概率逻辑及其在统计学基础中的应用

A Logic of Probability, with Application to the Foundations of Statistics

Journal of the Royal Statistical Society. Series B: Statistical Methodology · 1993
被引 112
ABS 4

中文导读

经典概率理论蕴含比柯尔莫哥洛夫概率演算更多的内容,本文提出一种新的概率演算并发展出新的概率解释,主张放弃建立通用经验概率理论,转而关注概率逻辑,并应用于概率预测检验和统计模型。

Abstract

SUMMARY A simple example shows that the classical theory of probability implies more than one can deduce via Kolmogorov's calculus of probability. Developing Dawid's ideas I propose a new calculus of probability which is free from this drawback. This calculus naturally leads to a new interpretation of probability. I argue that attempts to create a general empirical theory of probability should be abandoned and we should content ourselves with the logic of probability establishing relations between probabilistic theories and observations. My approach to the logic of probability is based on a variant of Ville's principle of the excluded gambling strategy. In addition to the classical theory of probability this approach is applied to the probabilistic theories provided by the problem of testing validity of probability forecasts and by statistical models.

概率论概率逻辑统计学基础贝叶斯概率经验概率