AS.test {abctools} | R Documentation |

## 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)
```

### 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). |

### 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.

### 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. |

### 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.

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

### Examples

```
#create two fake posterior samples:
x1<-runif(10000)
x2<-rnorm(10000)
AS.test(x1=x1,x2=x2,supp=range(x2))
```

*abctools*version 1.1.7 Index]