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#'
#' #' Correlation prior
#' #'
#' #' @param delta
#' #' @param rho
#' #'
#' #' @return
#' #' @export
#' #'
#' #' @examples
#' cor.prior <- function(delta, rho, rooti){
#'
#'
#' k <- length(delta)
#'
#' y <- qnorm(delta)
#'
#' det <- sqrt((2*pi)^k) * exp(sum(y^2) / 2)
#'
#' # f <- function(i) -y[i]*(-y[i] -(k-1)*y[i]*rho + rho*sum(x[-i])) / (rho-1)*(1+rho*(k-1))
#' #
#' # det * exp(0.5*sum(sapply(seq(k), f )))/
#' # sqrt( (-1)^(k-1) * (1 + (k-1) * rho) * (rho - 1)^(k-1) )
#' sigma <- matrix(rho, ncol=k, nrow=k)
#' diag(sigma) <- 1
#'
#' if(missing(rooti)) rooti <- backsolve(chol(sigma),diag(k))
#'
#' quads <- colSums((crossprod(rooti,y))^2)
#' exp(-(k/2)*log(2*pi) + sum(log(diag(rooti))) - .5*quads) * det
#'
#' }
#'
#' # Code from bayesm
#' # seen at gallery.rcpp.org/articles/dmvnorm_arma
#' #
#' # dMvn <- function(X,mu,Sigma)
#' # k <- ncol(X)
#' # rooti <- backsolve(chol(Sigma),diag(k))
#' # quads <- colSums((crossprod(rooti,(t(X)-mu)))^2)
#' # return(exp(-(k/2)*log(2*pi) + sum(log(diag(rooti))) - .5*quads))
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