# Summary statistics selection by minimizing a posterior sample measure.

### Description

The function cycles through all possible subsets of summary statistics and computes a criterion from the posterior sample. The subset which achieves the minimum is chosen as the most informative subset.

### Usage

1 2 3 4 |

### Arguments

`obs` |
(matrix of) 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). |

`abcmethod` |
a function to perform ABC inference, e.g. the |

`crit` |
a function to minimize to measure information from a posterior sample, e.g. |

`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. |

`verbose` |
a boolean value indicating whether informative statements should be printed to screen. |

`do.crit` |
a boolean value indicating whether the measure on the posterior sample should be returned. |

`do.err` |
a boolean value indicating whether the simulation error should be returned. Note: if |

`final.dens` |
a boolean value indicating whether the posterior sample should be returned. |

`errfn` |
an error function to assess ABC inference performance. |

`...` |
any other optional arguments to the ABC inference procedure (e.g. arguments to the |

### Details

The function uses a criterion (e.g.sample entropy) as a proxy for information in a posterior sample. The criterion for each possible subset of statistics is computed, and the best subset is judged as the one which minimises this vector of values.

### Value

A list with the following components:

`best` |
the best subset(s) of statistics. |

`critvals` |
the calculated criterion values (if |

`err` |
simulation error (if |

`order` |
the subsets considered during the algorithm (same as the input |

`post.sample` |
an array of dimension |

`sumsubs` |
an index into the subsets considered during the algorithm. |

### Warning

These functions are computationally intensive due to the cyclic ABC inference procedure.

### Author(s)

Matt Nunes

### References

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.

### See Also

`nn.ent`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
# load example data:
data(coal)
data(coalobs)
param<-coal[,2]
simstats<-coal[,4:6]
# use matrix below just in case to preserve dimensions.
obsstats<-matrix(coalobs[1,4:6],nrow=1)
obsparam<-matrix(coalobs[1,1])
# example of entropy minimization algorithm:
tmp <-mincrit(obsstats, param, simstats, tol=.01, method="rejection",
do.crit=TRUE)
tmp$critvals
``` |