I have a data, that comes from two sources. Two collections ofsources; the two data sets were obtained from different geographical locationlocations and at different historical timetimes. I do not want to pool them into one data set sample and looselose information about differing values of parameters that generated those collections, but I also cannot use Bayesian hierarchical model, since there would be just two unobservables from which I could not learn anything about hyperparameters. Is there any possible models that could be used in such a problems? I
I know that the question is a bit vague, but I am open to various possibilities.
EDIT
I have a Poissonian countsThe data are counts, distributed as Poisson with some intensities $\lambda _{1}$ and $\lambda _{2}$. Suppose I have two data samples that comes from similar objects and represents number of failures over some period of time. I want to estimate both rates. I dontdon't want to pool them because, for example, the operating conditions (environmental conditions) were different for those two data sources so that intensities were not identical. But I want to be able to borrow some information from each data sample like in hierarchical Bayesian model. But, as I already said, for hierarchical model there is just not enough data sources.