman, Galin Jones, and Xiao-Li Meng. Chapman & Hall/CRC. http://arxiv.org/abs/1206.1901.
O’Neill, Melissa E. 2014. “PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation.” HMC-CS-2014-0905. Claremont, CA: Harvey Mudd College. https://www.cs.hmc.edu/tr/hmc-cs-2014-0905.pdf.
Phipson, Belinda, and Gordon K Smyth. 2010. “Permutation P-Values Should Never Be Zero: Calculating Exact P-Values When Permutations Are Randomly Drawn.” Statistical Applications in Genetics and Molecular Biology 9: Article39. https://doi.org/10.2202/1544-6115.1585.
Robbins, Herbert, and Sutton Monro. 1951. “A Stochastic Approximation Method.” Ann. Math. Statist. 22 (3): 400–407. https://doi.org/10.1214/aoms/1177729586.
Roberts, Gareth O., and Jeffrey S. Rosenthal. 1998. “Optimal Scaling of Discrete Approximations to Langevin Diffusions.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 60 (1): 255–68. https://doi.org/10.1111/1467-9868.00123.
Sunnåker, Mikael, Alberto Giovanni Busetto, Elina Numminen, Jukka Corander, Matthieu Foll, and Christophe Dessimoz. 2013. “Approximate Bayesian Computation.” PLoS Computational Biology 9 (1): e1002803. https://doi.org/10.1371/journal.pcbi.1002803.
Titsias, Michalis K., and Miguel Lázaro-Gredilla. 2014. “Doubly Stochastic Variational Bayes for Non-Conjugate Inference.” In Proceedings of the 31th International Conference on Machine Learning, ICML 2014, Beijing, China, 21-26 June 2014, 1971–9. http://proceedings.mlr.press/v32/titsias14.html.
Wilkinson, Richard. 2013. “Approximate Bayesian Computation (ABC) Gives Exact Results Under the Assumption of Model Error.” Stat. Appl. Genet. Mol. Biol. 12 (2). https://arxiv.org/abs/0811.3355.
Wilkinson, Richard, and Simon Tavaré. 2008. “Approximate Bayesian Computation: A Simulation Based Approach to Inference.” http://www0.cs.ucl.ac.uk/staff/C.Archambeau/AIS/Talks/rwilkinson_ais08.pdf.