Can different samples be merged?

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In my comment, “chain” refers to a single sequence of n NUTS draws from the posterior, starting at some initial (random) point. Re-setting to a different starting point and generating a new sequence therefore generates a new chain.

By default, these are done in parallel in PyMC3, with one core of a CPU devoted to sampling from a single chain.

This can be expanded to multiple CPUs by providing each CPU with a copy of the entire dataset.

Splitting the dataset up across multiple CPUs (“batching”) is another matter entirely, and is an active area of research generally. See here for some ideas:

Using MCMC based model in closed loop

There are a couple of cases that work trivially out of the box. Variational approximations work just fine, since at each presentation of a new dataset we have \pi_{k+1}(\theta) = \mathrm{argmin}_\mathcal{q} \mathrm{KL}[q(\theta) || P(D_{k+1}|\theta)\pi_k(\theta)] so the information propagates. The drawback is that none of the \pi_i will converge to the true posterior. Resampling methods also work out of the box, since the weights update in the same cumulative way: w_i^{(k+1)} = w_i^{(k)}P[D…