The 2005 Neyman Lecture: Dynamic Indeterminism in Science

arXiv:0808.0620v1 [stat.ME] 5 Aug 2008 Statistical Science 2008, Vol. 23, No. 1, 48–64 DOI: 10.1214/07-STS246 c ⃝Institute of Mathematical Statistics, 2008 The 2005 Neyman Lecture: Dynamic Indeterminism in Science1 David R. Brillinger Abstract. Jerzy Neyman’s life history and some of his contributions to applied statistics are reviewed. In a 1960 article he wrote: “Currently in the period of dynamic indeterminism in science, there is hardly a serious piece of research which, if treated realistically, does not involve operations on stochastic processes. The time has arrived for the theory of stochastic processes to become an item of usual equipment of every applied statistician.” The emphasis in this article is on stochastic pro- cesses and on stochastic process data analysis. A number of data sets and corresponding substantive questions are addressed. The data sets concern sardine depletion, blowfly dynamics, weather modification, elk movement and seal journeying. Three of the examples are from Ney- man’s work and four from the author’s joint work with collaborators. Key words and phrases: Animal motion, ATV motion, elk, Jerzy Ney- man, lifetable, monk seal, population dynamics, sardines, stochastic differential equations, sheep blowflies, simulation, synthetic data, time series, weather modification. 1. INTRODUCTION This paper is meant to be a tribute to Jerzy Ney- man’s substantive work with data sets. There is an emphasis on scientific questions, statistical modeling and inference for stochastic processes. The title of this work comes from Neyman (1960) where one finds, “The essence of dynamic indeterminism in science consists in an effort to invent a hypothetical chance mechanism, called a ‘stochastic model,’ operating on vari- ous clearly defined hypothetical entities, David Brillinger is Professor, Department of Statistics, University of California, Berkeley, California 94720, USA (e-mail: brill@stat.berkeley.edu). 1Discussed in 10.1214/07-STS246B and 10.1214/07-STS246A; rejoinder at 10.1214/07-STS246REJ. This is an electronic reprint of the original article published by the Institute of Mathematical Statistics in Statistical Science, 2008, Vol. 23, No. 1, 48–64. This reprint differs from the original in pagination and typographic detail. such that the resulting frequencies of vari- ous possible outcomes correspond approx- imately to those actually observed.” Here and elsewhere Neyman appeared to use the adjective “indeterministic” where others would use “stochastic,” “statistical” or “nondeterministic”; see, for example, Neyman and Scott (1959). Perhaps Ney- man had some deeper or historical context in mind, but that is not clear. In this paper the emphasis is on the word “dynamic.” Jerzy Neyman (JN) led a full life. Reid (1998) con- tains many details and anecdotes, a lot of them in Neyman’s own words. Other sources include the pa- pers: Neyman (1970), Le Cam and Lehmann (1974), Kendall, Bartlett and Page (1982), Scott (1985), Lehmann (1994) and Le Cam (1995). The article has six sections: 1. Introduction, 2. Jerzy Neyman, 3. Some formal methods, 4. Three exam- ples of JN’s applied statistics work, 5. Four exam- ples of random process data analysis, 6. Conclusion. The focus is on applied work in the environmental sciences and phenomena. This last is a word that Neyman often employed. 1 2 D. BRILLINGER In particular the examples show how random pro- cess modeling can prove both helpful and not all that difficult to implement. The thought driving this pa- per is that by examining a number of examples, uni- fying methods and principles may become apparent. One connecting thread is “synthetic” data, in the language of Neyman, Scott and Shane (1953) and Neyman and Scott (1956). Synthetic data, based on simulations, are an exploratory tool for model val- idation that has the advantage of suggesting how to create another model if the resemblance of the simulation to the actual data is not good. There are quotes throughout to create a flavor of JN’s statistical approaches. 2. JERZY NEYMAN “His devotion to Poland and its culture and traditions was very marked, and when his influence on statistics and statisticians had become worldwide it was fashionable ... to say that ‘we have all learned to speak statistics with a Polish accent’ . . . ” (Kendall, Bartlett and Page, 1982). The life of Neyman is well documented by JN and others; see, for example, Reid (1998), LeCam and Lehmann (1974) and Scott (1985). Other sources are cited later. Neyman was of Polish ancestry and as the above quote makes clear he was very Polish! Table 1 records some of the basic events of his life. One sees a flow from Poland to London to Berke- ley with many sidetrips intermingled throughout his life. These details are from Scott (1985) and Reid (1998). Neyman’s education involved a lot of formal math- ematics (integration, analysis, . . . ) and probability. He often mentioned the book, The Grammar of Sci- ence (Pearson, 1900) as having been very imp

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