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B.G. Lindsay 87ture. In the so-called admixture problem, the goal was to determine the racialcomponents of a mixed human population; see, e.g., Wang (2003).This whole process was a great discovery for me. I found the ability ofstatistics to ferret out the hidden information (the home rivers of each salmon)to be the most fascinating thing I had seen to date. It was done with themagic of likelihood. The fact that I could find the methods on my own, inthe literature, and make some sense of them, also gave me some confidence.My lesson was learned, statistics could be empowering. And I had ignited apassion.In retrospect, I was also in the right place at the right time. As I nowlook back at the fisheries literature, I now see that the scientific team thatapproached me with this problem was doing very cutting edge research. Thedecade of the 80s saw considerable development of maximum likelihood methodsfor unscrambling mixed populations. Indeed, I later collaborated on apaper that identified in detail the nature of the maximum likelihood solutions,as well as the identifiability issues involved (Roeder et al., 1989). In thiscase, the application was a different biological problem involving plants andthe fertility of male plants as it depended on the distance from the femaleplants. In fact, there are many interesting applications of this model.A consultant needs to do more than identify a model, he or she also needs toprovide an algorithm for computation. In providing a solution to this problem,I also first discovered the EM algorithm in the literature. Mind you, thereexisted no algorithm called the “EM” until 1977, a year or two after thisproject (Dempster et al., 1977). But like many other discoveries in statistics,there were many prequels. The version I provided to the client was called the“gene-counting” algorithm, but the central idea of the EM, filling in missingdata by expectation, was already there (Ott, 1977).This algorithm became its own source of fascination to me. How and whydid it work? Since that period the EM algorithm has become a powerful toolfor unlocking hidden structures in many areas of statistics, and I was fortunateto be an early user, advocate, and researcher. Its key feature is its reliability incomplex settings, situations where other methods are likely to fail. WheneverI teach a mixture models course, one of my first homework assignments is forthe student to understand and program the EM algorithm.So there you have it. Through my choice of graduate education, by takingaconsultingclass,andbydrawingtherightconsultingclient,Ihadenteredatan early stage into the arenas of mixture models and the EM algorithm, bothof which were to display considerable growth for the next thirty years. I gotin on the ground floor, so to speak. I think the message for young people isto be open to new ideas, and be ready to head in surprising directions, evenif they are not popular or well known.In many ways the growth of mixture models and the EM algorithm camefrom a shift in computing power. As an old-timer, I feel some obligation to offerhere a brief side discussion on the history of computing in statistics during