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24Statistical inference from aDempster–Shafer perspectiveArthur P. DempsterDepartment of StatisticsHarvard University, Cambridge, MA24.1 IntroductionWhat follows is a sketch of my 2013 viewpoint on how statistical inferenceshould be viewed by applied statisticians. The label DS is an acronym for“Dempster–Shafer” after the originators of the technical foundation of thetheory. Our foundation remains essentially unchanged since the 1960s and1970s when I and then Glenn Shafer were its initial expositors.Present issues concern why and how the theory has the potential to developinto a major competitor of the “frequentist” and “Bayesian” outlooks. This forme is a work in progress. My understanding has evolved substantially over thepast eight years of my emeritus status, during which DS has been my majorfocus. It was also a major focus of mine over the eight years beginning in 1961when I first had the freedom that came with academic tenure in the HarvardStatistics Department. Between the two periods I was more an observer andteacher in relation to DS than a primary developer. I do not attempt here toaddress the long history of how DS got to where I now understand it to be,including connections with R.A. Fisher’s controversial “fiducial” argument.DS draws on technical developments in fields such as stochastic modelingand Bayesian posterior computation, but my DS-guided perception of the natureof statistical inference is in different ways both narrower and broader thanthat of its established competitors. It is narrower because it maintains thatwhat “frequentist” statisticians call “inference” is not inference in the naturallanguage meaning of the word. The latter means to me direct situation-specificassessments of probabilistic uncertainties that I call “personal probabilities.”For example, I might predict on September 30, 2013 that with personal probability.31 the Dow Jones Industrials stock index will exceed 16,000 at the endof business on December 31, 2013.267