概率論沉思錄

前言

The following material is addressed to readers who are already familiar with applied math- ematics, at the advanced undergraduate level or preferably higher, and with some field, such as physics, chemistry, biology, geology, medicine, economics, sociology, engineering, operations research, etc., where inference is needed.1 A previous acquaintance with proba- bility and statistics is not necessary; indeed, a certain amount of innocence in this area may be desirable, because there will be less to unlearn.We are concerned with probability theory and all of its conventional mathematics, but now viewed in a wider context than that of the standard textbooks. Every chapter after the first has 'new' （i.e. not previously published） results that we think will be found interesting and useful. Many of our applications lie outside the scope of conventional probability theory as currently taught. But we think that the results will speak for themselves, and that something like the theory expounded here will become the conventional probability theory of the future.

內(nèi)容概要

本書將概率和統(tǒng)計(jì)推斷融合在一起，用新的觀點(diǎn)生動(dòng)地描述了概率論在物理學(xué)、數(shù)學(xué)、經(jīng)濟(jì)學(xué)、化學(xué)和生物學(xué)等領(lǐng)域中的廣泛應(yīng)用，尤其是它闡述了貝葉斯理論的豐富應(yīng)用，彌補(bǔ)了其他概率和統(tǒng)計(jì)教材的不足。全書分為兩大部分。第一部分包括10章內(nèi)容，講解抽樣理論、假設(shè)檢驗(yàn)、參數(shù)估計(jì)等概率論的原理及其初等應(yīng)用；第二部分包括12章內(nèi)容，講解概率論的高級應(yīng)用，如在物理測量、通信理論中的應(yīng)用。本書還附有大量習(xí)題，內(nèi)容全面，體例完整。　　本書內(nèi)容不局限于某一特定領(lǐng)域，適合涉及數(shù)據(jù)分析的各領(lǐng)域工作者閱讀，也可作為高年級本科生和研究生相關(guān)課程的教材。

作者簡介

E.T.Jaynes（1922—1998）已故著名數(shù)學(xué)家和物理學(xué)家。生前曾任華盛頓大學(xué)圣路易斯分校和斯坦福大學(xué)教授。他因?yàn)樘岢隽藷釀?dòng)力學(xué)的最大熵原理（1957年）和量子光學(xué)的Jaynes-Cummings／模型（1963年）而聞名于世。此后的幾十年，他一直在探求將概率和統(tǒng)計(jì)推斷作為整個(gè)科學(xué)的邏輯基礎(chǔ)這一重大課題，其成果和心得最終凝結(jié)為本書。

書籍目錄

Part I　Principles and elementary applications  1　Plausible reasoning　  2　The quantitative rules　  3　Elementary sampling theory　  4　Elementary hypothesis testing　86  5　Queer uses for probability theory　119  6　Elementary parameter estimation　149  7　The central, Gaussian or normal distribution　  8　Sufficiency, ancillarity, and all that　  9　Repetitive experiments: probability and frequency　  10　Physics of ‘random experiments'　Part Ⅱ　Advanced applications  11　Discrete prior probabilities: the entropy principle　  12　Ignorance priors and transformation groups　  13　Decision theory, historical background　  14　Simple applications of decision theory　  15　Paradoxes of probability theory　  16　Orthodox methods: historical background　  17　Principles and pathology of orthodox statistics　  18　The Ap distribution and rule of succession　  19　Physical measurements　  20　Model comparison601  21　Outliers and robustness　  22　Introduction to communication theory　Appendix A　Other approaches to probability theory　Appendix B　Mathematical formalities and style　Appendix C　Convolutions and cumulants　ReferencesBibliographyAuthor indexSubject index

章節(jié)摘錄

插圖：This kind of conceptualizing often leads one to suppose that these distributions represent not just our prior state of knowledge about the data, but the actual long-run variability of the data in such experiments. Clearly, such a belief cannot be justified; anyone who claims to know in advance the long-run results in an experiment that has not been performed is drawing on a vivid imagination, not on any fund of actual knowledge of the phenomenon. Indeed, if that infinite population is only imagined, then it seems that we are free to imagine any population we please.From a mere act of the imagination we cannot learn anything about the real world. To suppose that the resulting probability assignments have any real physical meaning is just another form of the mind projection fallacy. In practice, this diverts our attention to irrelevancies and away from the things that really matter （such as information about the real world that is not expressible in terms of any sampling distribution, or does not fit into the urn picture, but which is nevertheless highly cogent for the inferences we want to make）. Usually, the price paid for this folly is missed opportunities; had we recognized that information, more accurate and/or more reliable inferences could have been made.  Urn-type conceptualizing is capable of dealing with only the most primitive kind of information, and really sophisticated applications require us to develop principles that go far beyond the idea of urns. But the situation is quite subtle, because, as we stressed before in connection with Godel's theorem, an erroneous argument does not necessarily lead to a wrong conclusion. In fact, as we shall find in Chapter 9, highly sophisticated calculations sometimes lead us back to urn-type distributions, for purely mathematical reasons that have nothing to do conceptually with urns or populations. The hypergeometric and binomial distributions found in this chapter will continue to reappear, because they have a fundamental mathematical status quite independent of arguments that we used to find them here.

媒體關(guān)注與評論

“這是幾十年來最重要的一部概率論著作。它解決了許多長期困擾我的問題。概率、統(tǒng)計(jì)、模式識別、數(shù)據(jù)分析、機(jī)器學(xué)習(xí)、數(shù)據(jù)挖掘……只要你的工作涉及不完全和不確定信息的處理，就應(yīng)該仔細(xì)研讀本書。它將大大改變你思考問題的方式。”     ——KevIn S．Van Horn，資深計(jì)算機(jī)技術(shù)和概率統(tǒng)詩專家“本書廣受歡迎。讀者會(huì)在書中發(fā)現(xiàn)很多引人深思的內(nèi)容，不僅涉及日常實(shí)踐，更深人統(tǒng)骨和概率理論本身。無論對于統(tǒng)計(jì)學(xué)者還是各應(yīng)用領(lǐng)域的科技工作者，本書都是必讀之作?！?   ——美國《數(shù)學(xué)評論》“這不是一本普通的教材。它全面、徹底地闡述了統(tǒng)計(jì)中的貝葉斯方法。書中有上百個(gè)例子，足夠讓你透徹理解其中的理論和應(yīng)用。每個(gè)對統(tǒng)計(jì)問題或統(tǒng)計(jì)應(yīng)用感興趣的人都應(yīng)該仔細(xì)研讀?！?   ——sIAM News

編輯推薦

《概率論沉思錄(英文版)》不僅適合概率和統(tǒng)計(jì)專業(yè)人士閱讀。也是需要應(yīng)用統(tǒng)計(jì)推斷的各領(lǐng)域科技工作者的必讀之作?！陡怕收摮了间?英文版)》是一部奇書。它是著名數(shù)學(xué)物理學(xué)家Jaynes的遺作，凝聚了他對概率論長達(dá)40年的深刻思考。原版出版后產(chǎn)生了巨大影響，深受眾多專家和學(xué)者的好評，并獲得Amazon網(wǎng)上書店讀者全五星評價(jià)。 在書中，作者在H.Jeffreys、R.T.Cox、C.E.Shannon和G.Polya等數(shù)學(xué)大師思想的基礎(chǔ)上繼續(xù)探索，將概率論置于更大的背景下考察，提出將概率推斷作為整個(gè)科學(xué)的邏輯基礎(chǔ)，以適應(yīng)實(shí)際科學(xué)研究中對象往往都是信息不完全或者不確定的這一難題，從而超越了傳統(tǒng)的概率論，也超越了傳統(tǒng)的數(shù)理邏輯思維定式。

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