Mirror Transition Kernels

NMirror and UMirror transition kernels described in Thawornwattana et al. (2018).

kernel_nmirror(
  mu = 0,
  scale = 1,
  warmup = 500L,
  nadapt = 4L,
  arate = 0.4,
  lb = -.Machine$double.xmax,
  ub = .Machine$double.xmax,
  fixed = FALSE,
  scheme = "joint"
)

kernel_umirror(
  mu = 0,
  scale = 1,
  warmup = 500L,
  nadapt = 4L,
  arate = 0.4,
  lb = -.Machine$double.xmax,
  ub = .Machine$double.xmax,
  fixed = FALSE,
  scheme = "joint"
)

Arguments

mu, scale

Either a numeric vector or a scalar. Proposal mean and scale. If scalar, values are recycled to match the number of parameters in the objective function.

warmup

Integer. Number of steps required before starting adapting the chains.

nadapt

Integer. Number of times the scale is adjusted for adaptation during the warmup (burn-in) period.

arate

Double. Target acceptance rate used as a reference during the adaptation process.

lb, ub

Either a numeric vector or a scalar. Lower and upper bounds for bounded kernels. When of length 1, the values are recycled to match the number of parameters in the objective function.

fixed, scheme

For multivariate functions, sets the update plan. See plan_update_sequence().

Value

An object of class fmcmc_kernel. fmcmc_kernel objects are intended to be used with the MCMC() function.

Details

The kernel_nmirror and kernel_umirror functions implement simple symmetric transition kernels that pivot around an approximation of the asymptotic mean.

In the multidimensional case, this implementation just draws a vector of independent draws from the proposal kernel, instead of using, for example, a multivariate distribution of some kind. This will be implemented in the next update of the package.

During the warmup period (or burnin as described in the paper), the algorithm adapts both the scale and the reference mean of the proposal distribution. While the mean is adapted continuously, the scale is updated only a handful of times, in particular, nadapt times during the warmup time. The adaptation is done as proposed by Yang and Rodriguez (2013) in which the scale is adapted four times.

References

Thawornwattana, Y., Dalquen, D., & Yang, Z. (2018). Designing Simple and Efficient Markov Chain Monte Carlo Proposal Kernels. Bayesian Analysis, 13(4), 1037–1063. doi:10.1214/17-BA1084

Yang, Z., & Rodriguez, C. E. (2013). Searching for efficient Markov chain Monte Carlo proposal kernels. Proceedings of the National Academy of Sciences, 110(48), 19307–19312. doi:10.1073/pnas.1311790110

See also

Other kernels: kernel_adapt(), kernel_new(), kernel_normal(), kernel_ram(), kernel_unif()

Examples

# Normal mirror kernel with 5 adaptations and 1000 steps of warmup (burnin)
kern <- kernel_nmirror(nadapt = 5, warmup = 1000)

# Same as before but using a uniform mirror and choosing a target acceptance
# rate of 24 %
kern <- kernel_umirror(nadapt = 5, warmup = 1000, arate = .24)