Metropolis-Hastings sample reusal

I have a posterior distribution from which I calculate some statistics using sampling, for example I calculate expectation. So I draw 1000 samples using Metropolis-Hastings and then I calculate their mean. After I calculate the statistic, I modify the posterior (using the Bayes law) and I want to recalculate the statistics again, this process repeats indefinitely. Now the question: can I reuse the samples somehow so that I do not have to regenerate all 1000 samples (too slow)? Can I do something smart so that when my posterior is a bit different I can use some of the old samples?

• Can you clarify how/why you modify the posterior? Do you obtain new data? – Juho Kokkala Oct 6 '14 at 17:16
• I observe more data point. Basically I start with a uniform prior, and I observe data points one by one. After observing a data point I update the probability distribution, and I want to calculate a statistic, for example the expectation. A simple example: throw the coin several times and after each throw calculate the expected value. – Artem Grotov Oct 7 '14 at 10:56