Metropolis_OAAT_adaptive {HydroPortailStats}

Adaptive One-At-A-Time Metropolis sampler

Description

Performs nsim iterations of the Adaptive version of the OAAT Metropolis sampler (see ?Metropolis_OAAT). Adaptation is performed by monitoring move rates every batch.length iterations, and increasing / decreasing the jump standard deviation if the move rate is not within specified bounds.

Usage

Metropolis_OAAT_adaptive(
  f,
  x0,
  sdjump,
  ...,
  batch.length = 100,
  batch.n = 100,
  moverate.min = 0.1,
  moverate.max = 0.5,
  mult.down = 0.9,
  mult.up = 1.1
)

Arguments

f

function, log-pdf of the target distribution

x0

numeric vector, starting point

sdjump

numeric vector, initial standard deviation of the Gaussian jump for each component

...

other arguments passed to f

batch.length

integer, length of each non-adaptive batch

batch.n

integer, number of batches (= adaptation period). Total number of simulations is nsim=batch.n*batch.length

moverate.min

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

moverate.max

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

mult.down

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

mult.up

numeric (>1, avoid 1/mult.down) multiplication factor used to increase jump size when move rate is too high.

Value

A list with the following components:

x

numeric matrix nsim*length(x0), MCMC simulations

fx

numeric vector, corresponding values f(x)

Examples

# Bivariate target distribution: beta(0.8,0.4) X exp(1)
f=function(x){stats::dbeta(x[1],0.8,0.4,log=TRUE)+stats::dexp(x[2],log=TRUE)}
x0=c(0.5,2)
sdjump=c(0.5,1)
mcmc=Metropolis_OAAT_adaptive(f,x0,sdjump)
graphicalpar=par(mfrow=c(1,3))
plot(mcmc$x);hist(mcmc$x[,1]); hist(mcmc$x[,2])
par(graphicalpar)