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#CONTRA 6 LOOPS UPDATE#
Even the simplest and bestīehaved Markov chains exhibit this phenomenon.Ĭonsider an AR(1) time series, having an update defined by Some starting points are better than others. This practice has no theoreticalĪnyone who has ever done any Markov chain simulation has noticed that Of the MCMC community of only using initial distributions of the form So from a theoretical point of view, burn-in is the cultural practice The official notation for that distribution is mP n,īut that doesn't help us calculate it or say much about it. Start with a sample from m and then run n steps. Which is that burn-in gives a recipe for a probability distribution: You don't have to understand this notation to understand the point, The Markov chain transition probability matrix or kernel. Used in calculations) is denoted mP n, where P is Then the real starting distribution (the distribution of the first iterate
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Has the probability distribution m and the burn-in period is n. In fact, from the theoretical point of view, burn-in is just one way of See Proposition 17.1.6 in Meyn and Tweedie, 1993.) (The technicalĬondition that guarantees this behavior is called Harris recurrence, If they hold for any one initial distribution (the equilibrium distribution,įor example) then they hold for every initial distribution. Hold regardless of the distribution of the starting position.
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Nowhere in the theory is anything said about burn-in. Only difference from ordinary independent-sample Monte Carlo. We need Markov chain versions of the SLLN and CLT, but that's the Limit theorem (CLT) guarantees that the error will obey the square root The strong law of large numbers (SLLN) guarantees that theĪverage converges to the expectation with probability one. In MCMC we use the sample average over a run of the Markov chain toĪpproximate an expectation with respect to the equilibrium distribution There is nothing in MCMC theory, properly understood, that justifies There's more wrong than just the word, there's something fishy about Running longer may cure the first, but a dead transistor is deadįorever. (nonconvergence) is different from electronic component failure. So a burn-in is done at the factory to eliminate the Many electronics components fail quickly. This is the burn-in period.Īfter the burn-in you run normally, using each iterate in your MCMC Says you start somewhere, say at x, then you run the MarkovĬhain for n steps, from which you throw away all theĭata (no output). TheĬan limit the discussion to just one run. What is Burn-In? Burn-in is a colloquial term that describes the practice of throwingĪway some iterations at the beginning of an MCMC run. Pointless) we need to work through a number of issues. To see clearly why burn-in is unnecessary (harmless but generally If everyone takes it for granted, what can be wrong with it? Humble author, have woofed about burn-in in their MCMC papers. People find this surprising, because many people, including your Good method, of finding a good starting point. The purpose of this web page is to explain why the practiceĬalled burn-in is not a necessary part of Markov chain Monte Carloīurn-in is only one method, and not a particularly