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X.-L. Meng 557(a) Given partial knowledge of the recording/response mechanism for a (large)biased sample, what is the optimal way to create an intentionally biasedsub-sampling scheme to counter-balance the original bias so the resultingsub-sample is guaranteed to be less biased than the original biased samplein terms of the sample mean, or other estimators, or predictive power?(b) What should be the key considerations when combining small randomsamples with large non-random samples, and what are the sensible “cornercutting”guidelines when facing resource constraints? How can the combineddata help to estimate ρ N (x, p)? In what ways can such estimatorsaid multi-source inference?(c) What are theoretically sound and practically useful defect indices for prediction,hypothesis testing, model checking, clustering, classification, etc.,as counterparts to the defect index for estimation, ρ N (x, p)? What aretheir roles in determining information bounds for multi-source inference?What are the relevant information measures for multi-source inference?45.5 The ultimate prize or priceAlthough we have discussed the trio of inference problems separately, manyreal-life problems involve all of them. For example, the aforementioned On-TheMap application has many resolution levels (because of arbitrary zoom-in),many sources of data (more than 20 sources), and many phases of pre-process(even God would have trouble keeping track of all the processing that thesetwenty some survey, census, and administrative data sets have endured!), includingthe entire process of producing the synthetic data themselves. Personalizedmedicine is another class of problems where one typically encounters allthree types of complications. Besides the obvious resolution issue, typically thedata need to go through pre-processing in order to protect the confidentialityof individual patients (beyond just removing the patient’s name). Yet individuallevel information is most useful. To increase the information content, weoften supplement clinical trial data with observational data, for example, onside effects when the medications were used for another disease.To bring the message home, it is a useful exercise to imagine ourselvesin a situation where our statistical analysis would actually be used to decidethe best treatment for a serious disease for a loved one or even for ourselves.Such a “personalized situation” emphasizes that it is my interest/life at stake,which should encourage us to think more critically and creatively, not just topublish another paper or receive another prize. Rather, it is about getting tothe bottom of what we do as statisticians — to transform whatever empiricalobservations we have into the best possible quantitative evidence for scientific