Are Bayesian models subject to the same problems as frequentist ones, where we cannot run a bunch of different models due to Type I error? For example, let's say I have a large data frame on airplanes, dependent variable miles flown, independent variable total passengers, and a grouping variable of airline company (made-up example). For frequentist statistics, I really shouldn't split the data frame into a bunch of smaller ones based on airline company and run a different regression for each company, I should run a single regression with company as an included variable (otherwise, I get major increases in Type I error). Do the same rules apply if I approach the same problem from a Bayesian perspective?
Since Bayesian approaches are more calculation-heavy and take forever on larger datasets, it would be helpful to be able to split the data frame and run multiple models, combining the results from the CIs at the end. But I'm new to Bayesian stats, so I'm not sure if this is a bad thing to do.