COUNTABLE ADDITIVITY AND THE FOUNDATIONS OF BAYESIAN STATISTICS

JOHN V. HOWARD

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COUNTABLE ADDITIVITY AND THE FOUNDATIONS OF BAYESIAN STATISTICS

机译：可数可加性和贝叶斯统计的基础

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At a very fundamental level an individual (or a computer) can process only a finite amount of information in a finite time. We can therefore model the possibilities facing such an observer by a tree with only finitely many arcs leaving each node. There is a natural field of events associated with this tree, and we show that any finitely additive probability measure on this field will also be countably additive. Hence when considering the foundations of Bayesian statistics we may as well assume countable additivity over a σ -field of events.

机译：从根本上讲，个人（或计算机）在有限的时间内只能处理有限数量的信息。因此，我们可以通过一棵树来模拟面对这样一个观察者的可能性，而只有有限的许多弧离开每个节点。这棵树有一个自然的事件场，我们证明了在该场上的任何有限加性概率测度也将是可数加性的。因此，在考虑贝叶斯统计的基础时，我们还可以假设事件的σ场具有可数的加性。

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来源
《Theory and Decision》 |2006年第3期|p.127-135|共9页
作者
JOHN V. HOWARD;
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作者单位

Departments of Operational Research and Statistics, London School of Economics, Houghton Street, London, WC2A 2AE, UK;

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原文格式 PDF
正文语种 eng
中图分类社会科学总论;
关键词
bayesian statistics; foundations; countable additivity; finite additivity;

机译：贝叶斯统计;基础;可加性;有限可加性;

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COUNTABLE ADDITIVITY AND THE FOUNDATIONS OF BAYESIAN STATISTICS

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