  Bayesian computational algorithms tend to scale poorly as data size
increases. This has motivated divide-and-conquer-based approaches for scalable
inference. These divide the data into subsets, perform inference for each
subset in parallel, and then combine these inferences. While appealing
theoretical properties and practical performance have been demonstrated for
independent observations, scalable inference for dependent data remains
challenging. In this work, we study the problem of Bayesian inference from very
long time series. The literature in this area focuses mainly on approximate
approaches that usually lack rigorous theoretical guarantees and may provide
arbitrarily poor accuracy in practice. We propose a simple and scalable
divide-and-conquer method, and provide accuracy guarantees. Numerical
simulations and real data applications demonstrate the effectiveness of our
approach.
