Create object to adapt proposal with per dimension scales based on estimates of target distribution variances.

Corresponds to variance variant of Algorithm 2 in Andrieu and Thoms (2009), which is itself a restatement of method proposed in Haario et al. (2001).

Usage

variance_shape_adapter(kappa = 1, initial_shape = NULL)

kappa: Decay rate exponent in [0.5, 1] for adaptation learning rate. Value of 1 (default) corresponds to computing empirical variances.
initial_shape: Optional numeric vector of length equal to the target distribution dimension, specifying the per-dimension proposal scales to use as the initial variance estimate. When supplied, takes precedence over both any current proposal shape and the default unit initialisation. When NULL (default), the adapter reads the current proposal shape at initialisation time (to carry over state from a previous warm-up stage) and falls back to unit variances if no current shape is available.

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.

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

Haario, H., Saksman, E., & Tamminen, J. (2001). An adaptive Metropolis algorithm. Bernoulli, 7(2): 223-242.

proposal <- barker_proposal()
adapter <- variance_shape_adapter()
adapter$initialize(proposal, chain_state(c(0, 0)))