  We present a method to transform multivariate unimodal non-Gaussian posterior
probability densities into approximately Gaussian ones via non-linear mappings,
such as Box--Cox transformations and generalisations thereof. This permits an
analytical reconstruction of the posterior from a point sample, like a Markov
chain, and simplifies the subsequent joint analysis with other experiments.
This way, a multivariate posterior density can be reported efficiently, by
compressing the information contained in MCMC samples. Further, the model
evidence integral (i.e. the marginal likelihood) can be computed analytically.
This method is analogous to the search for normal parameters in the cosmic
microwave background, but is more general. The search for the optimally
Gaussianising transformation is performed computationally through a
maximum-likelihood formalism; its quality can be judged by how well the
credible regions of the posterior are reproduced. We demonstrate that our
method outperforms kernel density estimates in this objective. Further, we
select marginal posterior samples from Planck data with several distinct
strongly non-Gaussian features, and verify the reproduction of the marginal
contours. To demonstrate evidence computation, we Gaussianise the joint
distribution of data from weak lensing and baryon acoustic oscillations (BAO),
for different cosmological models, and find a preference for flat $\Lambda$CDM.
Comparing to values computed with the Savage-Dickey density ratio, and
Population Monte Carlo, we find good agreement of our method within the spread
of the other two.
