# Logarithm of unnormalized probability of a given model This function calculates the logarithm of unnormalized probability of a given set of covariates for both survival and binary response data. It uses the inverse moment nonlocal prior (iMOM) for non zero coefficients and beta binomial prior for the model space. ```r ModProb( X, resp, mod_cols, nlptype = "piMOM", tau, r, a, b, family = c("logistic", "survival") ) ``` ## Arguments - `X`: The design matrix. It is assumed that the design matrix has standardized columns. It is recommended that to use the output of `PreProcess` function of the package. - `resp`: For logistic regression models, this variable is the binary response vector. For Cox proportional hazard models this is a two column matrix where the first column contains the survival time vector and the second column is the censoring status for each observation. - `mod_cols`: A vector of column indices of the design matrix, representing the model. - `nlptype`: Determines the type of nonlocal prior that is used in the analyses. It can be "piMOM" for product inverse moment prior, or "pMOM" for product moment prior. The default is set to piMOM prior. - `tau`: Hyperparameter `tau` of the iMOM prior. - `r`: Hyperparameter `r` of the iMOM prior. - `a`: First parameter in the beta binomial prior. - `b`: Second parameter in the beta binomial prior. - `family`: Determines the type of data analysis. `logistic` is for binary outcome and logistic regression model whereas, `survival` represents survival outcomes and the Cox proportional hazard model. ## Returns It returns the unnormalized probability for the selected model. ## Examples ```r ### Simulating Logistic Regression Data n <- 400 p <- 1000 set.seed(123) Sigma <- diag(p) full <- matrix(c(rep(0.5, p*p)), ncol=p) Sigma <- full + 0.5*Sigma cholS <- chol(Sigma) Beta <- c(1,1.8,2.5) X = matrix(rnorm(n*p), ncol=p) X = X%*%cholS beta <- numeric(p) beta[c(1:length(Beta))] <- Beta XB <- X%*%beta probs <- as.vector(exp(XB)/(1+exp(XB))) y <- rbinom(n,1,probs) ### Calling the function for a subset of the true model, with an arbitrary ### parameters for prior densities mod <- c(1:3) Mprob <- ModProb(X, y, mod, tau = 0.7, r = 1, a = 7, b = 993, family = "logistic") Mprob ``` ## References Nikooienejad, A., Wang, W., and Johnson, V. E. (2016). Bayesian variable selection for binary outcomes in high dimensional genomic studies using nonlocal priors. Bioinformatics, 32(9), 1338-1345. Nikooienejad, A., Wang, W., & Johnson, V. E. (2020). Bayesian variable selection for survival data using inverse moment priors. Annals of Applied Statistics, 14(2), 809-828. ## See Also `CoefEst` ## Author(s) Amir Nikooienejad

ModProb function