統(tǒng)計(jì)推斷原理

前言

　　Most statistical work is concerned directly with the provision and implementa-tion of methods for study design and for the analysis and interpretation of data.The theory of statistics deals in principle with the general concepts underlyingall aspects of such work and from this perspective the formal theory of statisticalinference is but a part of that full theory. Indeed， from the viewpoint of indi-vidual applications， it may seem rather a small part. Concern is likely to be moreconcentrated on whether models have been reasonably formulated to addressthe most fruitful questions， on whether the data are subject to unappreciatederrors or contamination and， especially， on the subject-matter interpretation ofthe analysis and its relation with other knowledge of the field.　　Yet the formal theory is important for a number of reasons. Without somesystematic structure statistical methods for the analysis of data become a col-lection of tricks that are hard to assimilate and interrelate to one another， orfor that matter to teach. The development of new methods appropriate for newproblems would become entirely a matter of ad hoc ingenuity. Of course suchingenuity is not to be undervalued and indeed one role of theory is to assimilate，generalize and perhaps modify and improve the fruits of such ingenuity.　　Much of the theory is concerned with indicating the uncertainty involved inthe conclusions of statistical analyses， and with assessing the relative merits ofdifferent methods of analysis， and it is important even at a very applied level tohave some understanding of the strengths and limitations of such discussions.This is connected with somewhat more philosophical issues connected withthe nature of probability. A final reason， and a very good one， for study of thetheory is that it is interesting.　　The object of the present book is to set out as compactly as possible thekey ideas of the subject， in particular aiming to describe and compare the mainideas and controversies over more foundational issues that have rumbled on atvarying levels of intensity for more than 200 years.

內(nèi)容概要

本書是統(tǒng)計(jì)學(xué)名家名作，包含9章內(nèi)容和兩個(gè)附錄，前面幾章介紹一些基本概念，如參數(shù)、似然、主元等，然后介紹顯著性檢驗(yàn)、漸進(jìn)理論以及比較復(fù)雜的統(tǒng)計(jì)推斷問題。還特別介紹了實(shí)驗(yàn)設(shè)計(jì)中基于隨機(jī)化的統(tǒng)計(jì)推斷。核心概念的解釋非常清晰，即使跳過其中的數(shù)學(xué)細(xì)節(jié)，也能使讀者理解。    本書可作為工科、管理類學(xué)科專業(yè)本科生、研究生的教材或參考書，也可供教師、工程技術(shù)人員自學(xué)之用。

作者簡介

　　D.R.Cox，世界著名統(tǒng)計(jì)學(xué)家，英國皇家學(xué)會(huì)會(huì)員暨英國社會(huì)科學(xué)院院士，美國科學(xué)院、丹麥皇家科學(xué)院外籍院士。曾任國際統(tǒng)計(jì)協(xié)會(huì)、伯努利數(shù)理統(tǒng)汁與概率學(xué)會(huì)、英國皇家統(tǒng)計(jì)學(xué)會(huì)主席。主要學(xué)術(shù)貢獻(xiàn)包括Cox過程和影響深遠(yuǎn)且應(yīng)用廣泛的Cox比例風(fēng)險(xiǎn)模型等。

書籍目錄

1　Preliminaries　Summary　1.1  Starting point　1.2  Role of formal theory of inference　1.3  Some simple models　1.4  Formulation of objectives　1.5  Two broad approaches to statistical inference　1.6  Some further discussion　1.7  Parameters　Notes 12　Some concepts and simple applications　Summary　2.1  Likelihood　2.2  Sufficiency　2.3  Exponential family　2.4  Choice of priors for exponential family problems　2.5  Simple frequentist discussion　2.6  Pivots　Notes 23　Significance tests　Summary　3.1  General remarks　3.2  Simple significance test　3.3  One- and two-sided tests　3.4  Relation with acceptance and rejection　3.5  Formulation of alternatives and test statistics　3.6  Relation with interval estimation　3.7  Interpretation of significance tests　3.8  Bayesian testing　Notes 34　More complicated situations　Summary　4.1  General remarks　4.2  General Bayesian formulation　4.3  Frequentist analysis　4.4  Some more general frequentist developments　4.5  Some further Bayesian examples　Notes 45　Interpretations of uncertainty　Summary　5.1  General remarks　5.2  Broad roles of probability　5.3  Frequentist interpretation of upper limits　5.4  Neyman-Pearson operational criteria　5.5  Some general aspects of the frequentist approach　5.6  Yet more on the frequentist approach　5.7  Personalistic probability　5.8  Impersonal degree of belief　5.9  Reference priors　5.10 Temporal coherency　5.11 Degree of belief and frequency　5.12 Statistical implementation of Bayesian analysis　5.13 Model uncertainty　5.14 Consistency of data and prior　5.15 Relevance of frequentist assessment　5.16 Sequential stopping　5.17 A simple classification problem　Notes 56　Asymptotic theory　Summary　6.1  General remarks　6.2  Scalar parameter　……7　Further aspects of maximum likelihood8　Additional objectives9　Randomization-based analysis

媒體關(guān)注與評論

　　“這是偉大統(tǒng)計(jì)學(xué)家的偉大著作。千萬不能錯(cuò)過！　　——Ronaid Christensen。Journal of the American StatisticaI Association　　“本書是現(xiàn)代統(tǒng)計(jì)學(xué)之父的力作，深入闡述了統(tǒng)計(jì)推斷的內(nèi)容，行文流暢、語言優(yōu)美。對所有從事統(tǒng)計(jì)工作的人來說，本書不可不讀?！薄　　狣avtd Hand（倫敦大學(xué)帝國學(xué)院）　　“非常優(yōu)秀的一本教材，在頻率學(xué)派和貝葉斯學(xué)派之間找到了絕好的平衡，給出不偏不倚的觀點(diǎn)?！薄　　稇?yīng)用統(tǒng)計(jì)》雜志

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