Olli Saarela (statistician)

I am a Finnish statistician currently working as an assistant professor at the Department of Epidemiology, Biostatistics and Occupational Health of McGill University, Montreal, Quebec, Canada. I was born in Tuusula, Finland, and studied at the University of Helsinki. After obtaining my master's degree in 2004 (with a thesis on variance estimation from imputed survey data), I worked as a statistician in the cardiovascular epidemiology project MORGAM at the National Institute for Health and Welfare (THL), Helsinki, Finland. Meanwhile I also pursued PhD studies under the supervision of professor Elja Arjas and docent Sangita Kulathinal. I defendend my PhD thesis, entitled On probability-based inference under data missing by design, on 24 September 2010 against professor Ørnulf Borgan. My areas of interest include Bayesian inference, missing data problems, epidemiological study designs, in particular case-cohort and nested case-control designs, survival analysis, and fundamentals of statistical inference.

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On probability

The mathematical (measure-theoretical) axiomatic definition of probability is free of interpretations. In contrast to mathematicians, due to the applied nature of the field, the interpretation or essence of probability is a topic on which every statistician has to form some kind of stance. This in turn tends to divide statisticians into various quarreling factions. In choosing between these factions, I place myself in the followers of E. T. Jaynes, who promoted probability theory as a generalization of binary logic, where truth values are obtained as limits of degrees of plausibility when information increases. This interpretation of probability is studied in depth in Jaynes' posthumously published 2003 book (see also the unofficial errata hosted by Kevin S. Van Horn and his guide to R. T. Cox's theorem). While I concede that objective Bayesianism (a term which Jaynes himself does not use) is not necessarily very helpful for practical statistical work (completely non-informative priors have proven to be elusive), and taken into its logical extreme leads into hard determinism, to me personally reading Jaynes' book in 2010 made everything crystal clear (although admittedly things have again gotten a bit murkier since then). However, in the end it matters less whether the decision maker assigning the probabilities is a subjective 'You' in the sense of de Finetti, or an objective 'robot' in the sense of Jaynes. More important is that probabilities are interpreted as measures of information (instead of say, frequencies), since it is this interpretation which ties together statistical inference and everyday human plausible reasoning. As noted by de Finetti (1974, p. 122),

"Probability as degree of belief is surely known by anyone: it is that feeling which makes him more or less confident or dubious or sceptical about the truth of an assertion, the success of an enterprise, the occurrence of a specific event whatsoever, and that guides him, consciously or not, in all his actions and decisions."

Probability as so interpreted is a concept much more general than mere frequency. To quote Jaynes (2003, p. 292):

"In our terminology, a probability is something that we assign, in order to represent a state of knowledge, or that we calculate from previously assigned probabilities according to the rules of probability theory. A frequency is a factual property of the real world that we measure or estimate. The phrase 'estimating a probability' is just as much a logical incongruity as 'assigning a frequency' or 'drawing a square circle'.

The fundamental, inescapable distinction between probability and frequency lies in this relativity principle: probabilities change when we change our state of knowledge; frequencies do not. It follows that the probability p(E) that we assign to an event E can be equal to its frequency f(E) only for certain particular states of knowledge. Intuitively, one would expect this to be the case when the only information we have about E consists of its observed frequency; and the mathematical rules of probability theory confirm this in the following way."

(Goes on to Laplace's rule of succession.) To sum up, I am perfectly happy to study frequentist statistical methods, but at the same time acknowledging this difference between probabilities and frequencies.

Last updated: 2014-04-01