recalibrationABC {abctools}

ABC inference with a recalibration adjustment

Description

This function post-processes ABC output with the aim of calibrating its credible intervals to have the correct probabilities. The approach can be thought of as extending coverage tests to correct deviations from the desired posterior. See the reference for details.

Usage

  recalibrationABC(target, param, sumstat, eps, tol, method="rejection",
  multicore=FALSE, cores=NULL, abc.p.options=list(method="loclinear"), ...)

Arguments

target

A vector of the observed summary statistics.

param

A data frame of the simulated parameter values.

sumstat

A data frame of the simulated summary statistics.

eps

The ABC acceptance threshold i.e. max acceptable distance. This or tol must be specified (but not both).

tol

The ABC acceptance tolerance i.e. proportion of simulations to accept. This or eps must be specified (but not both).

method

A character string indicating the type of ABC algorithm to be applied. Possible values are "rejection", "loclinear", "neuralnet" and "ridge".

multicore

Whether to use the parallel package to perform analyses of test datasets in parallel.

cores

Number of cores to use when multicore==TRUE.

abc.p.options

A list of further arguments to be supplied to the abc command when applying regression correction to the p-values based on the summary statistics.

...

Further arguments to be supplied to the abc command when performing inference for each simulated data set. Typically these will control regression correction. If omitted no correction is performed.

Value

A list with the following components is returned.

sample.abc is the ordinary ABC output sample (with any regression correction requested). The rows represent accepted samples and the columns represent the parameters.

sample.recal is the ABC output sample following recalibration. The rows are Monte Carlo draws from an approximation to the posterior and the columns represent the parameters.

sample.regrecal is the ABC output sample following coverage correction including regression correction of p-values. It has a similar form to sample.recal.

weights are weights for the ABC output. These apply to all types of ABC.

Each row of pvalues corresponds to a particular accepted dataset. It gives the p-values of the true parameters within the ABC sample generated from this data.

Each row of pvalues.reg corresponds to pvalues after a regression-adjustment has been performed on them.

svalues is a subset of the rows of sumstat corresponding to accepted datasets. These can be used in conjunction with pvalues to perform a recalibration correction manually.

Author(s)

Dennis Prangle and Guilherme Rodrigues

References

G. S. Rodrigues, D. Prangle and S. A. Sisson (2017) Recalibration: A post-processing method for approximate Bayesian computation. In submission

Examples

  ## Not run: 
  data(musigma2)
  P <- data.frame(par.sim)
  S <- data.frame(stat.sim)
  out <- recalibrationABC(target=stat.obs, param=P, sumstat=S, tol=0.3)
  plot(rbind(out$sample.plain[1:500,], out$sample.recal[1:500,]),
  col=c(rep("red",500), rep("blue", 500)))
  ##Red shows plain ABC sample, blue shows recalibrated output

## End(Not run)