DREAM: DREAM

In BayesianTools: General-Purpose MCMC and SMC Samplers and Tools for Bayesian Statistics

DREAM

Description

DREAM

Usage

DREAM(
  bayesianSetup,
  settings = list(iterations = 10000, nCR = 3, gamma = NULL, eps = 0, e = 0.05, pCRupdate
    = TRUE, updateInterval = 10, burnin = 0, thin = 1, adaptation = 0.2, parallel = NULL,
    DEpairs = 2, consoleUpdates = 10, startValue = NULL, currentChain = 1, message =
    TRUE)
)

Arguments

bayesianSetup	Object of class 'bayesianSetup' or 'bayesianOuput'.
settings	list with parameter values
iterations	Number of model evaluations
nCR	parameter determining the number of cross-over proposals. If nCR = 1 all parameters are updated jointly.
updateInterval	determining the intervall for the pCR update
gamma	Kurtosis parameter Bayesian Inference Scheme
eps	Ergodicity term
e	Ergodicity term
pCRupdate	If T, crossover probabilities will be updated
burnin	number of iterations treated as burn-in. These iterations are not recorded in the chain.
thin	thin thinning parameter. Determines the interval in which values are recorded.
adaptation	Number or percentage of samples that are used for the adaptation in DREAM (see Details).
DEpairs	Number of pairs used to generate proposal
startValue	eiter a matrix containing the start values (see details), an integer to define the number of chains that are run, a function to sample the start values or NUll, in which case the values are sampled from the prior.
consoleUpdates	Intervall in which the sampling progress is printed to the console
message	logical determines whether the sampler's progress should be printed

Details

Insted of a bayesianSetup, the function can take the output of a previous run to restart the sampler from the last iteration. Due to the sampler's internal structure you can only use the output of DREAM. If you provide a matrix with start values the number of rows determines the number of chains that are run. The number of coloumns must be equivalent to the number of parameters in your bayesianSetup.

There are several small differences in the algorithm presented here compared to the original paper by Vrugt et al. (2009). Mainly the algorithm implemented here does not have an automatic stopping criterion. Hence, it will always run the number of iterations specified by the user. Also, convergence is not monitored and left to the user. This can easily be done with coda::gelman.diag(chain). Further the proposed delayed rejectio step in Vrugt et al. (2009) is not implemented here.

During the adaptation phase DREAM is running two mechanisms to enhance the sampler's efficiency. First the disribution of crossover values is tuned to favor large jumps in the parameter space. The crossover probabilities determine how many parameters are updated simultaneously. Second outlier chains are replanced as they can largely deteriorate the sampler's performance. However, these steps destroy the detailed balance of the chain. Consequently these parts of the chain should be discarded when summarizing posterior moments. This can be done automatically during the sampling process (i.e. burnin > adaptation) or subsequently by the user. We chose to distinguish between the burnin and adaptation phase to allow the user more flexibility in the sampler's settings.

Value

mcmc.object containing the following elements: chains, X, pCR

Author(s)

Stefan Paul

References

Vrugt, Jasper A., et al. "Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling." International Journal of Nonlinear Sciences and Numerical Simulation 10.3 (2009): 273-290.

See Also

DREAMzs

Examples

library(BayesianTools)

ll <- generateTestDensityMultiNormal(sigma = "no correlation")
bayesianSetup <- createBayesianSetup(likelihood = ll, 
                                     lower = rep(-10, 3), 
                                     upper = rep(10, 3))

settings = list(iterations = 200)
out <- runMCMC(bayesianSetup = bayesianSetup, sampler = "DEzs", settings = settings)
summary(out)

# DE family samplers are population MCMCs that run a number of internal chains
# in parallel. Here examples how to change the internal chains
# note that internal chains can be executedi n parallel
settings = list(startValue = 4, iterations = 200)
out <- runMCMC(bayesianSetup = bayesianSetup, sampler = "DEzs", settings = settings)
summary(out)

# Modify the start values of the internal chains (note that this is a matrix
# of dim nChain * nPar)
settings = list(startValue = matrix(rnorm(12), nrow = 4, ncol = 3), 
                iterations = 200)
out <- runMCMC(bayesianSetup = bayesianSetup, sampler = "DEzs", settings = settings)
summary(out)

# In the DE sampler family with Z matrix, the previous chains are written in 
# a common matrix, from which proposals are generated. Per default this matrix
# is started with samples from the prior, but we can change this. Often useful
# to improve sampler convergence, 
# see  https://github.com/florianhartig/BayesianTools/issues/79
settings = list(startValue = matrix(rnorm(12), nrow = 4, ncol = 3),
                Z = matrix(rnorm(300), nrow = 100, ncol = 3),
                iterations = 200)
out <- runMCMC(bayesianSetup = bayesianSetup, sampler = "DEzs", settings = settings)
summary(out)

BayesianTools documentation built on Feb. 16, 2023, 8:44 p.m.