OBsProb: Objective Posterior Probabilities from Bayesian Screening...

In OBsMD: Objective Bayesian Model Discrimination in Follow-Up Designs

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.

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.

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.

Note

The function is a wrapper to call the FORTRAN subroutine ‘obm’, modification of Daniel Meyer's original program, ‘mbcqp5.f’, for the application of Objective Bayesian follow-up design.

Author(s)

Laura Deldossi. Adapted for R by Marta Nai Ruscone.

References

Consonni, G. and Deldossi, L. (2016) Objective Bayesian Model Discrimination in Follow-up design., Test 25(3), 397–412. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11749-015-0461-3")}.

Meyer, R. D., Steinberg, D. M. and Box, G. E. P. (1996) Follow-Up Designs to Resolve Confounding in Multifactor Experiments (with discussion)., Technometrics 38(4), 303–332. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/1271297")}.

See Also

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

Examples

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)

OBsMD documentation built on Nov. 14, 2023, 5:10 p.m.