Pierre Jacob and I got this email from a student about our parallel Rao-Blackwellisation paper. Here are some parts of the questions and our answer:
Although I understand how the strategy proposed in the paper helps in variance reduction, I do not understand why you set b=1 (mentioned in Section 3.2) and why it plays no role in the comparison. If b=1 and p=4 for example, every chains (out of the 4 chains of the block) has a length of 4 samples. And there are no additional blocks. How is this length enough for the sampler to converge and sample the distribution adequately? You mention that you do 10000 independent runs (Which means you do the above procedure 10000 times independently) but aren’t all these runs equally short and inadequate? Even for p=100, aren’t the chains too short? Continue reading
