By P. A. Moran
Книга An creation to likelihood idea An creation to chance idea Книги Математика Автор: P. A. Moran Год издания: 1984 Формат: pdf Издат.:Oxford collage Press, united states Страниц: 550 Размер: 21,2 ISBN: 0198532423 Язык: Английский0 (голосов: zero) Оценка:"This vintage textual content and reference introduces chance idea for either complex undergraduate scholars of information and scientists in similar fields, drawing on genuine purposes within the actual and organic sciences. "The booklet makes likelihood exciting." --Journal of the yank Statistical organization
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Additional resources for An Introduction to Probability Theory
Clearly, for given x, f (x|θ) is not a probability distribution or density for θ. No such distribution or density can be inferred from x and f (x|θ). The ML method is just an extension to a parameterized family of models of the simple preference scheme ﬁrst discussed for two models: prefer the model having the highest probability of giving the data. If no information other than the data and the function f (x|θ) is to be used in the estimation, it is diﬃcult to see any alternative to ML. How else can one obtain a value within the range Θ of the unknown parameter from such raw material?
Inductive Inference Bayesian decision theory save (we hope) some useful comments about prior probabilities. Bayesian decision theory does not require or involve making any statement about the “best” or most probable model of the data, nor does it involve any estimation of parameters. In fact, it really makes no inference about the source of the data other than a statement of the form: “Our knowledge of the source of the data is such that the action of least expected cost is a ˆ”, which is not about the source, but about our knowledge of it.
11 Expectation 27 The positive “expectation” of g or “expected net gain” is an indication that the wager is biased in my favour. Were it to be repeated 1000 times, I could expect to win about 214 dollars, and even though there will in fact be only the one wager, Eg represents a fair assessment of how beneﬁcial (in purely monetary terms) the wager is likely to be to me. Note that this use of the term “expectation” (and “expected value”) is a technical deﬁnition which does some violence to the normal English meaning of the word.
An Introduction to Probability Theory by P. A. Moran