Abstract
This article presents methods and results in the application of the Markov Chain Monte Carlo (MCMC) analysis to a problem in missing data. The data used here are from The Atlantic Slave Trade Database (TASTD), 2010 version, available online. Of the currently known 35,000 slaving voyages, original data on the size of the cargo of captives exist for some 25 percent of voyage embarkations in Africa and for about 50 percent of arrivals in the Americas. Previous efforts to estimate the missing data (and project the to- tal number of captives who made the transatlantic migration) have proceeded through eclectic projections of maximum likelihood estimates of captives per voyage, without error margins. This paper creates new estimates of total mi- grant flow through two methods: one is a formally frequentist set of multiple methods, and the other is through Markov Chain Monte Carlo methodology. Comparison of the three methods, all based on the same raw data, show that the results of the two new methods are fairly close to one another and they yield total flows of migrant captives of more than 20 percent higher than the previous estimates. Quantitative results, presented in simplified graphs and tables within the text and in detailed spreadsheets available online, 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.
Highlights
This article presents methods and results in the application of the Markov Chain Monte Carlo (MCMC) analysis to a problem in missing data
Detailed research has explored the numbers embarked on slave vessels at various African ports, the numbers who lost their lives in the course of the voyages of two months or more across the Atlantic, and the numbers who disembarked at the end of the voyage, mostly in the Americas
The use of established statistical techniques confirms the basic approach of previous work, but suggests specific historical estimates that differ from previous estimates in important particulars
Summary
This article presents methods and results in the application of the Markov Chain Monte Carlo (MCMC) analysis to a problem in missing data. Markov Chain Monte Carlo (MCMC) analysis provides a systematic and comprehensive method for estimating missing data. The work of Philip Curtin, The Atlantic Slave Trade: A Census, presented comprehensive estimates of the volume of slave trade (Curtin 1969) He offered a total of 9.5 million persons—for the number of arrivals (that is, disembarkations) of captive Africans in the Americas from the fifth century to 1870. Curtin carried out his research through secondary works and with a wide range of methods His estimated total, which was smaller than previously thought, brought an outpouring of research into primary documents. After twenty years of debate, the estimated volume of the slave trade had crept up by a million or so, and clearer distinctions were made on estimates of embarkations, arrivals, and mortality at various stages in the trade (Lovejoy 1982, 1989)
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