This function proposes an MCMC candidate variable, and either accepts or rejects the candidate

This function receives a current MCMC variable, then calculates a possible successor and returns it in the case of acceptance. It returns the (old) current state upon rejection of the candidate.

Usage

automatic_update(
  simulate,
  logLikelihood = ll,
  dprior = function(x) prod(dnorm(x)),
  gradLogLikelihood = NULL,
  gprior = NULL,
  fisherInformation = NULL,
  fisherInformationPrior = NULL,
  Sigma = NULL,
  parAcceptable = function(p) {
     TRUE
 }
)

Arguments

simulate

a function that simulates the model for a given parMCMC

logLikelihood

a function that calculates log-likelihood values for given parMCMC

dprior

prior density function

gradLogLikelihood

a function that calculates the gradient of the log-likelihood for given parMCMC

gprior

gradient of the prior density

fisherInformation

a function that calculates approximates Fisher information matrices

fisherInformationPrior

a constant matrix, the prior distributions fisher information

Sigma

alternatively, Sigma=solve(fisherInformationPrior), [the inverse to fisherInformationPrior] can be specified for the metropolis algorithm

parAcceptable

a user shaped function that returns a Boolean scalar indicating whether a proposed parameter satisfies any user chosen constraints. A value of FALSE will trigger an early return and the model will not be simulated.

Value

a function that returns possibly updated states of the Markov chain

Details

The Markov chain has a current state (the MCMC variable, often x in literature), but in the context of sampling the MCMC variables are used as the parameters to a scientific model of some sort (and these often have state variables, also x, or y). This is why we call the variables parMCMC (parABC), or parCurrent|Given|Proposal, and similar.