# Simultaneous confidence sets from empirical joint distribution.

### Description

Calcualte simultaneous confidence sets according to Besag et al. (1995) from a empirical joint distribution of a parameter vector. Joint empirical distributions might be obtained from WinBUGS or OpenBUGS calls.

### Usage

1 2 3 4 5 6 7 8 9 10 11 12 13 |

### Arguments

`x` |
a matrix N-times-P matrix or an object of class |

`conf.level` |
a single numeric value between 0.5 and 1, the simultaneous confidence level |

`alternative` |
a single character string, one of |

`whichp` |
a single character string, naming an element of the |

`...` |
further arguments, currently not used |

### Details

Let P be the number of parameters in the parameter vector and N be the total number of values obtained for the empirical joint distribution of the parameter vector, e.g. as can be obtaine e.g., from Gibbs sampling.

### Value

An object of class "SCSnp", a list with elements

`conf.int ` |
a P-times-2 matrix containing the lower and upper confidence limits |

`estimate ` |
a numeric vector of length P, containing the medians of the P marginal empirical distributions |

`x ` |
the input object |

`k ` |
the number of values outside the SCS, i.e. conf.level*N |

`N ` |
the number of values used to construct the confidence set |

`conf.level ` |
a single numeric value, the nominal confidence level, as input |

`alternative ` |
a single character string, as input |

### Author(s)

Frank Schaarschmidt, adapting an earliere version of Gemechis D. Djira

### References

Besag J, Green P, Higdon D, Mengersen K (1995): Bayesian Computation and Stochastic Systems. Statistical Science 10 (1), 3-66.

### See Also

`CInp`

for a wrapper to `quantile`

to compute simple percentile intervals on each of P marginal distributions

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
# Assume a 1000 times 4 matrix of 4 mutually independent
# normal variables:
X<-cbind(rnorm(1000), rnorm(1000), rnorm(1000), rnorm(1000))
SCSts<-SCSnp(x=X, conf.level=0.9, alternative="two.sided")
SCSts
SCS<-SCSts$conf.int
in1<-X[,1]>=SCS[1,1] & X[,1]<=SCS[1,2]
in2<-X[,2]>=SCS[2,1] & X[,2]<=SCS[2,2]
in3<-X[,3]>=SCS[3,1] & X[,3]<=SCS[3,2]
in4<-X[,4]>=SCS[4,1] & X[,4]<=SCS[4,2]
sum(in1*in2*in3*in4)
``` |