Hi,

I am trying to get some information about identifiability with Bayesian inference and especially with mixture models. I have found a paper on this topic (Markov Chain Monte Carlo Methods and the Label Switching Problem in Bayesian Mixture Modeling) but I feel like I am not any smarter than before.

Jasra, Holmes and Stephens write:

“One of the main challenges of a Bayesian analysis

using mixtures is the nonidentifiability of the components.

That is, if exchangeable priors are placed upon

the parameters of a mixture model, then the resulting

posterior distribution will be invariant to permutations

in the labelling of the parameters. As a result,

the marginal posterior distributions for the parameters

will be identical for each mixture component. Therefore,

during MCMC simulation, the sampler encounters

the symmetries of the posterior distribution and the

interpretation of the labels switches. It is then meaningless

to draw inference directly from MCMC output

using ergodic averaging. Label switching significantly

increases the effort required to produce a satisfactory

Bayesian analysis of the data, but is a prerequisite of

convergence of an MCMC sampler and therefore must

be addressed.”

Is there any way to explain this in a more simple way? Any help would be appreciated!