Research Memorandum No.1129

December 3, 2010

Words of Probability

ISHIGURO, Makio(The Institute of Statistical Mathematics)

Words of Probability

ISHIGURO, Makio(The Institute of Statistical Mathematics)

Key Words: subjective probability, conﬁdence, belief, frequency, verbal expression

Abstract

There are everyday expressions such that ’probably’; ’might be’;’could be’ etc., to describe the strengths of one’s conﬁdence in the occurrence of events in the future. On the other hand there are probability theory expressions such that ”the probability of the occurrence of event E is 0.1”. The situation is almost the same with the color names. There are everyday expressions such that ’blue’; ’red’;’yellow’ etc., to describe the colors of objects in the sight. On the other hand there are scientiﬁc expressions such that ”the wavelength of the light in sight is 620 nm”. There will be no consensus about the pinpoint assignment of probability values to the everyday expressions of the strength of the conﬁdence. But there might be some stable distributions of those assignment by common people. I conducted a small scale opinion poll mainly among my friends. The purpose of this memorandum is to summarize contributed answers and record some of my thought on the subject.

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HTML version of this article is accessible. ( http://www.ism.ac.jp/ ishiguro/Poﬁss/pfs.@090311.@025203.labo/verbal/memo.g1frm.html ) You need MatEx-2D display ActiveX, which is easily installed using installer ( http://ftp.ism.ac.jp:8000/ISMLIB/matex/MatEx2D-v*-*-Pkg.exe ) on your windows PC.

Contents

1 Introduction 2 Data 3 Aggregation of Data 3.1 Blurring . . . . . . . . . . . . . 3.2 A few more examples . . . . . . 3.3 Boxplot representation . . . . . 3.4 Bayesian Posterior Distribution 3 3 4 4 6 7 7 10 10 11 13 13

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4 Discussion 4.1 Othe ways of Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Words of Probability and Words of Frequency . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Words of Estimative Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 References

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Introduction

There are everyday expressions such that ’probably’; ’might be’;’could be’ etc., to describe the strengths of one’s conﬁdence in the occurrence of events in the future. On the other hand there are probability theory expressions such that ”the probability of the occurrence of event E is 0.1”. There will be no consensus about the pinpoint assignment of probability values to the everyday expressions of the conﬁdence. But there might be some stable distributions of those assignment by ”common people”, which could be captured via suitable opinion poll. I sent the following mail to my acquaintances and got some responses.

Recently, I am interested in subjective probabilities, and would like to know how do you assign occurrence probabilities of ... in the following expressions: possibly ... should be ... perhaps ... unusually ... likely ... maybe ... must be ... hardly ... frequently ... certainly ... can be ... could be ... little ... often ... probably ... might be ... seldom ... sometimes ... rarely ... perchance ... usually ... occasionally ...

The purpose of this memorandum is to give summarized view of contributed answers and record some of my thought on the subject.

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Data

There are several patterns in which respondents answered my request. All those patterns appeared in the answer from one of my friends. His answer was as follows:

--------------------------My...