Gaussian Transition Kernel

Gaussian Transition Kernel

kernel_normal(mu = 0, scale = 1, fixed = FALSE, scheme = "joint")

kernel_normal_reflective(
  mu = 0,
  scale = 1,
  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.

fixed, scheme

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

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.

Value

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

Details

The kernel_normal function provides the canonical normal kernel with symmetric transition probabilities.

The kernel_normal_reflective implements the normal kernel with reflective boundaries. Lower and upper bounds are treated using reflecting boundaries, this is, if the proposed \(\theta'\) is greater than the ub, then \(\theta' - ub\) is subtracted from \(ub\). At the same time, if it is less than lb, then \(lb - \theta'\) is added to lb iterating until \(\theta\) is within [lb, ub].

In this case, the transition probability is symmetric (just like the normal kernel).

See also

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

Examples

# Normal kernel with a small scale (sd) of 0.05
kern <- kernel_normal(scale = 0.05)

# Using boundaries for the second parameter of a two parameter chain
# to have values in [0, 100].
kern <- kernel_normal_reflective(
  ub = c(.Machine$double.xmax, 100),
  lb = c(-.Machine$double.xmax, 0)
  )