#' marg_lik
#'
#' Calculate log marginal likelihood under unit-information Zellner's g-prior
#'
#' @param y: Vector, outcomes
#' @param X: Matrix, design matrix
#'
#' @export
marg_lik = function(y,X) {
n = dim(X)[1]
p = dim(X)[2]
g = n
b.ols = as.vector(solve(crossprod(X),crossprod(X,y)))
R2 = 1 - crossprod(y - X %*% b.ols) / crossprod(y - mean(y))
return(lgamma((n - 1) / 2) -
(n - 1) * log(sqrt(pi)) -
log(sqrt(n)) -
(n - 1) * log(sqrt(sum((y - mean(y))^2))) +
(n - 1 - p) / 2 * log(1 + g) -
(n - 1) / 2 * log(1 + g * (1 - R2))
)
}
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