This article presents methods and results in the application of the Markov Chain Monte Carlo analysis to a problem in missing data. The data used here are The Atlantic Slave Trade Database (tastd), 2010 version, available online. The article begins with background to the Bayesian statistical framework, Markov chains, and Monte Carlo methods, as compared with the frequentist statistical framework, still more widely used in economic (and demographic?) analyses.. It then describes the data, their analysis, the results, and a discussion of their strengths and weaknesses. The results provide a new estimate of the volume of African embarkations and American arrivals in the transatlantic slave trade for the period from 1650 to 1870, by decade, for eleven African regions of embarkation and seven American and European regions of arrival. These results are compared with earlier estimates of Atlantic slave trade volume by frequentist methods.