Is Partial-Dimension Convergence a Problem for Inferences From MCMC Algorithms?


Gill, Jeff. “Is Partial-Dimension Convergence a Problem for Inferences From MCMC Algorithms?” Political Analysis 16, no. 2 (2008): 153-178.
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Increasingly, political science researchers are turning to Markov chain Monte Carlo methods to solve inferential
problems with complex models and problematic data.  This is an enormously powerful set of tools based on replacing
difficult or impossible analytical work with simulated empirical draws from the distributions of interest.
While practitioners are generally aware of the importance of convergence of the Markov chain, many are not fully aware
of the difficulties in fully assessing convergence across multiple dimensions.  In most applied circumstances
\emph{every} parameter dimension must be converged for the others to converge.  The usual culprit is slow mixing of
the Markov chain and therefore slow convergence towards the target distribution.  This work demonstrates the partial
convergence problem for the two dominant algorithms and illustrates these issues with empirical examples.