XDNUTS-package: Discontinuous Hamiltonian Monte Carlo with Varying Trajectory...

In XDNUTS: Discontinuous Hamiltonian Monte Carlo with Varying Trajectory Length

Discontinuous Hamiltonian Monte Carlo with Varying Trajectory Length

Description

Hamiltonian Monte Carlo for both continuous and discontinuous posterior distributions with customisable trajectory length termination criterion. See Nishimura et al. (2020) <doi:10.1093/biomet/asz083> for the original Discontinuous Hamiltonian Monte Carlo, Hoffman et al. (2014) <doi:10.48550/arXiv.1111.4246> and Betancourt (2016) <doi:10.48550/arXiv.1601.00225> for the definition of possible Hamiltonian Monte Carlo termination criteria.

Details

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The package allows to use a more efficient version of the Discontinuous Hamiltonian Monte Carlo proposed in \insertCitenishimura2020discontinuousXDNUTS, thanks to the use of recycled samples from each trajectory \insertCiteNishimura_2020XDNUTS and a termination criterion for identyfing the optimal discrete integration time of each trajectory \insertCitebetancourt2016identifyingXDNUTS. No models are at disposal, so the user must specify one through the definition of the function nlp. This function must evaluate the negative log posterior of the model and its gradient with respect to the first d-k parameters. d is the model dimension, while k is the number of parameters for which the sampling scheme will be based on the method described in \insertCitenishimura2020discontinuousXDNUTS. This method was born for treating discontinuous components but it is applicable to continuous one too. nlp must be a function with 3 arguments:

• the vector of parameters, current state of the chain/trajectory, for which the negative log posterior or its gradient must be evaluated.

• a list object that contains the necessary argouments, namely data and hyperparameters.

• a boolean value, TRUE to evaluate only the negative log posterior of the models, FALSE to evaluate its gradient with respect to the continuous components of the posterior.

The available algorithms are the following

NUTS

No U-Turn Sampler of \insertCitehoffman2014noXDNUTS.

XHMC

Hamiltonian Monte Carlo with a termination criterion based on the exhustion of the virial \insertCitebetancourt2016identifyingXDNUTS which require the specification of a threshold.

HMC

Hamiltonian Monte Carlo with trajectory length varying uniformly inside a user specified interval. Instead of proposing the last value of each trajectories a sample is drawn uniformly from them. Reference can be found in \insertCitebetancourt2017conceptualXDNUTS.

All of them are embedded into the framework described in \insertCitenishimura2020discontinuousXDNUTS which allows the use of Hamiltonian Monte Carlo with discontinuous posterior and hence to discrete parameter space by the definition of a step function shape density.

Author(s)

Paolo Manildo [aut, cre] (ORCID: <https://orcid.org/0009-0006-7056-7012>)

Maintainer: Paolo Manildo <[e-mail]>

References

\insertRef

hoffman2014noXDNUTS

\insertRefbetancourt2016identifyingXDNUTS

\insertRefbetancourt2017conceptualXDNUTS

\insertRefnishimura2020discontinuousXDNUTS

\insertRefNishimura_2020XDNUTS

XDNUTS documentation built on Aug. 24, 2025, 5:08 p.m.