Decision-making under risk and “statistical thinking” in the 20th century (selected models and persons)

• Authors: Wojciech Rybicki
• Languages of publication: EN PL

Abstracts

EN

The paper is the second part of the series of articles surveying chosen models of decision-making under “risky circumstances”. The first segment concerned the earlier period of development of so-called “statistical thinking” (up to the times of J. Neyman and E. Pearson) and has been published elsewhere. These “twins” of papers as a whole, are intended as essays (consciously avoiding any formalization) to introduce the subsequent parts of the cycle – conducted in a more formal style. Several problems were discussed in the first part of the series. The leitmotifs, i.e. Bayesian vs. “orthodox” approaches, and the subjective vs. objective probability meaning are continued in this article, and developed towards the “modern needs and directions”. The role of some outstanding scientists is stressed. The possibility of the unification of the different philosophies on the grounds of statistical decision theory (thanks to A. Wald and L.J. Savage) is noted. “Dynamic” or multistage statistical decision procedures will be also indicated (in contrast to “static, “one-shot” problems). The primary role in developing these ideas played by mathematicians A. Wald, L. Shapley, R. Bellman, D. Blackwell and H. Robbins (plus many others) is stressed. The outline is conducted in a “historical perspective” beginning with F. Ramsey’s work and finishing at H. Robbins achievements – as being very influential in the further development of the stochastic methodology. The list of models, to be discussed in the subsequent (“formal-mode”) article/s, is added at the end of the paper. The central role in the notes is played by the “procession” of the prominent representatives of the field. The first “series” of them was presented in the previous part of the cycle. The subsequent (nine) are placed here. These scientists built the milestones of statistical science, “created its spirit,” exquisitely embedding the subject in the “general stochastic world”. The presentation is supplemented with their portraits. The author hopes that some keystones determining the line-up can be recognized in the course of reading. It is not possible to talk about mathematics without mathematics (formulas, calculations, formal reasoning). On the other hand − such beings as probability, uncertainty, risk can be, first of all, regarded as philosophic and logic in their heart of hearts (as well as being somewhat “mysterious”). So, it can turn out illuminating (sometimes) to reveal and to show merely the ideas and “their” heroes (even at the expense of losing the precision!). The role of the bibliography should also be stressed – it is purposely made so large, and significantly completes the presentation.

Keywords

EN

statistics; risk; subjective probability; objective probability; frequentists; sequential analysis; stochastic approximation; stochastic game; empirical Bayes approach

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Mathematical Economics
• Year: 2018
• Issue: 14(21)
• Pages: 71-94

Contributors

author

Wojciech Rybicki