XDNUTS-package

tools:::Rd_package_title("XDNUTS")

tools:::Rd_package_description("XDNUTS") package

Details

The DESCRIPTION file: tools:::Rd_package_DESCRIPTION("XDNUTS")

tools:::Rd_package_indices("XDNUTS")

The package allows to use a more efficient version of the Discontinuous Hamiltonian Monte Carlo proposed in \insertCite nishimura2020discontinuousXDNUTS, thanks to the use of recycled samples from each trajectory \insertCite Nishimura_2020XDNUTS and a termination criterion for identyfing the optimal discrete integration time of each trajectory \insertCite betancourt2016identifyingXDNUTS. 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 \insertCite nishimura2020discontinuousXDNUTS. 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 \insertCite hoffman2014noXDNUTS.
• XHMC: Hamiltonian Monte Carlo with a termination criterion based on the exhustion of the virial \insertCite betancourt2016identifyingXDNUTS 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 \insertCite betancourt2017conceptualXDNUTS.

All of them are embedded into the framework described in \insertCite nishimura2020discontinuousXDNUTS 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)

tools:::Rd_package_author("XDNUTS")

Maintainer: tools:::Rd_package_maintainer("XDNUTS")

References

\insertRef hoffman2014noXDNUTS

\insertRef betancourt2016identifyingXDNUTS

\insertRef betancourt2017conceptualXDNUTS

\insertRef nishimura2020discontinuousXDNUTS

\insertRef Nishimura_2020XDNUTS