概率統(tǒng)計(jì)

內(nèi)容概要

　　這本舉世公認(rèn)的經(jīng)典概率論與數(shù)理統(tǒng)計(jì)教材，幾十年來暢銷不衰，被很多名校采用，包括卡內(nèi)基-梅隆大學(xué)、哈佛大學(xué)、麻省理工學(xué)院、華盛頓大學(xué)、芝加哥大學(xué)、康奈爾大學(xué)、杜克大學(xué)、加州大學(xué)洛杉磯分校等。
　　《華章統(tǒng)計(jì)學(xué)原版精品系列：概率統(tǒng)計(jì)（英文版·第4版）》包括概率論、數(shù)理統(tǒng)計(jì)兩部分，內(nèi)容豐富完整，適當(dāng)?shù)剡x擇某些章節(jié)，可以作為一學(xué)年的概率論與數(shù)理統(tǒng)計(jì)課程的教材，亦可作為一學(xué)期的概率論與隨機(jī)過程的教材。適合數(shù)學(xué)、統(tǒng)計(jì)學(xué)、經(jīng)濟(jì)學(xué)等專業(yè)高年級(jí)本科生和研究生用，也可供統(tǒng)計(jì)工作人員用作參考書。

作者簡(jiǎn)介

Morris
H.DeGroot（1931-1989），世界著名的統(tǒng)計(jì)學(xué)家。生前曾任國(guó)際統(tǒng)計(jì)學(xué)會(huì)、美國(guó)科學(xué)促進(jìn)會(huì)、統(tǒng)計(jì)學(xué)會(huì)、數(shù)理統(tǒng)計(jì)學(xué)會(huì)、計(jì)量經(jīng)濟(jì)學(xué)會(huì)會(huì)士?？▋?nèi)基·梅隆大學(xué)教授，1957年加入該校，1966年創(chuàng)辦該校統(tǒng)計(jì)系。DeGroot在學(xué)術(shù)上異常活躍和多產(chǎn)，曾發(fā)表一百多篇論文，還著有Optimal
StatisOcal Decisions和Statistics and the
Lawo為紀(jì)念他的著作對(duì)統(tǒng)計(jì)教學(xué)的貢獻(xiàn)，國(guó)際貝葉斯分析學(xué)會(huì)特別設(shè)立了DeGroot獎(jiǎng)表彰優(yōu)秀統(tǒng)計(jì)學(xué)著作。
　　Mark
J.Schervish，世界著名的統(tǒng)計(jì)學(xué)家，美國(guó)統(tǒng)計(jì)學(xué)會(huì)、數(shù)理統(tǒng)計(jì)學(xué)會(huì)會(huì)士。于1979年獲得伊利諾伊大學(xué)的博士學(xué)位，之后就在卡內(nèi)基·梅隆大學(xué)統(tǒng)計(jì)系工作，教授數(shù)學(xué)、概率、統(tǒng)計(jì)和計(jì)算金融等課程，現(xiàn)為該系系主任。Schervish在學(xué)術(shù)上非?；钴S，成果頗豐，還因在統(tǒng)計(jì)推斷和貝葉斯統(tǒng)計(jì)方面的基石性工作而聞名，除本書外，他還著有Theory
ofStatistics和 Rethinking the Foundations of Statistics。

書籍目錄

1 introduction to probability
 1.1 the history of probability
 1.2 interpretatio of probability
 1.3 experiments and events
 1.4 set theory
 1.5 the definition of probability
 1.6 finite sample spaces
 1.7 counting methods
 1.8 combinatorial methods
 1.9 multinomial coefficients
 1.10 the probability of a union of events
 1.11 statistical swindles
 1.12 supplementary exercises
2 conditional probability
 2.1 the definition of conditional probability
 2.2 independent events
 2.3 bayes’ theorem
 2.4 the gambler’s ruin problem
 2.5 supplementary exercises
3 random variables and distributio
 3.1 random variables and discrete distributio
 3.2 continuous distributio
 3.3 the cumulative distribution function
 3.4 bivariate distributio
 3.5 marginal distributio
 3.6 conditional distributio
 3.7 multivariate distributio
 3.8 functio of a random variable
 3.9 functio of two or more random variables
 3.10 markov chai
 3.11 supplementary exercises
4 expectation
 4.1 the expectation of a random variable
 4.2 properties of expectatio
 4.3 variance
 4.4 moments
 4.5 the mean and the median
 4.6 covariance and correlation
 4.7 conditional expectation
 4.8 utility
 4.9 supplementary exercises
5 special distributio
 5.1 introduction
 5.2 the bernoulli and binomial distributio
 5.3 the hypergeometric distributio
 5.4 the poisson distributio
 5.5 the negative binomial distributio
 5.6 the normal distributio
 5.7 the gamma distributio
 5.8 the beta distributio
 5.9 the multinomial distributio
 5.10 the bivariate normal distributio
 5.11 supplementary exercises
6 large random samples
 6.1 introduction
 6.2 the law of large numbe
 6.3 the central limit theorem
 6.4 the correction for continuity
 6.5 supplementary exercises
7 estimation
 7.1 statistical inference
 7.2 prior and posterior distributio
 7.3 conjugate prior distributio
 7.4 bayes estimato
 7.5 maximum likelihood estimato
 7.6 properties of maximum likelihood estimato
 7.7 sufficient statistics
 7.8 jointly sufficient statistics
 7.9 improving an estimator
 7.10 supplementary exercises
8 sampling distributio of estimato
 8.1 the sampling distribution of a statistic
 8.2 the chi-square distributio
 8.3 joint distribution of the sample mean and sample
variance
 8.4 the t distributio
 8.5 confidence intervals
 8.6 bayesian analysis of samples from a normal
distribution
 8.7 unbiased estimato
 8.8 fisher information
 8.9 supplementary exercises
9 testing hypotheses
 9.1 problems of testing hypotheses
 9.2 testing simple hypotheses
 9.3 uniformly most powerful tests
 9.4 two-sided alternatives
 9.5 the t test
 9.6 comparing the mea of two normal
distributio
 9.7 the f distributio
 9.8 bayes test procedures
 9.9 foundational issues
 9.10 supplementary exercises
10 categorical data and nonparametric methods
 10.1 tests of goodness-of-fit
 10.2 goodness-of-fit for composite hypotheses
 10.3 contingency tables
 10.4 tests of homogeneity
 10.5 simpson’s paradox
 10.6 kolmogorov-smirnov tests
 10.7 robust estimation
 10.8 sign and rank tests
 10.9 supplementary exercises
11 linear statistical models
 11.1 the method of least squares
 11.2 regression
 11.3 statistical inference in simple linear regression
 11.4 bayesian inference in simple linear regression
 11.5 the general linear model and multiple regression
 11.6 analysis of variance
 11.7 the two-way layout
 11.8 the two-way layout with replicatio
 11.9 supplementary exercises
12 simulation
 12.1 what is simulation?
 12.2 why is simulation useful?
 12.3 simulating specific distributio
 12.4 importance sampling
 12.5 markov chain monte carlo
 12.6 the bootstrap
 12.7 supplementary exercises
tables
a we to odd-numbered exercises
references
index

章節(jié)摘錄

版權(quán)頁：   插圖：   The events B1, B2，……B11 in Example 2.1.12 can be thought of in much the same way as the two events B1 and B2 that determine the mixture of long and short bolts in Example 2.1.11. There is only one box of bolts, but there is uncertainty about its composition. Similarly in Example 2.1.12, there is only one group of patients,but we believe that it has one of 11 possible compositions determined by the events B1, B2，……B11. To call these events, they must be subsets of the sample space for the experiment in question. That will be the case in Example 2.1.12 if we imagine that the experiment consists not only of observing the numbers of successes and failures among the patients but also of potentially observing enough additional patients to be able to compute p, possibly at some time very far in the future. Similarly, in Example 2.1.11, the two events B1 and B2 are subsets of the sample space if we imagine that the experiment consists not only of observing one sample bolt but also of potentially observing the entire composition of the box. Throughout the remainder of this text, we shall implicitly assume that experi-ments are augmented to include outcomes that determine the values of quantities such as p. We shall not require that we ever get to observe the complete outcome of the experiment so as to tell us precisely what p is, but merely that there is an exper-iment that includes all of the events of interest to us, including those that determine quantities like p.Augmented Experiment. If desired, any experiment can be augmented to include the potential or hypothetical observation of as much additional information as we would find useful to help us calculate any probabilities that we desire. Definition 2.1.3 is worded somewhat vaguely because it is intended to cover a wide variety of cases. Here is an explicit application to Example 2.1.12.

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《概率統(tǒng)計(jì)(英文版?第4版)》中內(nèi)容豐富完整，適當(dāng)?shù)剡x擇某些章節(jié)，可以作為一學(xué)年的概率論與數(shù)理統(tǒng)計(jì)課程的教材，亦可作為一學(xué)期的概率論與隨機(jī)過程的教材。

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