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Performs and Approximate Bayesian Computation as a Particle Filter

ABCSMC.Rd

Given a set of simulation experiments (list), a model, parameter boundaries, this function will draw a sample of parameters from the posterior probability density of the given problem.

Usage

ABCSMC(
  objectiveFunction,
  startPar,
  Sigma = 2 * cov(startPar),
  dprior,
  delta = c(2, 0.5),
  parAcceptable = function(p) {
     all(is.finite(p))
 },
  verbose = interactive()
)

Arguments

objectiveFunction

a function that can simulate the model for a batch of parameter vectors provided as a matrix of columns (batches)

startPar

a matrix that has the same shape as the desired sample, but transposed, this can be a sample from the prior or a pre-conditioned sample that approximates the posterior, e.g.: t(rprior(1000))

Sigma

multivariate normal covariance of Markov chain transition kernel

dprior

a function that returns prior probability density values

delta

ABC acceptance threshold, either a scalar, then it is the initial value of delta, or a pair of values, then it is the starting value and the final value of delta: c(initialDelta,finalDelta)

parAcceptable

is a rejection-shortcut function; if parAcceptable(p) returns FALSE for a specific value of p, it means that simulations shouldn't even be attempted.

verbose

a logical value indicating whether log messages should be printed

Value

a list containing a sample matrix and a vector of scores (values of delta for each sample)

Details

This is a variant of ABC where the entire batch is simulated with one call to the simulator. startPar is the initial batch to be simulated: it is a matrix where columns are different parameter vectors (e.g. prior sample members). In other words: startPar[,i] must be a valid argument for the objectiveFunction.

The objective function is a closure

The Objective-Function objectiveFuntion(P) should return a matrix with n rows, where n is the number of simulation experiments (and thus data-sets), and m columns, where m is the number of parameterizations NCOL(P).

Examples

  library(parallel)
  opt <- options(mc.cores=2) # use [detectCores()] here
  f <- uqsa_example("AKAR4")
  m <- model_from_tsv(f)
  ex <- experiments(m,as_ode(m,cla=FALSE))
  G <- as_cme(m)         # for Gillespie solver
  C <- generate_code(G)
  c_path(G) <- write_c_code(C)
  so_path(G) <- shlib(G)
  muX <- m$Parameter$value
  sdX <- m$Parameter$stdv
  rprior <- rNormalPrior(log(muX^2/(muX^2+sdX^2)),sqrt(log(1+sdX^2/muX^2)))
  dprior <- dNormalPrior(log(muX^2/(muX^2+sdX^2)),sqrt(log(1+sdX^2/muX^2)))
  s <- simstoch(ex,G,logParMap)
  O <- makeObjective(ex,s)
  X <- rprior(100)
  colnames(X) <- rownames(m$Parameter)
  if (interactive()) {
     posterior <- ABCSMC(O,t(X),Sigma=cov(X),dprior=dprior,delta=c(0.4,1.5))
  }
  options(opt) # restore original options