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45Atrioofinferenceproblemsthatcouldwinyou a Nobel Prize in statistics (if you helpfund it)Xiao-Li MengDepartment of StatisticsHarvard University, Cambridge, MAStatistical inference is a field full of problems whose solutions require the sameintellectual force needed to win a Nobel Prize in other scientific fields. Multiresolutioninference is the oldest of the trio. But emerging applications such asindividualized medicine have challenged us to the limit: infer estimands withresolution levels that far exceed those of any feasible estimator. Multi-phaseinference is another reality because (big) data are almost never collected,processed, and analyzed in a single phase. The newest of the trio is multisourceinference, which aims to extract information in data coming from verydifferent sources, some of which were never intended for inference purposes. Allof these challenges call for an expanded paradigm with greater emphases onqualitative consistency and relative optimality than do our current inferenceparadigms.45.1 Nobel Prize? Why not COPSS?The title of my chapter is designed to grab attention. But why Nobel Prize(NP)? Wouldn’t it be more fitting, for a volume celebrating the 50th anniversaryof COPSS, to entitle it “A Trio of Inference Problems That Could WinYou a COPSS Award (and you don’t even have to fund it)?” Indeed, somemedia and individuals have even claimed that the COPSS Presidents’ Awardis the NP in Statistics, just as they consider the Fields Medal to be the NPin Mathematics.No matter how our egos might wish such a claim to be true, let us face thereality. There is no NP in statistics, and worse, the general public does not537