adaptive_proposal_control: Adaptive proposal control

In mrc-ide/mcstate: Monte Carlo Methods for State Space Models

Adaptive proposal control

Description

Control for adaptive proposals, used in pmcmc_control for deterministic models.

Usage

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
)

Arguments

initial_vcv_weight	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.
initial_scaling	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.
initial_scaling_weight	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)).
min_scaling	The minimum scaling of the variance covariance matrix to be used to generate the multivariate normal proposal for the random-walk Metropolis-Hastings algorithm.
scaling_increment	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.
log_scaling_update	Logical, whether or not changes to the scaling parameter are made on the log-scale.
acceptance_target	The target for the fraction of proposals that should be accepted (optimally) for the adaptive part of the mixture model.
forget_rate	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.
forget_end	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.
adapt_end	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.
pre_diminish	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.

Details

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.

mrc-ide/mcstate documentation built on July 3, 2024, 1:34 p.m.