# SCSnp: Simultaneous confidence sets from empirical joint... In BSagri: Statistical methods for safety assessment in agricultural field trials

## 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``` ```## Default S3 method: SCSnp(x, conf.level = 0.95, alternative = "two.sided", ...) ## S3 method for class 'bugs' SCSnp(x, conf.level = 0.95, alternative = "two.sided", whichp = NULL, ...) ## S3 method for class 'CCRatio' SCSnp(x, ...) ## S3 method for class 'CCDiff' SCSnp(x, ...) ```

## Arguments

 `x` a matrix N-times-P matrix or an object of class `CCRatio` or `CCDiff` `conf.level` a single numeric value between 0.5 and 1, the simultaneous confidence level `alternative` a single character string, one of `"two.sided"`, `"less"`, `"greater"`, for two-sided, upper and lower limits `whichp` a single character string, naming an element of the `sims.list` if `x` is a `bugs` object, ignored otherwise `...` 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.

`CInp` for a wrapper to `quantile` to compute simple percentile intervals on each of P marginal distributions
 ``` 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) ```