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Markov Chain Monte Carlo: What is a quasi-stationary distribution?
How does one determine if the chain has reached a quasi-stationary distribution?
There are a few ways to test for it, but one common approach is to monitor the distribution of the chain using trace plots and autocorrelation functions. If the plot shows that the chain has converged and the autocorrelation function has decayed to a minimum, it's more likely that a quasi-stationary distribution has been reached.