stage2 {abctools}

stage2

Description

Summary statistics selection for ABC inference using estimated posterior error.

Usage

stage2(obs, param, sumstats, obspar = NULL, init.best, dsets = 100, 
sumsubs = 1:ncol(sumstats), limit = length(sumsubs), do.only=NULL, 
do.err = FALSE, final.dens = FALSE,  ...)

Arguments

obs

observed summary statistics.

param

matrix of simulated model parameter values.

sumstats

matrix of simulated summary statistics.

obspar

optional observed parameters (for use to assess simulation performance).

init.best

an initial estimate of the best summary statistics subset. Can be either an index into the summaries combination table (see combmat) or a vector of indices into 1:nstats. See details.

dsets

the number of simulated datasets to treat as observed when estimating the posterior error. See details.

sumsubs

an optional index into the summary statistics to limit summary selection to a specific subset of summaries.

limit

an optional integer indicating whether to limit summary selection to subsets of a maximum size.

do.only

an optional index into the summary statistics combination table. Can be used to limit entropy calculations to certain summary statistics subsets only.

do.err

a boolean value indicating whether the simulation error should be returned. Note: if do.err=TRUE, obspar must be supplied.

final.dens

a boolean value indicating whether the posterior sample should be returned.

...

any other optional arguments to the ABC inference procedure (e.g. arguments to the abc function).

Details

The function uses the init.best set of summaries to determine the dsets simulated datasets which are closest (in Euclidean norm) to the observed dataset. Since the model parameters generating the summary statistics are known for these simulated datasets, for each candidate subset of summary statistics, we can compute the error under ABC inference for each of these datasets. The best subset of summary statistics is that which minimizes this (average) error over all dsets datasets.

Value

A list with the following components:

best

the best subset of statistics.

closest

the indices of the dsets simulated datasets closest to the oberved dataset as measured by the init.best subset of summaries.

err

simulation error (if obspar is supplied and do.err=TRUE).

order

the subsets considered during the algorithm (same as the input do.only.

post.sample

an array of dimension nacc x npar x ndatasets giving the posterior sample for each observed dataset. Not returned if final.dens=FALSE.

sumsubs

an index into the subsets considered during the algorithm.

Warning

This function is computationally intensive due to its cyclic ABC inference procedure.

Author(s)

Matt Nunes

References

Blum, M. G. B, Nunes, M. A., Prangle, D. and Sisson, S. A. (2013) A comparative review of dimension reduction methods in approximate Bayesian computation. Stat. Sci. 28, Issue 2, 189–208.

Nunes, M. A. and Balding, D. J. (2010) On Optimal Selection of Summary Statistics for Approximate Bayesian Computation. Stat. Appl. Gen. Mol. Biol. 9, Iss. 1, Art. 34.

Nunes, M. A. and Prangle, D. (2016) abctools: an R package for tuning approximate Bayesian computation analyses. The R Journal 7, Issue 2, 189–205.

Examples

# load example data:

data(coal)
data(coalobs)

param<-coal[,2]
simstats<-coal[,5:8]

# use matrix below just in case to preserve dimensions.

obsstats<-matrix(coalobs[1,5:8],nrow=1)
obsparam<-matrix(coalobs[1,1])

## Not run: 
tmp<-stage2(obsstats, param, simstats, init.bes=c(1,3), dsets = 10) 
tmp$best

## End(Not run)