  In Chib (1995), a method for approximating marginal densities in a Bayesian
setting is proposed, with one proeminent application being the estimation of
the number of components in a normal mixture. As pointed out in Neal (1999) and
Fruhwirth-Schnatter (2004), the approximation often fails short of providing a
proper approximation to the true marginal densities because of the well-known
label switching problem (Celeux et al., 2000). While there exist other
alternatives to the derivation of approximate marginal densities, we reconsider
the original proposal here and show as in Berkhof et al. (2003) and Lee et al.
(2008) that it truly approximates the marginal densities once the label
switching issue has been solved.
