In passing it might be noted that unidentifiability causes no real difficulties in the Bayesian approach. If the likelihood does not involve a particular parameter, θ1 say, when written in the natural form, then the conditional distribution of θ1, given the remaining parameters, will be the same before and after the data. This will not typically be true of the marginal distribution of θ1 because of the changes in assessment of the other parameters caused by the data, though if θ1 is independent of them, it will be. For example, unidentifiable (or unestimable) parameters in linear least squares theory are like θ1, and do not appear in the likelihood. Notice, however, that with certain types of prior distribution having strong association between θ1 and the other parameters, data not involving θ1 can provide a lot of information about it. Effectively this is what happens in the case under discussion.