Probability of statisticians and logicians

Probability of statisticians and logicians

There are two ways of looking at probability: statistical probability, which treats a subject as a whole at once, and subjective probability, which varies according to individual contexts and circumstances. The former is a method of measuring the likelihood of things happening in terms of frequency based on the accumulation of past data and has been used primarily by statisticians. A representative figure is Ronald A. Fisher, a statistician who has been a leading figure in the field of statistical analysis since the 1960s. He developed objective statistical methods, such as the null hypothesis test, and developed the viewpoint of "probability in the repetition of events. This probability is very useful in scientific experiments, epidemiological studies, and large censuses. It is good at taking a holistic view of the whole and capturing trends, and its essence is to "look at a surface rather than a point.

In contrast, "subjective probability" is a more logical and philosophical approach, as it is a probability judged by an individual in response to given information and changing circumstances. It is used, for example, in considering how a person judges the likelihood of a one-time event. The leading logician who theorized this position was Frank P. Ramsey. He laid the foundation for the Bayesian approach, which views probability as a "degree of rational belief" and links it to subjective expected utility. This way of thinking comes in handy in areas such as cybersecurity, gambling, and medical decisions, where conditions change from moment to moment. This is because forecasting relies more on "interpretation of the information that is currently available" than on "overall statistics.

This distinction between the two is especially important in the security field. For example, when considering the "probability that this encryption key will be broken," even if past statistics show zero cases of breakage, one may subjectively feel that the risk has increased due to improvements in attacker resources and techniques. In other words, what "has not happened in the past" does not guarantee that it will not happen in the future.

Therefore, the ability to distinguish between these two probability concepts is required today. A statistical perspective that looks at the whole picture, and a subjective perspective based on logical consistency and situational judgment. It is on the basis of this balance that real-world risk assessment and decision-making are established.