Dakota Reference Manual: laplace_approx

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laplace_approx

Calculate model evidence using the Laplace approximation

## Specification

Alias: none

Argument(s): none

## Description

The `laplace_approx` keyword for model evidence indicates that a pre-solve will be used prior to the Bayesian MCMC sampling to estimate the Maximum A Posteriori (MAP) point. The Laplace approximation assumes the posterior density is nearly Gaussian and is given by a formula which involves the likelihood at the MAP point, the prior density at the MAP point, and the Hessian of the log-posterior at the MAP point. The formula is given in the Dakota User's manual. This method is efficient at estimating the model evidence for posterior densities with weak non-Gaussian characteristics but it does require a MAP solve (so `pre-solve` should be specified) and it does require gradient and Hessians of the response to be on.

Default Behavior

Expected Output Currently, the model evidence will be printed in the screen output with prefacing text indicating if it is calculated by the Laplace approximation.

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