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We establish general conditions under which Markov chains produced by the Hamiltonian Monte Carlo method will and will not be geometrically ergodic.
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[author] Betancourt, MJM., Byrne, SimonS., Livingstone, SamuelS. and Girolami, MarkM. (2016). The Geometric Foundations of Hamiltonian Monte Carlo. Bernoulli forthcoming
2016
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[author] Carpenter, BobB., Gelman, AndrewA., Hoffman, MattM., Lee, DanielD., Goodrich, BenB., Betancourt, MichaelM., Brubaker, Michael AM. A., Guo, JiqiangJ., Li, PeterP. and Riddell, AllenA. (2016). Stan: A probabilistic programming language. Journal of Statistical Software
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[author] Ottobre, MichelaM., Pillai, Natesh SN. S., Pinski, Frank JF. J., Stuart, Andrew MA. M. et al. (2016). A function space HMC algorithm with second order Langevin diffusion limit. Bernoulli 22 60–106
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[author] Bou-Rabee, NawafN. and Sanz-Serna, Jesús MaríaJ. M. (2018). Geometric integrators and the Hamiltonian Monte Carlo method. Acta Numerica 27 113–206
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[author] Livingstone, SamuelS., Betancourt, MichaelM., Byrne, SimonS. and Girolami, MarkM. (2018). Supplement to “On the Geometric Ergodicity of Hamiltonian Monte Carlo"
2018
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Livingstone, S., Betancourt, M., Byrne, S. and Girolami, M. (2019). On the geometric ergodicity of Hamiltonian Monte Carlo. Bernoulli
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