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Piecewise deterministic Markov processes for scalable Monte Carlo on restricted domains

Author

Listed:
  • Bierkens, Joris
  • Bouchard-Côté, Alexandre
  • Doucet, Arnaud
  • Duncan, Andrew B.
  • Fearnhead, Paul
  • Lienart, Thibaut
  • Roberts, Gareth
  • Vollmer, Sebastian J.

Abstract

Piecewise Deterministic Monte Carlo algorithms enable simulation from a posterior distribution, whilst only needing to access a sub-sample of data at each iteration. We show how they can be implemented in settings where the parameters live on a restricted domain.

Suggested Citation

  • Bierkens, Joris & Bouchard-Côté, Alexandre & Doucet, Arnaud & Duncan, Andrew B. & Fearnhead, Paul & Lienart, Thibaut & Roberts, Gareth & Vollmer, Sebastian J., 2018. "Piecewise deterministic Markov processes for scalable Monte Carlo on restricted domains," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 148-154.
    • Handle: RePEc:eee:stapro:v:136:y:2018:i:c:p:148-154
    DOI: 10.1016/j.spl.2018.02.021
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    References listed on IDEAS

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    1. Geweke, John, 1986. "Exact Inference in the Inequality Constrained Normal Linear Regression Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(2), pages 127-141, April.
    2. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521766555, January.
    3. Gerhard Tutz & Jan Gertheiss, 2014. "Rating Scales as Predictors—The Old Question of Scale Level and Some Answers," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 357-376, July.
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    Cited by:

    1. Gael M. Martin & David T. Frazier & Christian P. Robert, 2022. "Computing Bayes: From Then `Til Now," Monash Econometrics and Business Statistics Working Papers 14/22, Monash University, Department of Econometrics and Business Statistics.
    2. M Ludkin & C Sherlock, 2023. "Hug and hop: a discrete-time, nonreversible Markov chain Monte Carlo algorithm," Biometrika, Biometrika Trust, vol. 110(2), pages 301-318.
    3. Bertazzi, Andrea & Bierkens, Joris & Dobson, Paul, 2022. "Approximations of Piecewise Deterministic Markov Processes and their convergence properties," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 91-153.
    4. Murray Pollock & Paul Fearnhead & Adam M. Johansen & Gareth O. Roberts, 2020. "Quasi‐stationary Monte Carlo and the ScaLE algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1167-1221, December.
    5. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    6. Quan Zhou & Jun Yang & Dootika Vats & Gareth O. Roberts & Jeffrey S. Rosenthal, 2022. "Dimension‐free mixing for high‐dimensional Bayesian variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1751-1784, November.
    7. Saifuddin Syed & Alexandre Bouchard‐Côté & George Deligiannidis & Arnaud Doucet, 2022. "Non‐reversible parallel tempering: A scalable highly parallel MCMC scheme," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 321-350, April.

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