Bayesian analysis used merely as a computational tool? I have sometimes seen some statisticians used bayesian analysis and related techniques such as MCMC simply as a tool when a frequentist approach is not satisfying, typically for example when the maximum likelihood estimator is hard to find or takes too much time to compute.
In these case they focus only on the definition of the model and estimation (by MCMC for example) and barely on the choice prior distributions (from what I've seen).
I guess they use flat distributions by default but the particular choice of a prior is never discussed, maybe because of the large number of parameters the model may have and the difficulty to assign a meaningful prior distribution to each one of them.
Is it something usual to switch to a bayesian analysis and use it merely a as computational counterpart of a frequentist approach when the latter performs poorly?
My feeling is that bayesian and frequentist are very distinct statistical framework (at least that's what my teachers taught me!) and using one or another shouldn't be justified simply by computational purposes and moreover the choice of the prior distributions should at least be carefully made.
I know this is not really a statistical question but I just would like to know what pure bayesians think about this kind of use of bayesian analysis. Sorry in advance if it does not fit this site.

Other reasons to use Bayesian approaches include

*

*getting more accurate inference when the log-likelihood is very non-Gaussian.  For example, in binary logistic regression standard p-values and confidence intervals may be inaccurate whereas Bayesian quantities are exact.

*getting accurate uncertainty intervals for complex derived parameters.  In the frequentist world we frequently have to resort to the delta method to get approximate confidence intervals.  Not only is this labor intensive, but the result is often very unsatisfactory because such intervals are forced to be symmetric when they should have been asymmetric in order to have accurate coverage with respect to both tails.  One example is state occupancy probabilities in a state transition model, which involve recursive matrix multiplications are a mess to deal with in the frequentist domain.  With MCMC (let's say you have 4000 posterior draws from the multivariate distribution of all parameters together) you just compute the complex derived parameter 4000 times and estimate the highest posterior density interval from those 4000 numbers.

