TMB (version 1.7.5)

run_mcmc.nuts: [BETA VERSION] Draw MCMC samples from a model posterior using the No-U-Turn (NUTS) sampler with dual averaging.

Description

[BETA VERSION] Draw MCMC samples from a model posterior using the No-U-Turn (NUTS) sampler with dual averaging.

Usage

run_mcmc.nuts(nsim, fn, gr, params.init, max_doublings = 4, eps = NULL, Madapt = NULL, delta = 0.5, covar = NULL, diagnostic = FALSE)

Arguments

nsim

The number of samples to return.

fn

A function that returns the log of the posterior density.

gr

A function that returns a vector of gradients of the log of the posterior density (same as fn).

params.init

A vector of initial parameter values.

max_doublings

Integer representing the maximum times the path length should double within an MCMC iteration. Default of 4, so 16 steps. If a U-turn has not occured before this many steps the algorithm will stop and return a sample from the given tree.

eps

The length of the leapfrog steps. If a numeric value is passed, it will be used throughout the entire chain. A NULL value will initiate adaptation of eps using the dual averaging algorithm during the first Madapt steps.

Madapt

An optional argument for how many iterations to adapt eps in the dual averaging algorithm. A value of NULL results in a default of Madapt=nsim/2.

delta

The target acceptance rate for the dual averaging algorithm. Defaults to 50%. NUTS does not include an accept/reject Metropolis step, so this rate can be understood as the "average acceptance probability that HMC would give to the position-momentum states explored during the final doubling iteration."

covar

An optional covariance matrix which can be used to improve the efficiency of sampling. The lower Cholesky decomposition of this matrix is used to transform the parameter space. If the posterior is approximately multivariate normal and covar approximates the covariance, then the transformed parameter space will be close to multivariate standard normal. In this case the algorithm will be more efficient, but there will be overhead in the matrix calculations which need to be done at each step. The default of NULL specifies to not do this transformation.

diagnostic

Whether to return a list of diagnostic metrics about the chain. Useful for assessing efficiency and tuning chain.

Value

If diagnostic is FALSE (default), returns a matrix of nsim samples from the posterior. Otherwise returns a list containing samples ('par'), vector of steps taken at each iteration ('steps.taken'), and the total function and gradient calls ('n.calls'), which in the case of NUTS is dynamic, and finally the average eps ('epsbar') from the dual averaging algorithm if used (otherwise NULL).

Details

This function implements algorithm 6 of Hoffman and Gelman (2014), which includes adaptive step sizes (eps) via an algorithm called dual averaging. In theory neither the step length nor step size needs to be input by the user to obtain efficient sampling from the posterior.

References

• Neal, R. M. (2011). MCMC using Hamiltonian dynamics. Handbook of Markov Chain Monte Carlo.
• Hoffman and Gelman (2014). The No-U-Turn sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. J. Mach. Learn. Res. 15:1593-1623.

See Also

run_mcmc, run_mcmc.hmc, run_mcmc.rwm