# OBsProb: Objective Posterior Probabilities from Bayesian Screening... In OBsMD: Objective Bayesian Model Discrimination in Follow-Up Designs

 OBsProb R Documentation

## 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")}.

`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.