OBsMD (version 3.0)

OBsProb: Objective Posterior Probabilities from Bayesian Screening Experiments

Description

Objective model posterior probabilities and marginal factor posterior probabilities from Bayesian screening experiments according to Consonni and Deldossi procedure.

Usage

OBsProb(X, y, abeta=1, bbeta=1, blk, mFac, mInt, nTop)

Arguments

X

Matrix. The design matrix.

y

vector. The response vector.

abeta

First parameter of the Beta prior distribution on model space

bbeta

Second parameter of the Beta prior distribution on model space

blk

integer. Number of blocking factors (>=0). These factors are accommodated in the first columns of matrix X. There are ncol(X)-blk design factors.

mFac

integer. Maximum number of factors included in the models.

mInt

integer <= 3. Maximum order of interactions among factors considered in the models.

nTop

integer <=100. Number of models to print ordered according to the highest posterior probability.

Value

Below a list with all output parameters of the FORTRAN subroutine obm. The names of the list components are such that they match the original FORTRAN code. Small letters are used for capturing program's output.

X

matrix. The design matrix.

Y

vector. The response vector.

N

integer. Number of runs of the screening experiment.

COLS

integer. Number of design factors.

abeta

integer. First parameter of the Beta prior distribution on model space

bbeta

integer. Second parameter of the Beta prior distribution on model space

BLKS

integer. Number of blocking factors accommodated in the first columns of matrix X.

MXFAC

integer. Maximum number of factors considered in the models.

MXINT

integer. Maximum interaction order among factors considered in the models.

NTOP

integer. Number of models to print ordered according to the highest posterior probability

.

mdcnt

integer. Total number of models evaluated.

ptop

vector. Vector of posterior probabilities of the top ntop models.

nftop

integer. Number of factors in each of the top ntop models.

jtop

matrix. Matrix of the factors' labels of the top ntop models.

prob

vector. Vector of factor posterior probabilities.

sigtop

vector. Vector of residual variances of the top ntop models.

ind

integer. Indicator variable. ind is 1 if the obm subroutine exited properly. Any other number correspond to the format label number in the FORTRAN subroutine script.

Details

Model and factor posterior probabilities are computed according to Consonni and Deldossi Objective Bayesian procedure. The design factors are accommodated in the matrix X after blk columns of the blocking factors. So, ncol(X)-blk design factors are considered. A Beta(abeta, bbeta) distribution is assumed as a prior on model space. The function calls the FORTRAN subroutine obm and captures summary results. The complete output of the FORTRAN code is save in the OBsPrint.out file in the working directory. The output is a list of class OBsProb for which print, plot and summary methods are available.

References

Consonni, G. and Deldossi, L. (2015), "Objective Bayesian model discrimination in follow-up experimental designs" DOI 10.1007/s11749-015-0461-3. TEST.

Meyer, R. D., Steinberg, D. M. and Box, G. E. P. (1996). "Follow-Up Designs to Resolve Confounding in Multifactor Experiments (with discussion)". Technometrics, Vol 38 No. 4. pp. 303--332.

See Also

print.OBsProb, plot.OBsProb, summary.OBsProb.

Examples

# NOT RUN {
library(OBsMD)
data(OBsMD.es5, package="OBsMD")
X <- as.matrix(OBsMD.es5[,1:5])
y <- OBsMD.es5[,6]
# Using for model prior probability a Beta with parameters a=1 b=1
es5.OBsProb <- OBsProb(X=X,y=y, abeta=1, bbeta=1, blk=0,mFac=5,mInt=2,nTop=32)
print(es5.OBsProb)
summary(es5.OBsProb)
# }