Metropolis {BayesianTools}

Creates a Metropolis-type MCMC with options for covariance adaptatin, delayed rejection, Metropolis-within-Gibbs, and tempering

Description

Creates a Metropolis-type MCMC with options for covariance adaptatin, delayed rejection, Metropolis-within-Gibbs, and tempering

Usage

Metropolis(
  bayesianSetup,
  settings = list(startValue = NULL, optimize = T, proposalGenerator = NULL,
    consoleUpdates = 100, burnin = 0, thin = 1, parallel = NULL, adapt = T,
    adaptationInterval = 500, adaptationNotBefore = 3000, DRlevels = 1, proposalScaling =
    NULL, adaptationDepth = NULL, temperingFunction = NULL, gibbsProbabilities = NULL,
    message = TRUE)
)

Arguments

bayesianSetup

either an object of class bayesianSetup created by createBayesianSetup (recommended), or a log target function

settings

a list of settings - possible options follow below

startValue

startValue for the MCMC and optimization (if optimize = T). If not provided, the sampler will attempt to obtain the startValue from the bayesianSetup

optimize

logical, determines whether an optimization for start values and proposal function should be run before starting the sampling

proposalGenerator

optional proposalgenerator object (see createProposalGenerator)

proposalScaling

additional scaling parameter for the proposals that controls the different scales of the proposals after delayed rejection (typical, after a rejection, one would want to try a smaller scale). Needs to be as long as DRlevels. Defaults to 0.5^(- 0:(mcmcSampler$settings$DRlevels -1)

burnin

number of iterations treated as burn-in. These iterations are not recorded in the chain.

thin

thinning parameter. Determines the interval in which values are recorded.

consoleUpdates

integer, determines the frequency with which sampler progress is printed to the console

adapt

logical, determines wheter an adaptive algorithm should be implemented. Default is TRUE.

adaptationInterval

integer, determines the interval of the adaption if adapt = TRUE.

adaptationNotBefore

integer, determines the start value for the adaption if adapt = TRUE.

DRlevels

integer, determines the number of levels for a delayed rejection sampler. Default is 1, which means no delayed rejection is used.

temperingFunction

function to implement simulated tempering in the algorithm. The function describes how the acceptance rate will be influenced in the course of the iterations.

gibbsProbabilities

vector that defines the relative probabilities of the number of parameters to be changes simultaniously.

message

logical determines whether the sampler's progress should be printed

Details

The 'Metropolis' function is the main function for all Metropolis based samplers in this package. To call the derivatives from the basic Metropolis-Hastings MCMC, you can either use the corresponding function (e.g. AM for an adaptive Metropolis sampler) or use the parameters to adapt the basic Metropolis-Hastings. The advantage of the latter case is that you can easily combine different properties (e.g. adapive sampling and delayed rejection sampling) without changing the function.

Author(s)

Florian Hartig

References

Haario, H., E. Saksman, and J. Tamminen (2001). An adaptive metropolis algorithm. Bernoulli , 223-242.

Haario, Heikki, et al. "DRAM: efficient adaptive MCMC." Statistics and Computing 16.4 (2006): 339-354.

Hastings, W. K. (1970). Monte carlo sampling methods using markov chains and their applications. Biometrika 57 (1), 97-109.

Green, Peter J., and Antonietta Mira. "Delayed rejection in reversible jump Metropolis-Hastings." Biometrika (2001): 1035-1053.

Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller (1953). Equation of state calculations by fast computing machines. The journal of chemical physics 21 (6), 1087 - 1092.

Examples

# Running the metropolis via the runMCMC with a proposal covariance generated from the prior 
# (can be useful for complicated priors)

ll = function(x) sum(dnorm(x, log = TRUE))
setup = createBayesianSetup(ll, lower = c(-10,-10), upper = c(10,10))

samples = setup$prior$sampler(1000)

generator = createProposalGenerator(diag(1, setup$numPars))
generator = updateProposalGenerator(generator, samples, manualScaleAdjustment = 1, message = TRUE)

settings =  list(proposalGenerator = generator, optimize = FALSE, iterations = 500)  

out = runMCMC(bayesianSetup = setup, sampler = "Metropolis", settings = settings)