expect_mcmc_reversible: Test of MCMC chain assuming reversibility of the chain

In mcunit: Unit Tests for MC Methods

Description

Test of MCMC steps having the correct stationary distribution assuming reversibility of the chain. Uses ideas from \insertCitebesag_clifford_1989;textualmcunit as extended to possible ties in \insertCitegandy_scott_2019;textualmcunit.

Usage

expect_mcmc_reversible(
  object,
  control = NULL,
  thinning = NULL,
  nsteps = 10,
  p = 1,
  tolerance = 1e-08
)

Arguments

object	A list describing the MCMC sampler with the following elements: genprior: A function with no arguments that generates a sample of the prior distribution. No default value. gendata: A function that takes as input the parameter value (of the type generated by genprior) and returns the observed data as an arbitrary R object. No default value. stepMCMC: A function that takes three arguments: theta: the current position of the chain (of the same type as produced by the prior), dat: the observed data (of the same type as produced by gendat) thinning: the number of steps the chain should take. 1 corresponds to one step. test: Function that takes either one or two arguments, and returns a vector with components which will be used for checking the MCMC sampler. The first argument is interpreted as a parameter value, and if a second argument exists, it is interpreted as a data value. An example is the identity function: function(x) x. Alternatively, if you have access to the model's likelihood function, you could use: function(x,y) likelihood(x,y).
control	a list controlling the algorithm n number of samples to be taken in the first step. Default: 1e3 maxseqsteps: Number of sequential attempts to use. Default: 7. incn: Factor by which to multiply n from the second sequential attempt onward. Default: 4. level: bound on the type I error, ie the probability of wrongly rejecting a sampler with the correct distribution. Default: 1e-5. debug: If positive then debug information will be printed via 'message()'. Default: 0.
thinning	Amount of thinning for the MCMC chain. 1 corresponds to no thinning. Default: automatically computed to ensure an autocorrelation of at most 0.5 at lag 1.
nsteps	Number of steps of the chain to use. Default: 10.
p	The probability with which the MCMC updates the parameter as opposed to the data in a given step. If less than 1.0, then the MCMC is a random scan on both data and parameters. Default: 1.0.
tolerance	Absolute error where value of the samplers are treated as equal. Default: 1e-8.

Value

The first argument, invisibly, to allow chaining of expectations.

References

\insertAllCited

See Also

expect_mcmc

Examples

object <- list(genprior=function() rnorm(1),
               gendata=function(theta) rnorm(5,theta),
               stepMCMC=function(theta,data,thinning){
                  f <- function(x) prod(dnorm(data,x))*dnorm(x)  
                  for (i in 1:thinning){
                     thetanew = rnorm(1,mean=theta,sd=1)
                     if (runif(1)<f(thetanew)/f(theta))
                     theta <- thetanew
                  }
                  theta
               },
               test=function(x) x
               )
expect_mcmc_reversible(object)

mcunit documentation built on April 2, 2021, 5:06 p.m.