Laplace Approximation, Package: LaplacesDemon. The LaplaceApproximation function deterministically maximizes the logarithm of the unnormalized joint posterior density with one of several optimization algorithms. The goal of Laplace Approximation is to estimate the posterior mode and variance of each parameter. This function is useful for optimizing initial values and estimating a covariance matrix to be input into the LaplacesDemon or PMC function, or sometimes for model estimation in its own right.