How does the EMis algorithm compare with the Imputation-Posterior algorithm?

1. The Imputation Posterior (IP) algorithm enables us to draw random simulations from the multivariate normal observed data posterior $P(D_{\textrm{mis}}\vert D_{\textrm{obs}})$ by MCMC methods. MCMC methods represent one of the most exciting developments in statistics in recent years, but MCMC algorithms are difficult to use and slow. Their iterations converge to the right answer only asymptotically. As such, there is considerable disagreement within the statistics literature on how to assess convergence. IP also has the problem that multiple imputation requires draws that are independent, which is not a characteristic of successive draws from Markov chain methods like IP. Some scholars reduce this dependency by taking every $r$th random draw from IP but this requires interperting interpreting autocorrelation functions (requiring analysts of cross-sectional data to be familiar with time series methods); whereas, the difficulty of running separate chains is that the run time is increased by a factor of $m$, the number of imputations. Either way, since the convergence and independence problems depend on the worst-converging parameter, a conscientious user would need to evaluate them all, which means consulting at least $2p+p(p+1)$ graphs (with 40 variables, this is 6560 graphs).

2. EMis provides the same answers at IP, since it produces multiple imputations from the exact, finite sample posterior distribution, $P(D_{\textrm{mis}}\vert D_{\textrm{obs}})$. It supplements the Expectation Maximization (EM) algorithm that yields deterministic maximum likelihood values for the parameters with simulations and importance sampling both to add back in the estimation uncertainty and to deal with small sample problems, respectively. It is very fast and does not rely on stochastic convergence criteria.