@article{gelman1992inference,
  title={Inference from iterative simulation using multiple sequences},
  author={Gelman, Andrew and Rubin, Donald B},
  journal={Statistical science},
  pages={457--472},
  year={1992},
  publisher={JSTOR}
}

@online{stan_rhat,
  title = {{Potential scale reduction}, Stan Manual},
  url = {https://mc-stan.org/docs/2_27/reference-manual/notation-for-samples-chains-and-draws.html#potential-scale-reduction},
}

@online{stan_ess,
  title = {{Effective sample size}, Stan Manual},
  url = {https://mc-stan.org/docs/2_27/reference-manual/effective-sample-size-section.html},
}

@online{stan_hmc_param,
  title = {{HMC Algorithm Parameters}, Stan Manual},
  url = {https://mc-stan.org/docs/2_20/reference-manual/hmc-algorithm-parameters.html},
}

@online{jax_finfo,
  title = {{jax.numpy.finfo}, JAX Documentation},
  url = {https://jax.readthedocs.io/en/latest/_autosummary/jax.numpy.finfo.html},
}

@online{progress_bar,
  author = {Jeremie Coullon},
  title = {How to add a progress bar to JAX scans and loops},
  url = {https://www.jeremiecoullon.com/2021/01/29/jax_progress_bar/},
}

@online{nuts_uturn,
  url = {https://discourse.mc-stan.org/t/nuts-misses-u-turns-runs-in-circles-until-max-treedepth/9727/46},
}

@book{gelman1995bayesian,
  title={Bayesian data analysis},
  author={Gelman, Andrew and Carlin, John B and Stern, Hal S and Rubin, Donald B},
  year={1995},
  publisher={Chapman and Hall/CRC}
}

@article{geyer1992practical,
  title={Practical Markov Chain Monte Carlo},
  author={Geyer, Charles J},
  journal={Statistical science},
  pages={473--483},
  year={1992},
  publisher={JSTOR}
}

@article{geyer2011introduction,
  title={Introduction to Markov Chain Monte Carlo},
  author={Geyer, Charles J},
  journal={Handbook of Markov Chain Monte Carlo},
  volume={20116022},
  pages={45},
  year={2011},
  publisher={Boca Raton}
}

@article{titsias2018auxiliary,
  title={Auxiliary gradient-based sampling algorithms},
  author={Titsias, Michalis K and Papaspiliopoulos, Omiros},
  journal={Journal of the Royal Statistical Society. Series B (Statistical Methodology)},
  volume={80},
  number={4},
  pages={749--767},
  year={2018},
  publisher={JSTOR}
}

@inproceedings{neklyudov2022orbital,
  title={Orbital MCMC},
  author={Neklyudov, Kirill and Welling, Max},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={5790--5814},
  year={2022},
  organization={PMLR}
}

@inproceedings{hoffman2022tuning,
  title={Tuning-free generalized Hamiltonian Monte Carlo},
  author={Hoffman, Matthew D and Sountsov, Pavel},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={7799--7813},
  year={2022},
  organization={PMLR}
}

@article{nesterov2009primal,
  title={Primal-dual subgradient methods for convex problems},
  author={Nesterov, Yurii},
  journal={Mathematical programming},
  volume={120},
  number={1},
  pages={221--259},
  year={2009},
  publisher={Springer}
}

@article{hoffman2014no,
  title={The No-U-Turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo.},
  author={Hoffman, Matthew D and Gelman, Andrew and others},
  journal={J. Mach. Learn. Res.},
  volume={15},
  number={1},
  pages={1593--1623},
  year={2014}
}

@inproceedings{murray2010elliptical,
  title={Elliptical slice sampling},
  author={Murray, Iain and Adams, Ryan and MacKay, David},
  booktitle={Proceedings of the thirteenth international conference on artificial intelligence and statistics},
  pages={541--548},
  year={2010},
  organization={JMLR Workshop and Conference Proceedings}
}

@article{bou2018geometric,
  title={Geometric integrators and the Hamiltonian Monte Carlo method},
  author={Bou-Rabee, Nawaf and Sanz-Serna, Jes{\'u}s Maria},
  journal={Acta Numerica},
  volume={27},
  pages={113--206},
  year={2018},
  publisher={Cambridge University Press}
}

@article{mclachlan1995numerical,
  title={On the numerical integration of ordinary differential equations by symmetric composition methods},
  author={McLachlan, Robert I},
  journal={SIAM Journal on Scientific Computing},
  volume={16},
  number={1},
  pages={151--168},
  year={1995},
  publisher={SIAM}
}

@inproceedings{brofos2021evaluating,
  title={Evaluating the Implicit Midpoint Integrator for Riemannian Hamiltonian Monte Carlo},
  author={Brofos, James and Lederman, Roy R},
  booktitle={Proceedings of the 38th International Conference on Machine Learning},
  pages={1072--1081},
  year={2021},
  editor={Meila, Marina and Zhang, Tong},
  volume={139},
  series={Proceedings of Machine Learning Research},
  month={18--24 Jul},
  publisher={PMLR}
}

@book{schlick2010molecular,
  title={Molecular modeling and simulation: an interdisciplinary guide},
  author={Schlick, Tamar},
  volume={2},
  year={2010},
  publisher={Springer}
}

@article{blanes2014numerical,
  title={Numerical integrators for the Hybrid Monte Carlo method},
  author={Blanes, Sergio and Casas, Fernando and Sanz-Serna, Jes{\'u}s Mar{\i}a},
  journal={SIAM Journal on Scientific Computing},
  volume={36},
  number={4},
  pages={A1556--A1580},
  year={2014},
  publisher={SIAM}
}

@article{betancourt2017geometric,
  title={The Geometric Foundations of Hamiltonian Monte Carlo},
  author={Betancourt, Michael and Byrne, Simon and Livingstone, Sam and Girolami, Mark},
  journal={arXiv preprint arXiv:arXiv:1410.5110},
  year={2017}
}

@inproceedings{lu2017relativistic,
  title={Relativistic Monte Carlo},
  author={Lu, Xiaoyu and Perrone, Valerio and Hasenclever, Leonard and Teh, Yee Whye and Vollmer, Sebastian},
  booktitle={Artificial Intelligence and Statistics},
  pages={1236--1245},
  year={2017},
  organization={PMLR}
}

@article{betancourt2017conceptual,
  title={A conceptual introduction to Hamiltonian Monte Carlo},
  author={Betancourt, Michael},
  journal={arXiv preprint arXiv:1701.02434},
  year={2017}
}

@article{phan2019composable,
  title={Composable effects for flexible and accelerated probabilistic programming in NumPyro},
  author={Phan, Du and Pradhan, Neeraj and Jankowiak, Martin},
  journal={arXiv preprint arXiv:1912.11554},
  year={2019}
}

@article{lao2020tfp,
  title={tfp. mcmc: Modern Markov chain Monte Carlo tools built for modern hardware},
  author={Lao, Junpeng and Suter, Christopher and Langmore, Ian and Chimisov, Cyril and Saxena, Ashish and Sountsov, Pavel and Moore, Dave and Saurous, Rif A and Hoffman, Matthew D and Dillon, Joshua V},
  journal={arXiv preprint arXiv:2002.01184},
  year={2020}
}

@article{neal2020non,
  title={Non-reversibly updating a uniform [0, 1] value for Metropolis accept/reject decisions},
  author={Neal, Radford M},
  journal={arXiv preprint arXiv:2001.11950},
  year={2020}
}

@article{coullon2022sgmcmcjax,
  title={SGMCMCJax: a lightweight JAX library for stochastic gradient Markov chain Monte Carlo algorithms},
  author={Coullon, Jeremie and Nemeth, Christopher},
  journal={Journal of Open Source Software},
  volume={7},
  number={72},
  pages={4113},
  year={2022}
}

@inproceedings{chen2014stochastic,
  title={Stochastic gradient Hamiltonian Monte Carlo},
  author={Chen, Tianqi and Fox, Emily and Guestrin, Carlos},
  booktitle={International conference on machine learning},
  pages={1683--1691},
  year={2014},
  organization={PMLR}
}

@article{robbins1951stochastic,
  title={A stochastic approximation method},
  author={Robbins, Herbert and Monro, Sutton},
  journal={The annals of mathematical statistics},
  pages={400--407},
  year={1951},
  publisher={JSTOR}
}

@article{baker2019control,
  title={Control variates for stochastic gradient MCMC},
  author={Baker, Jack and Fearnhead, Paul and Fox, Emily B and Nemeth, Christopher},
  journal={Statistics and Computing},
  volume={29},
  pages={599--615},
  year={2019},
  publisher={Springer}
}

@article{dau2020waste,
  title={Waste-free sequential Monte Carlo},
  author={Dau, Hai-Dang and Chopin, Nicolas},
  journal={arXiv preprint arXiv:2011.02328},
  year={2020}
}

@inproceedings{betancourt2013general,
  title={A general metric for Riemannian manifold Hamiltonian Monte Carlo},
  author={Betancourt, Michael},
  booktitle={Geometric Science of Information: First International Conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings},
  pages={327--334},
  year={2013},
  organization={Springer}
}

@article{betancourt2013generalizing,
  title={Generalizing the no-U-turn sampler to Riemannian manifolds},
  author={Betancourt, Michael J},
  journal={arXiv preprint arXiv:1304.1920},
  year={2013}
}

@article{zhang2022pathfinder,
  title={Pathfinder: Parallel quasi-Newton variational inference},
  author={Zhang, Lu and Carpenter, Bob and Gelman, Andrew and Vehtari, Aki},
  journal={Journal of Machine Learning Research},
  volume={23},
  number={306},
  pages={1--49},
  year={2022}
}

@article{deng2020contour,
  title={A contour stochastic gradient Langevin dynamics algorithm for simulations of multi-modal distributions},
  author={Deng, Wei and Lin, Guang and Liang, Faming},
  journal={Advances in neural information processing systems},
  volume={33},
  pages={15725--15736},
  year={2020}
}

@article{deng2022interacting,
  title={Interacting Contour Stochastic Gradient Langevin Dynamics},
  author={Deng, Wei and Liang, Siqi and Hao, Botao and Lin, Guang and Liang, Faming},
  journal={arXiv preprint arXiv:2202.09867},
  year={2022}
}

@article{roeder2017sticking,
  title={Sticking the landing: Simple, lower-variance gradient estimators for variational inference},
  author={Roeder, Geoffrey and Wu, Yuhuai and Duvenaud, David K},
  journal={Advances in Neural Information Processing Systems},
  volume={30},
  year={2017}
}

@article{agrawal2020advances,
  title={Advances in black-box VI: Normalizing flows, importance weighting, and optimization},
  author={Agrawal, Abhinav and Sheldon, Daniel R and Domke, Justin},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={17358--17369},
  year={2020}
}

@article{wang2022exact,
  title={Exact convergence analysis of the independent Metropolis-Hastings algorithms},
  author={Wang, Guanyang},
  journal={Bernoulli},
  volume={28},
  number={3},
  pages={2012--2033},
  year={2022},
  publisher={Bernoulli Society for Mathematical Statistics and Probability}
}

@book{gelman2014bayesian,
  title={Bayesian data analysis},
  author={Gelman, Andrew and Carlin, John B and Stern, Hal S and Rubin, Donald B},
  year={2014},
  publisher={Chapman and Hall/CRC}
}

@article{ding2014bayesian,
  title={Bayesian sampling using stochastic gradient thermostats},
  author={Ding, Nan and Fang, Youhan and Babbush, Ryan and Chen, Changyou and Skeel, Robert D and Neven, Hartmut},
  journal={Advances in neural information processing systems},
  volume={27},
  year={2014}
}

@article{ma2015complete,
  title={A complete recipe for stochastic gradient MCMC},
  author={Ma, Yi-An and Chen, Tianqi and Fox, Emily},
  journal={Advances in neural information processing systems},
  volume={28},
  year={2015}
}

@article{liu2016stein,
  title={Stein variational gradient descent: A general purpose bayesian inference algorithm},
  author={Liu, Qiang and Wang, Dilin},
  journal={Advances in neural information processing systems},
  volume={29},
  year={2016}
}

@inproceedings{hoffman2021adaptive,
  title={An adaptive-mcmc scheme for setting trajectory lengths in hamiltonian monte carlo},
  author={Hoffman, Matthew and Radul, Alexey and Sountsov, Pavel},
  booktitle={International Conference on Artificial Intelligence and Statistics},
  pages={3907--3915},
  year={2021},
  organization={PMLR}
}

@misc{steeg2021hamiltonian,
      title={Hamiltonian Dynamics with Non-Newtonian Momentum for Rapid Sampling},
      author={Greg Ver Steeg and Aram Galstyan},
      year={2021},
      eprint={2111.02434},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}

@misc{robnik2023microcanonical,
      title={Microcanonical Hamiltonian Monte Carlo},
      author={Jakob Robnik and G. Bruno De Luca and Eva Silverstein and Uroš Seljak},
      year={2023},
      eprint={2212.08549},
      archivePrefix={arXiv},
      primaryClass={stat.CO}
}

@misc{robnik2023microcanonical2,
  title={Microcanonical Langevin Monte Carlo},
  author={Robnik, Jakob and Seljak, Uro{\v{s}}},
  journal={arXiv preprint arXiv:2303.18221},
  year={2023}
}

@article{Livingstone2022Barker,
    author = {Livingstone, Samuel and Zanella, Giacomo},
    title = "{The Barker Proposal: Combining Robustness and Efficiency in Gradient-Based MCMC}",
    journal = {Journal of the Royal Statistical Society Series B: Statistical Methodology},
    volume = {84},
    number = {2},
    pages = {496-523},
    year = {2022},
    month = {01},
    issn = {1369-7412},
    doi = {10.1111/rssb.12482},
    url = {https://doi.org/10.1111/rssb.12482},
    eprint = {https://academic.oup.com/jrsssb/article-pdf/84/2/496/49322274/jrsssb\_84\_2\_496.pdf},
}


@misc{huang2021schrodingerfollmer,
      title={Schr{\"o}dinger-F{\"o}llmer Sampler: Sampling without Ergodicity},
      author={Jian Huang and Yuling Jiao and Lican Kang and Xu Liao and Jin Liu and Yanyan Liu},
      year={2021},
      eprint={2106.10880},
      archivePrefix={arXiv},
      primaryClass={stat.CO}
}
