What happens if I use this model twice: once with the first half of
n_channelsand in a second step with the second half? Will I get more-or-less the same results?
If you were to sample this model twice like you described, you’d get back two different posteriors \pi_1 and \pi_2 distributions over parameters, one conditioned on the first subset and a second one conditioned on the second subset. Unfortunately, there isn’t a straightforward to combine these the samples from these two posteriors into samples from a master prior “\pi_3 = \pi_1 + \pi_2”, see here for a discussion.
So no, you can’t parallelize like this. The closest thing I can think of (which doesn’t quite help with parallelization) is that you can theoretically use your posterior \pi_1 over the first subset as your prior over the second subset. In practice you have to do something like a KDE in-between these steps since you don’t actually have \pi_1 but rather samples, which can lead to approximation error. See this notebook for an example. This might help you if you have a massive amount of data (too much to run all at once) and don’t care how long it takes to get the job done, but you have to do this sequentially so this isn’t really a method to get a speedup.