abctools (version 1.1.7)

AS.test: Test for relative approximate sufficiency between two posterior samples.

Description

The function tests to determine adding a (set of) statistics is informative in ABC inference.

Usage

AS.test(grid = 10, x1, x2, supp=NULL)

Value

extreme

a boolean value indicating whether the alternative posterior sample is more informative than the first (i.e. the extra summary statistics add information.

Arguments

grid

the number of bins into which to divide the posterior sample for the approximate sufficiency calculation.

x1

the posterior sample using the first set of summary statistics.

x2

the posterior sample using the second (alternative) set of summary statistics.

supp

the "support" of the prior (e.g. uniform bounds).

Author

Matt Nunes

Details

After dividing each posterior sample into a number of bins (specified by grid), the function computes the ratio of the posterior densities. This is seen as a measure of information added (sufficiency) by using the alternative posterior sample instead of the first posterior sample. If the ratio exceeds a particular threshold (a number of standard deviations away from the expected counts in each bin), then the alternative set of summaries is seen as being more informative.

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.

Joyce, P. and P. Marjoram (2008) Approximately sufficient statistics and Bayesian computation. Stat. Appl. Gen. Mol. Biol. 7 Article 26.

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.

See Also

AS.select

Examples

#create two fake posterior samples:

x1<-runif(10000)
x2<-rnorm(10000)

AS.test(x1=x1,x2=x2,supp=range(x2))