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540 NP-hard inferencesignal or noise depends entirely on our choice of the primary resolution. Themulti-resolution framework described below is indeed inspired by my learningof wavelets and related multi-resolution methods (Bouman et al., 2005, 2007;Lee and Meng, 2005; Hirakawa and Meng, 2006), and motivated by the needto deal with Big Data, where the complexity of emerging questions has forcedus to go diving for perceived signals in what would have been discarded asnoise merely a decade ago.But how much of the signal that our inference machine recovers will berobust to the assumptions we make (e.g., via likelihood, prior, estimating equations,etc.) and how much will wash out as noise with the ebb and flow of ourassumptions? Such a question arose when I was asked to help analyze a largenational survey on health, where the investigator was interested in studyingmen over 55 years old who had immigrated to the US from a particular country,among other such “subpopulation analyses.” You may wonder what is sospecial about wanting such an analysis. Well, nothing really, except that therewas not a single man in the dataset who fit the description! I was thereforebrought in to deal with the problem because the investigator had learned thatI could perform the magic of multiple imputation. (Imagine how much datacollection resource could have been saved if I could multiply impute myself!)Surely I could (and did) build some hierarchical model to “borrow information,”as is typical for small area estimations; see Gelman et al. (2003) andRao (2005). In the dataset, there were men over 55, men who immigratedfrom that country, and even men over 55 who immigrated from a neighboringcountry. That is, although we had no direct data from the subpopulation ofinterest, we had plenty of indirect data from related populations, however defined.But how confident should I be that whatever my hierarchical machineproduces is reproducible by someone who actually has direct data from thetarget subpopulation?Of course you may ask why did the investigator want to study a subpopulationwith no direct data whatsoever? The answer turned out to be rathersimple and logical. Just like we statisticians want to work on topics that arenew and/or challenging, (social) scientists want to do the same. They aremuch less interested in repeating well-established results for large populationsthan in making headway on subpopulations that are difficult to study. Andwhat could be more difficult than studying a subpopulation with no data? Indeed,political scientists and others routinely face the problem of empty cellsin contingency tables; see Gelman and Little (1997) and Lax and Phillips(2009).If you think this sounds rhetorical or even cynical, consider the rapidlyincreasing interest in individualized medicine. If I am sick and given a choice oftreatments, the central question to me is which treatment has the best chanceto cure me, not some randomly selected ‘representative’ person. There is nological difference between this desire and the aforementioned investigator’sdesire to study a subpopulation with no observations. The clinical trials testingthese treatments surely did not include a subject replicating my description