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Arthur P. Dempster contributed to multivariate analysis, incomplete-data inference and the representation of uncertain evidence. With Nan Laird and Donald Rubin, he developed the general expectation-maximization algorithm formulation published in 1977. Its expectation step averages a complete-data log likelihood using the current Conditional distribution of latent or missing variables; its maximization step updates parameters using that average. This makes a difficult incomplete-data likelihood accessible through a sequence of simpler calculations.

Harvard's institutional tribute also traces his work on Dempster-Shafer theory, in which evidence can leave an explicit component of uncertainty about an assertion. His dissertation concerned multivariate settings with more variables than observations, anticipating a central difficulty of high-dimensional statistics.^[ref]

Identity and life dates: Harvard Department of Statistics obituary and tribute.

By Andrew Gelman, John Carlin, Hal S. Stern, David Dunson, Aki Vehtari and Donald Rubin, as credited on the author-hosted book homepage. Third edition.

Official homepage: sites.stat.columbia.edu/gelman/book/

The homepage supplies the author list and an authorized PDF for noncommercial use. Cited here for the coauthorship of Hal S. Stern and the textbook’s Bayesian subject.

Donald Rubin's work connects Causal inference, missing data and Bayesian statistics. His Harvard profile lists Causal inference in experiments and observational studies, nonresponse in sample surveys, and Bayesian and empirical Bayesian methods as research interests.^[ref]

The potential outcomes framework makes a causal comparison explicit by distinguishing the outcomes that would occur under alternative treatments. Only the outcome under the received treatment is observed for each individual, so identifying an average treatment effect requires design or modelling assumptions. In missing-data analysis, multiple imputation propagates uncertainty by analyzing several completed datasets and pooling their results with Rubin's rules. These ideas explain why filling in one convenient value and then treating it as observed generally understates uncertainty.

Homepage: statistics.fas.harvard.edu/people/donald-b-rubin