Personal probabilities of probabilities
Personal probabilities of probabilities
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个人概率的概率
DOI：
10.1007/bf00169102
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发表时间：
1975
期刊：
影响因子：
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通讯作者：
R. L. Winkler
中科院分区：
文献类型：
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作者：
J. Marschak;M. Degroot;J. Marschak;K. Borch;H. Chernoff;Morris De Groot;Morris De Groot;R. Dorfman;W. Edwards;T. Ferguson;K. Miyasawa;P. Randolph;L. J. Savage;Robert Schlaifer;R. L. Winkler
根据定义，随机事件的主观概率分布是由（“理性的”）主体在赌注之间的选择所揭示的——这一观点由拉姆齐（F. Ramsey）、德菲内蒂（B. De Finetti）、萨维奇（L. J. Savage）表达，可以追溯到博雷尔（E. Borel），也可以追溯到贝叶斯（T. Bayes）。由于假设不是可观察到的事件，因此不能在假设上下注并获得回报。因此，假设的主观概率分布（或参数的主观概率分布，如在当前的“贝叶斯”统计文献中）是一种修辞，“好像”，在极限下是合理的。给定一长串先前的观察结果，仍然有待观察的事件的主观后验概率是通过使用一个数学表达式推导出来的，这个数学表达式近似于假设的主观概率分布，如果可以下注的话。M. H. De-Groot在加州大学洛杉矶分校行为科学数学跨学科研讨会上发表了关于停止规则的演讲后，J. Marschak发起了一场“循环赛”，大多数（但不是全部）受访者都持这一立场。其他参与者：K. Borch， H. Chernoif， R. Dorfman， W. Edwards， T. S. Ferguson， G. Graves， K. Miyasawa， P. Randolph， L. J. Savage， R. Schlaifer， R. L. Winkler。这一期K. Borch的文章也引起了人们的注意。
By definition, the subjective probability distribution of a random event is revealed by the (‘rational’) subject's choice between bets — a view expressed by F. Ramsey, B. De Finetti, L. J. Savage and traceable to E. Borel and, it can be argued, to T. Bayes. Since hypotheses are not observable events, no bet can be made, and paid off, on a hypothesis. The subjective probability distribution of hypotheses (or of a parameter, as in the current ‘Bayesian’ statistical literature) is therefore a figure of speech, an ‘as if’, justifiable in the limit. Given a long sequence of previous observations, the subjective posterior probabilities of events still to be observed are derived by using a mathematical expression that would approximate the subjective probability distribution of hypotheses,ifthese could be bet on. This position was taken by most, but not all, respondents to a ‘Round Robin’ initiated by J. Marschak after M. H. De-Groot's talk on Stopping Rules presented at the UCLA Interdisciplinary Colloquium on Mathematics in Behavioral Sciences. Other participants: K. Borch, H. Chernoif, R. Dorfman, W. Edwards, T. S. Ferguson, G. Graves, K. Miyasawa, P. Randolph, L. J. Savage, R. Schlaifer, R. L. Winkler. Attention is also drawn to K. Borch's article in this issue.