Create object to adapt proposal with shape based on estimate of target distribution covariance matrix.

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

Usage

covariance_shape_adapter(kappa = 1)

Arguments

kappa

Decay rate exponent in [0.5, 1] for adaptation learning rate. Value of 1 (default) corresponds to computing empirical covariance matrix.

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.

Details

Requires ramcmc package to be installed for access to efficient rank-1 Cholesky update function ramcmc::chol_update.

References

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.

Examples

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