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

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## 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.

See Also

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

Examples

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# 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)

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