Control for adaptive proposals, used in pmcmc_control for deterministic models.
adaptive_proposal_control(
initial_vcv_weight = 1000,
initial_scaling = 1,
initial_scaling_weight = NULL,
min_scaling = 0,
scaling_increment = NULL,
log_scaling_update = TRUE,
acceptance_target = 0.234,
forget_rate = 0.2,
forget_end = Inf,
adapt_end = Inf,
pre_diminish = 0
)Weight of the initial variance-covariance matrix used to build the proposal of the random-walk. Higher values translate into higher confidence of the initial variance-covariance matrix and means that update from additional samples will be slower.
The initial scaling of the variance covariance matrix to be used to generate the multivariate normal proposal for the random-walk Metropolis-Hastings algorithm. To generate the proposal matrix, the weighted variance covariance matrix is multiplied by the scaling parameter squared times 2.38^2 / n_pars (where n_pars is the number of fitted parameters). Thus, in a Gaussian target parameter space, the optimal scaling will be around 1.
The initial weight used in the scaling update.
The scaling weight will increase after the first pre_diminish
iterations, and as the scaling weight increases the adaptation of the
scaling diminishes. If NULL (the default) the value is
5 / (acceptance_target * (1 - acceptance_target)).
The minimum scaling of the variance covariance matrix to be used to generate the multivariate normal proposal for the random-walk Metropolis-Hastings algorithm.
The scaling increment which is added or
subtracted to the scaling factor of the variance-covariance
after each adaptive step. If NULL (the default) then an optimal
value will be calculated.
Logical, whether or not changes to the scaling parameter are made on the log-scale.
The target for the fraction of proposals that should be accepted (optimally) for the adaptive part of the mixture model.
The rate of forgetting early parameter sets from the
empirical variance-covariance matrix in the MCMC chains. For example,
forget_rate = 0.2 (the default) means that once in every 5th iterations
we remove the earliest parameter set included, so would remove the 1st
parameter set on the 5th update, the 2nd on the 10th update, and so
on. Setting forget_rate = 0 means early parameter sets are never
forgotten.
The final iteration at which early parameter sets can
be forgotten. Setting forget_rate = Inf (the default) means that the
forgetting mechanism continues throughout the chains. Forgetting early
parameter sets becomes less useful once the chains have settled into the
posterior mode, so this parameter might be set as an estimate of how long
that would take.
The final iteration at which we can adapt the multivariate normal proposal. Thereafter the empirical variance-covariance matrix, its scaling and its weight remain fixed. This allows the adaptation to be switched off at a certain point to help ensure convergence of the chain.
The number of updates before adaptation of the scaling
parameter starts to diminish. Setting pre_diminish = 0 means there is
diminishing adaptation of the scaling parameter from the offset, while
pre_diminish = Inf would mean there is never diminishing adaptation.
Diminishing adaptation should help the scaling parameter to converge
better, but while the chains find the location and scale of the posterior
mode it might be useful to explore with it switched off.
Efficient exploration of the parameter space during an MCMC might be difficult when the target distribution is of high dimensionality, especially if the target probability distribution present a high degree of correlation. Adaptive schemes are used to "learn" on the fly the correlation structure by updating the proposal distribution by recalculating the empirical variance-covariance matrix and rescale it at each adaptive step of the MCMC.
Our implementation of an adaptive MCMC algorithm is based on an adaptation of the "accelerated shaping" algorithm in Spencer (2021). The algorithm is based on a random-walk Metropolis-Hasting algorithm where the proposal is a multi-variate Normal distribution centered on the current point.
Spencer SEF (2021) Accelerating adaptation in the adaptive Metropolis–Hastings random walk algorithm. Australian & New Zealand Journal of Statistics 63:468-484.