Create object to adapt proposal scale to coerce average acceptance rate using a Robbins and Monro (1951) scheme.

When combined with covariance_shape_adapter() corresponds to Algorithm 4 in Andrieu and Thoms (2009).

Usage

stochastic_approximation_scale_adapter(
  initial_scale = NULL,
  target_accept_prob = NULL,
  kappa = 0.6
)

Arguments

initial_scale

Initial value to use for scale parameter. If not set explicitly a proposal and dimension dependent default will be used.

target_accept_prob

Target value for average accept probability for chain. If not set a proposal dependent default will be used.

kappa

Decay rate exponent in [0.5, 1] for adaptation learning rate.

Value

List of functions with entries

• initialize, a function for initializing adapter state and proposal parameters at beginning of chain,

• update a function for updating adapter state and proposal parameters on each chain iteration,

• finalize a function for performing any final updates to adapter state and proposal parameters on completion of chain sampling (may be NULL if unused).

• state a zero-argument function for accessing current values of adapter state variables.

References

Andrieu, C., & Thoms, J. (2008). A tutorial on adaptive MCMC. Statistics and Computing, 18, 343-373.

Robbins, H., & Monro, S. (1951). A stochastic approximation method. The Annals of Mathematical Statistics, 400-407.

Examples

proposal <- barker_proposal()
adapter <- stochastic_approximation_scale_adapter(
  initial_scale = 1., target_accept_prob = 0.4
)
adapter$initialize(proposal, chain_state(c(0, 0)))