Do you have unique identifiers that allow linking records across files without error?  If not, how to you account for linkage error in your models?

Do you check that the sets of data from two files are representative of the same population?  For instance, income in one file may be very (or somewhat) different than income in another file.  If the data are not representative of the same population, how to you adjust ('correct'), your statistical analysis?

Thanks for your answer Mr. Winkler, I am using Bayesian updating for a slightly different application. Let me add some detail. Assume that I have empirical data from a distribution of some past data. Now I would like to use this past data as an input to a Monte Carlo simulation. There is however an expert who is of the opinion that the future realizations of this distribution may be slightly different and suggests a different distribution. I am using Bayesian updating to aggregate the empirical data and this expert opinion in the Bayesian posterior. 

A good analogy is provided in the introduction to Credibility theory by Longley-Cook (https://www.casact.org/pubs/proceed/proceed62/62194.pdf). Credibility theory is used in the actuarial sciences to incorporate new information into knowledge about an existing data set. 

I am of the opinion that ordering of the files matters. The files are not likely to be simultaneous. Chronological ordering of the files must be done. The probability of a later information should be conditional on that of an earlier one.

Dear Mr Etuk, you are right. The ordering does matter, I have checked this with a few simple examples. When using multiple updates the weighting is highest for the information that is used earliest in the updating series. This makes intuitive sense to me, however I am unsure as how to this can be formally proved and how the theoretical reasoning is for this. Thanks!