# Simultaneous confidence sets from empirical joint distribution. 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. ```r ## 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. ## Returns 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 ## References Besag J, Green P, Higdon D, Mengersen K (1995): Bayesian Computation and Stochastic Systems. Statistical Science 10 (1), 3-66. ## Author(s) Frank Schaarschmidt, adapting an earliere version of Gemechis D. Djira ## See Also `CInp` for a wrapper to `quantile` to compute simple percentile intervals on each of P marginal distributions ## Examples ```r # 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) ```

SCSnp function