# Posterior Probabilities from Bayesian Screening Experiments Marginal factor posterior probabilities and model posterior probabilities from designed screening experiments are calculated according to Box and Meyer's Bayesian procedure. ```r BsProb(X, y, blk, mFac, mInt = 2, p = 0.25, g = 2, ng = 1, nMod = 10) ``` ## Arguments - `X`: Matrix. The design matrix. - `y`: vector. The response vector. - `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 considered in the models. - `p`: numeric. Prior probability assigned to active factors. - `g`: vector. Variance inflation factor(s) $\gamma$associated to active and interaction factors. - `ng`: integer <=20. Number of different variance inflation factors (`g`) used in calculations. - `nMod`: integer <=100. Number of models to keep with the highest posterior probability. ## Details Factor and model posterior probabilities are computed by Box and Meyer's 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. If `g`, the variance inflation factor (VIF) $\gamma$, is a vector of length 1, the same VIF is used for factor main effects and interactions. If the length of `g` is 2 and `ng` is 1, `g[1]` is used for factor main effects and `g[2]` for the interaction effects. If `ng` greater than 1, then `ng` values of VIFs between `g[1]` and `g[2]` are used for calculations with the same $gamma$ value for main effects and interactions. The function calls the FORTRAN subroutine bm and captures summary results. The complete output of the FORTRAN code is save in the BsPrint.out file in the working directory. The output is a list of class `BsProb` for which `print`, `plot` and `summary` methods are available. ## Returns A list with all output parameters of the FORTRAN subroutine bm . The names of the list components are such that they match the original FORTRAN code. Small letters used for capturing program's output. - **X**: matrix. The design matrix. - **Y**: vector. The response vector. - **N**: integer. The number of runs. - **COLS**: integer. The number of design factors. - **BLKS**: integer. The 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 considered in the models. - **PI**: numeric. Prior probability assigned to the active factors. - **INDGAM**: integer. If 0, the same variance inflation factor (`GAMMA`) is used for main and interactions effects. If `INDGAM ==1`, then `NGAM` different values of `GAMMA` were used. - **INDG2**: integer. If 1, the variance inflation factor `GAM2` was used for the interaction effects. - **NGAM**: integer. Number of different VIFs used for computations. - **GAMMA**: vector. Vector of variance inflation factors of length 1 or 2. - **NTOP**: integer. Number of models with the highest posterior probability. - **mdcnt**: integer. Total number of models evaluated. - **ptop**: vector. Vector of probabilities of the top `ntop` models. - **sigtop**: vector. Vector of sigma-squared of the top `ntop` models. - **nftop**: integer. Number of factors in each of the `ntop` models. - **jtop**: matrix. Matrix of the number of factors and their labels of the top `ntop` models. - **del**: numeric. Interval width of the `GAMMA` partition. - **sprob**: vector. Vector of posterior probabilities. If `ng>1` the probabilities are weighted averaged over `GAMMA`. - **pgam**: vector. Vector of values of the unscaled posterior density of `GAMMA`. - **prob**: matrix. Matrix of marginal factor posterior probabilities for each of the different values of `GAMMA`. - **ind**: integer. Indicator variable. `ind` is 1 if the bm subroutine exited properly. Any other number correspond to the format label number in the FORTRAN subroutine script. ## References Box, G. E. P and R. D. Meyer (1986). "An Analysis for Unreplicated Fractional Factorials". **Technometrics.** Vol. 28. No. 1. pp. 11--18. Box, G. E. P and R. D. Meyer (1993). "Finding the Active Factors in Fractionated Screening Experiments". **Journal of Quality Technology.** Vol. 25. No. 2. pp. 94--105. ## Author(s) R. Daniel Meyer. Adapted for by Ernesto Barrios. ## Note The function is a wrapper to call the FORTRAN subroutine bm , modification of Daniel Meyer's original program, mbcqp5.f , for the application of Bayesian design and analysis of fractional factorial experiments, part of the `mdopt` bundle, available at **StatLib**. ## See Also `print.BsProb`, `print.BsProb`, `summary.BsProb`. ## Examples ```r library(BsMD) data(BM86.data,package="BsMD") X <- as.matrix(BM86.data[,1:15]) y <- BM86.data["y1"] # Using prior probability of p = 0.20, and k = 10 (gamma = 2.49) drillAdvance.BsProb <- BsProb(X = X, y = y, blk = 0, mFac = 15, mInt = 1, p = 0.20, g = 2.49, ng = 1, nMod = 10) plot(drillAdvance.BsProb) summary(drillAdvance.BsProb) # Using prior probability of p = 0.20, and a 5 <= k <= 15 (1.22 <= gamma <= 3.74) drillAdvance.BsProbG <- BsProb(X = X, y = y, blk = 0, mFac = 15, mInt = 1, p = 0.25, g = c(1.22, 3.74), ng = 3, nMod = 10) plot(drillAdvance.BsProbG, code = FALSE, prt = TRUE) ```

BsProb function