Theory of Probability
Theory of Probability
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DOI：
10.1007/978-1-4939-6572-4_1
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
M. Bonamente
中科院分区：
文献类型：
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作者：
M. Bonamente
概率论是研究事件发生概率的数学框架。第一步是建立一种方法来分配事件的概率，例如，硬币在掷硬币后仰面着陆的概率。频率法或经验法和主观法或贝叶斯法是两种可用于计算概率的方法。有一种以上的方法可用于这一目的，这一事实不应被视为理论的局限性，而应被视为这样一个事实，即对于概率论的某些部分，尤其是对统计学而言，有一种主观性因素进入分析和对结果的解释。因此，统计学家的任务是跟踪分析中作出的任何假设，并在解释结果时说明这些假设。一旦建立了一种分配概率的方法，科尔莫戈洛夫公理就被引入为操纵概率所需的“规则”。被称为贝叶斯定理和全概率定理的基本结果被用来定义和解释统计独立性和条件概率的概念，这两个概念在本书中提供的许多材料中发挥了核心作用。
The theory of probability is the mathematical framework for the study of the probability of occurrence of events. The first step is to establish a method to assign the probability of an event, for example, the probability that a coin lands heads up after a toss. Thefrequentist—or empirical—approach and thesubjective—or Bayesian— approach are two methods that can be used to calculate probabilities. The fact that there is more than one method available for this purpose should not be viewed as a limitation of the theory, but rather as the fact that for certain parts of the theory of probability, and even more so for statistics, there is an element of subjectivity that enters the analysis and the interpretation of the results. It is therefore the task of the statistician to keep track of any assumptions made in the analysis, and to account for them in the interpretation of the results. Once a method for assigning probabilities is established, the Kolmogorov axioms are introduced as the “rules” required to manipulate probabilities. Fundamental results known as Bayes’ theorem and the theorem of total probability are used to define and interpret the concepts of statistical independence and of conditional probability, which play a central role in much of the material presented in this book.