Figure 56

Figure 56: Gaussian approximation (Laplace approximation) to a 6-dimensional posterior distribution for cosmological parameters, from WMAP1 and SDSS data. For all couples of parameters, panels show contours enclosing 68% and 95% of joint probability from 2 ⋅ 105 MC samples (black contours), along with the Laplace approximation (red ellipses). It is clear that the Laplace approximation captures the bulk of the posterior volume in parameter space in this case where there is little non-Gaussianity in the posterior PDF. Image reproduced from 2005 preprint of [894].