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86 Passion for statisticsTheir Biomathematics degree offered lots of room for me to explore myapplied mathematical interests. I took courses in ecology, fisheries, epidemiology,and population genetics as I looked about for interesting applications andinteresting applied mathematical areas. Certainly I have no regrets about mysecond choice of graduate schools. It had highly talented faculty and a broadrange of possibilities. I now always recommend that prospective graduate studentsselect schools based on these characteristics.As I took the required Biomathematics courses, I began to find statistics,and its applications, more deeply interesting. In particular, Bob Smythe’smathematical statistics course, where I first saw the magic of maximum likelihood,had me intrigued. And the more courses I took, the more I liked thesubject. It is not a cohesive subject, but it is a powerful one.Averyimportantpartofmyeducationwasnotconventionalcoursework.IwasinaconsultingclassintheCenterforQuantitativeScienceunit,whichmeant sitting in a room and seeing clients. My very positive experience therehas left me a proponent of graduate consulting classes all my life.One of my clients brought in a fisheries problem that did not seem to fitany of the traditional models we had learned in applied classes. If it was notregression or ANOVA or discrete data, what could it be?Salmon are fish with a complex life cycle. It starts when they are born in ahome river, but they soon leave this river to mature in the open ocean. Theyreturn to their home river at the end of their lives in order to lay and fertilizeeggs and die. The set of fish coming from a single river are thus a distinctsubpopulation with its own genetic identity. This was important in fisheriesmanagement, as many of the fish were caught in the open ocean, but withsome diagnostic measurements, one could learn about the river of origin.In the problem I was asked to consult upon, the salmon were being caughtin the Puget Sound, a waterway that connects to both American and Canadianrivers. Since each country managed its own stock of fish, the fisheries managerswanted to know how many of the caught fish came from “Canadian” riversand how many “American.”The data consisted of electrophoretic measurements, an early form of DNAanalysis, made on a sample of fish. It was important that the salmon fromvarious rivers were physically mixed together in this sample. It was also importantthat the scientists also had previously determined the genetic profileof salmon from each river system. However, these genetic “fingerprints” didnot provide a 100% correct diagnosis of the river that each fish came from.That would have made the problem a simple one of decoding the identities,and labelling the salmon, creating a multinomial problem.I now know that a very natural way to analyze such data is to build anappropriate mixture model, and then use maximum likelihood or a Bayesiansolution. At the time, having never seen a mixture model in my coursework,Iwasquitecluelessaboutwhattodo.However,Ididmyduediligenceasa consultant, talked to a population geneticist Joseph Felsenstein, and founda relevant article in the wider genetics literature — it had a similar struc-