据美国《科技新闻》报道,在一桩犯罪案件的审判中,陪审员提醒法官,在证据不完全或不确切时,为避免误判,应参照概率论原理。所谓的概率论只不过是把常识用数学公式表达出来,使用贝叶斯概率统计法能避免诸多误判。贝叶斯概率统计法贝叶斯方法被证明是非常客观且强大的推理框架。托马斯·贝叶斯曾是备受尊敬的牧师。遗憾的是,他非律师,也不是法官,后来成为业余数学家。他若是律师,那么今天的同行或许不会这么不情愿地使用其统计方式来洞察审判是否公正。实际上,贝叶斯当时的论文只是对统计问题的直接求解尝试,并不清楚他当时是不是已意识到这里面包含着深刻的思想。然而后来,贝叶斯方法改变了概率论,并将应用延伸到各个领域,所有需要作出概率预测的地方都可以见到贝叶斯方法的影子。特别地,贝叶斯是机器学习的核心方法之一。 According to the U.S. Science and Technology News, during a trial of a criminal case, jurors remind the judge that if the evidence is incomplete or imprecise, to avoid misjudgment, reference should be made to the principle of probability theory. The so-called probability theory is nothing more than common sense expressed in mathematical formulas, the use of Bayesian probability statistics can avoid a lot of miscarriage of justice. Bayesian Probability Statistics The Bayesian approach proved to be a very objective and powerful inference framework. Thomas Bayes was a highly respected pastor. Unfortunately, he was not a lawyer nor a judge and later became an amateur mathematician. If he is a lawyer, today’s colleagues may not be so reluctant to use their statistical methods to gain insight into the fairness of the trial. In fact, Bayes’ essay was just a direct attempt to solve the problem of statistics, and it was unclear whether he had realized at that time that there was a profound thought in it. Later, however, the Bayesian approach changed the theory of probability and extended the application to all areas, with the shadow of the Bayesian approach visible to all places where probabilistic prediction is needed. In particular, Bayesian machine learning is one of the core methods.