# Hyperparameter selection for iMOM prior density This function finds data specific hyperparameters for inverse moment prior density so that the overlap between the iMOM prior and null MLE density is $1/\sqrt p$. In this algorithm `r` is always chosen to be equal to 1 and `tau` is found based on the mentioned overlap. ```r HyperSelect( X, resp, eff_size = 0.7, nlptype = "piMOM", iter = 10000, mod_prior = c("unif", "beta"), family = c("logistic", "survival") ) ``` ## Arguments - `X`: The design matrix. `NA`'s should be removed and columns be scaled. It is recommended that the `PreProcess` function is run first and its output used for this argument. The columns are genes and rows represent the observations. The column names are used as gene names. - `resp`: For logistic regression models, it is the binary response vector. For Cox proportional hazard model, this is a two column matrix where the first column contains survival time vector and the second column is the censoring status for each observation. - `eff_size`: This is the expected effect size in the model for a standardized design matrix, which is basically the coefficient value that is expected to occur the most based on some prior knowledge. - `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. - `iter`: The number of iteration needed to simulate from null model in order to approximate the null MLE density. - `mod_prior`: Type of prior used for model space. `uniform` is for uniform binomial and `beta` is for beta binomial prior. In the former case, both hyper parameters in the beta prior are equal to `1` but in the latter case those two hyper parameters are chosen as explained in the reference papers. - `family`: Determines the type of data analysis. `logistic` is for binary outcome data where logistic regression modeling is used whereas `survival` is for survival outcome data using Cox proportional hazard model. ## Returns It returns a list having following object: - **tau**: The hyperparameter for iMOM prior density function, calculated using the proposed algorithm for the given dataset. ## Examples ```r ### Simulating Logistic Regression Data n <- 20 p <- 100 set.seed(321) 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, 1, 2), 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) colnames(X) <- paste("gene_",c(1:p),sep="") Xout <- PreProcess(X) XX <- Xout$X hparam <- HyperSelect(XX, y, iter = 1000, mod_prior = "beta", family = "logistic") hparam$tau ``` ## 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. Johnson, V. E., and Rossell, D. (2010). On the use of nonlocal prior densities in Bayesian hypothesis tests. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72(2), 143-170. ## Author(s) Amir Nikooienejad

HyperSelect function