RBaM (version 1.1.1)

MCMC_OAAT: Adaptive One-At-A-Time Metropolis sampler

Description

An adaptive Metropolis sampler that updates the parameter vector one component at a time using a 1-dimensional jump. This allows easily adapting the jump standard deviation for each component in order to comply with a specified move rate interval.

Usage

MCMC_OAAT(
  logPdf,
  x0,
  s0 = 0.05 * (abs(x0) + 0.1),
  nTheta = length(x0),
  nAdapt = 50,
  nCycles = 20,
  minMoveRate = 0.2,
  maxMoveRate = 0.5,
  downMult = 0.9,
  upMult = 1.1,
  ...
)

Value

A list with the following components:

samples

data frame, MCMC simulations.

components

data frame, corresponding values of the log-posterior, the log-prior and the log-likelihood.

sjump

numeric vector, the adapted jump standard deviations.

Arguments

logPdf

function, evaluating the log-density of the distribution to sample from (up to a proportionality constant). logPdf can return either a single numeric value, interpreted as the target log-pdf, or a list containing components named 'logPosterior', 'logLikelihood' and 'logPrior'.

x0

numeric vector, starting point.

s0

numeric vector, starting jump standard deviations.

nTheta

integer>0, size of the "theta" part of x0, i.e. components that represent the model parameters rather than structural errors parameters (gamma). This is used to speed-up the sampler by avoiding running the model for gamma components. nTheta=length(x0) (default) implies no attempt at speeding up.

nAdapt

integer > 1, number of iterations before adapting the jump standard deviations.

nCycles

integer > 1, number of adaption cycles. Total number of iterations is hence equal to nAdapt*nCycles. nCycles=1 leads to a non-adaptive one-at-a-time Metropolis sampler.

minMoveRate

numeric in (0;1), lower bound for the desired move rate interval.

maxMoveRate

numeric in (0;1), upper bound for the desired move rate interval.

downMult

numeric in (0;1), multiplication factor used to decrease the jump standard deviation when move rate is too low.

upMult

numeric (>1, avoid 1/downMult) multiplication factor used to increase the jump standard deviations when move rate is too high.

...

other arguments passed to function logPdf

Examples

# Define a 2-dimensional target log-pdf
logPdf <- function(x){
    p1=log(0.6*dnorm(x[1],0,1)+0.4*dnorm(x[1],2,0.5))
    p2=log(dlnorm(x[2],0,1))
    return(p1+p2)
}
# Sample from it
mcmc=MCMC_OAAT(logPdf,c(1,1))
plot(mcmc$samples)