Statistical Thought A Perspective and History

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780198525318 | 0198525311
Cover: Hardcover
Copyright: 7/3/2003

Rent

(Recommended)

$195.45

Term

Due

Price

Semester

Dec 12

$205.74

Quarter

Aug 13

$195.45

Short Term

Jul 27

$185.17

*This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping bag.
Buy New

Usually Ships in 3-5 Business Days

$263.40

In this unique monograph based on years of extensive work, Chatterjee presents the historical evolution of statistical thought from the perspective of various approaches to statistical induction. Developments in statistical concepts and theories are discussed alongside philosophical ideas on the ways we learn from experience.

Part I Perspective

(138)

1 Philosophical background

(13)

1.1 Statistical thought

(1)

1.2 Prolongation of inductive reasoning

(2)

Other viewpoints

(1)

Value judgements in statistics

(1)

Specialities of statistics

(1)

1.3 Means of knowledge

(3)

Deduction

(1)

Induction

(1)

Types of induction

(1)

Characteristics of induction

(1)

1.4 Systematization of deduction started first

(4)

Philosophy of induction begins

(1)

Francis Bacon

(1)

John Locke

(1)

Hume's problem of induction

(1)

1.5 Suggested solutions of Hume's problem

(4)

Statistical pragmatism

(2)

2 Statistical induction-when and how?

(20)

2.1 Two approaches in statistics

(1)

2.2 Constituents of statistical induction

(9)

Meaning of inductive inference

(1)

First feature evidential domain

(1)

Evidence as observations

(1)

Types of characters

(1)

Second feature-order unimportant

(1)

Operations generating observations

(1)

Third feature-extensibility, repeatability

(1)

Fourth feature-uncertainty assessable

(1)

Meanings of uncertainty

(1)

Meaning of probability

(2)

2.3 Assumptions imposed

(1)

Probability model-objective

(1)

Probability model-subjective

(1)

2.4 Inductive concern

(4)

Objective case

(1)

Subjective case

(1)

The two viewpoints

(2)

2.5 Uncertainty re conclusion

(2)

Large body of evidence

(1)

2.6 Design problem

(4)

3 Interpretation of probability: various nuances

(25)

3.1 Interpretation of probability

(1)

Objective and subjective

(1)

3.2 Objective interpretation of probability

(5)

3.2.1 Long-term relative frequency

(1)

3.2.2 Von-Mises-Reichenbach

(2)

3.2.3 Fisher and Russell

(1)

3.2.4 Formalistic development

(1)

3.2.5 Problem of instantiation

(2)

A priori principle

(1)

Popper's propensity

(1)

3.2.6 Subjectivity unavoidable

(1)

3.3 Subjective interpretation of probability

(5)

3.3.1 Natural domain and types

(1)

3.3.2 Impersonal subjective

(1)

3.3.3 Personal subjective

(3)

Operational determination

(1)

Coherence

(2)

3.3.4 Personalistic viewpoint-criticism, rejoinder

(1)

3.4 Plurality of terms and attitudes

(1)

3.5 Axiomatic development

(5)

3.5.1 Two conventions-events

(1)

3.5.2 Absolute probability axioms

(1)

3.5.3 Conditional probability axioms

(2)

3.5.4 Motivation behind axioms

(2)

3.6 Probabilistic independence

(1)

When independence?

(1)

3.7 Identical distribution

(1)

3.8 Exchangeability

(1)

3.9 Approximate probability

(3)

3.10 Non-standard probabilities

(2)

4 Bearing of interpretations of probability on statistical induction

(78)

4.1 Approaches to statistical induction

(1)

Variety of objective approaches

(1)

4.2 Objective-behavioural approach

(9)

4.2.1 Inductive behaviour

(1)

Choice of inductive rule

(1)

Assurance relates to rule

(1)

4.2.2 Point estimation

(3)

Interval estimation

(1)

Hypothesis testing

(1)

4.2.3 Assurance across heterogeneous situations

(2)

Relevance of conditioning

(1)

4.2.4 Decision Theory

(2)

4.2.5 Post-experimental randomization

(1)

4.2.6 Criticisims of the behavioural approach

(1)

4.3 Objective-instantial approach

(17)

4.3.1 Instance at hand emphasized

(2)

Contrast with behavioural approach

(1)

4.3.2 Forward and backward instantiation

(1)

Modes of instantial inference

(1)

4.3.3 Likelihood and likelihood ratio

(4)

Sufficient statistic and partition

(1)

Sufficiency principle

(1)

Minimal sufficiency of LR partition

(1)

4.3.4 Likelihood principle

(2)

4.3.5 Likelihood-based point estimation

(4)

Likelihood based interval estimation and testing

(2)

4.3.6 Extended modus tollens

(4)

Questions that arise

(2)

4.3.7 Fiducial inference

(12)

Motivation and description

(3)

Choice of pivot

(2)

Interpretation

(2)

4.3.8 Question of irrelevance

(5)

4.4 Objective-pro-subjective approach

100

(23)

4.4.1 Subjective probability in input

100

(1)

4.4.2 Posterior distribution

101

(1)

Sufficiency and likelihood principles

102

(1)

4.4.3 Choice of prior

102

(2)

Frequentist

103

(1)

Subjective-impersonal and personal

104

(1)

4.4.4 Impersonal prior

104

(9)

Non-informative prior-group-theoretic

105

(2)

Fiducial distribution as posterior

107

(1)

Non-informative prior a la Jeffreys

108

(2)

Interpretation of improper priors

110

(1)

Partially informative prior

111

(1)

Vindication of impersonal Bayesian analysis

112

(1)

4.4.5 Personal prior

113

(3)

Natural conjugate priors

113

(3)

The question of robustness

116

(1)

4.4.6 A unified approach

116

(5)

Point estimation

117

(1)

Large sample approximation

117

(1)

Interval and set estimation

118

(1)

Hypothesis testing

119

(1)

Decision problem

120

(1)

4.4.7 Discussion

121

(2)

4.5 Subjective approach

123

(13)

4.5.1 Distinguishing features

123

(2)

4.5.2 Conditional distribution of interest

125

(2)

4.5.3 Types of induction

127

(1)

4.5.4 Exchangeability

128

(4)

4.5.5 Sufficiency

132

(4)

Infinite exchangeability

133

(1)

Notional 'objective-pro-subjective'

133

(3)

4.5.7 A matter of choice

136

(1)

4.6 Concluding discussion

136

(3)

Part II History

139

(256)

5 Prehistory, beginning of history, and the toddling period

141

(32)

5.1 'Probability' before 'statistics'

141

(1)

Genesis of probability

141

(1)

5.2 The long period of gestation

141

(7)

5.2.1 Behaviour under uncertainty

141

(3)

5.2.2 Probabilistic ideas in Talmuds

144

(2)

Renaissance-mutation of 'probable'

145

(1)

Aleatory contracts

146

(1)

5.2.3 Probability from gaming and gambling

146

(2)

A mysterious reference in an Indian epic

147

(1)

Conditions in the West before the 16th century

148

(1)

5.3 The birth of probability theory

148

(9)

5.3.1 Cardano-an unrecognized pioneer

148

(3)

5.3.2 Galileo

151

(1)

5.3.3 Probability is officially born-Pascal and Fermat

151

(6)

Huygens

152

(1)

Problem of minimum number of trials

153

(1)

Division problem

153

(1)

Combinatorial solution

154

(1)

Recursive solution

154

(1)

The pioneers' world of probability

155

(2)

5.4 Beginning of data analysis

157

(7)

5.4.1 Ancient and medieval official statistics

157

(1)

5.4.2 London bills of mortality-John Graunt

158

(4)

Graunt's estimation of population

158

(2)

Graunt's life table

160

(1)

Graunt's other studies

161

(1)

Speciality of Graunt's methods

161

(1)

5.4.3 Impact of Graunt's work

162

(2)

5.5 Diffusion of probabilistic thinking-objective and subjective

164

(3)

5.5.1 Pascal and Port Royal Logic

164

(2)

Pascal's wager

165

(1)

5.5.2 Leibniz

166

(1)

5.6 An attempted synthesis of various concepts of probability

167

(4)

5.6.1 James Bernoulli Ars Conjectandi

167

(1)

5.6.2 Bernoulli's limit theorem

168

(2)

5.6.3 Bernoulli's probability

170

(1)

5.7 A historical puzzle

171

(2)

6 New concepts and methods-pre-Bayesian era

173

(21)

6.1 The century after Pascal-Fermat correspondence

173

(1)

6.2 Arbuthnott use of probability for hypothesis testing

174

(1)

6.3 Abraham De Moivre

175

(5)

Generating functions

176

(1)

Normal approximation to binomial

177

(2)

De Moivre's view of probability

179

(1)

6.4 Behaviour of observational errors

180

(4)

Thomas Simpson

181

(2)

Notable features of Simpson's work

183

(1)

6.5 Daniel Bernoulli

184

(10)

Testing a cosmogonical hypothesis

185

(1)

The maximum likelihood principle

186

(1)

The normal model

187

(1)

Inoculation problem-a survival model

188

(2)

St. Petersburg paradox and moral expectation

190

(2)

The rational expectation principle

192

(2)

7 Beginning of the pro-subjective approach

194

(29)

7.1 Parameter as random variable

194

(1)

7.2 Thomas Bayes

194

(11)

7.2.1 Bayes's life and his essay

194

(1)

7.2.2 Bayes's conception of probability

195

(1)

7.2.3 Probability rules-Bayes's derivation

196

(1)

7.2.4 Bayes's problem

197

(1)

7.2.5 Solution for a two-stage model

198

(2)

7.2.6 Solution of the general problem

200

(2)

7.2.7 Bayes's reticence

202

(3)

Price's commentary

202

(3)

7.3 Pierre-Simon Laplace

205

(16)

7.3.1 Laplace's life and career

205

(1)

7.3.2 Scientific contributions

206

(1)

7.3.3 Nature of Laplace's work on probability

207

(1)

7.3.4 Laplace's conception of probability

208

(1)

7.3.5 Laplace's form of Bayes's theorem

209

(2)

Posterior probability of a future event

210

(1)

Continuous versions

211

(1)

7.3.6 Posterior-based estimation

211

(3)

7.3.7 Posterior-based testing

214

(2)

7.3.8 Posterior-based prediction

216

(2)

7.3.9 Laplace's sample survey

218

(2)

7.3.10 Choice of prior-Laplace's prescription

220

(1)

7.4 Pro-subjective approach-later developments

221

(2)

8 Pro-subjective approach loses as sampling theory gains ground

223

(42)

8.1 First half of 19th century

223

(1)

8.2 Quest for a model for the estimation of a true value

224

(12)

8.2.1 Background

224

(1)

8.2.2 Carl Friedrich Gauss

225

(1)

8.2.3 A.M. Postulate and the normal law

225

(2)

8.2.4 Gauss's estimate of a true value

227

(2)

8.2.5 Implication of Gauss's derivation

229

(1)

8.2.6 Laplace's CLT

230

(3)

8.2.7 Laplace's response to Gauss's proposal

233

(1)

8.2.8 Postulate of elementary errors

234

(1)

8.2.9 Other postulates

235

(1)

8.3 Fitting of linear parametric curves

236

(14)

8.3.1 General problem of curve-fitting

236

(2)

8.3.2 Non-probabilistic methods

238

(4)

8.3.3 Gauss's first approach

242

(3)

8.3.4 Laplace's large-sample approach

245

(2)

8.3.5 Gauss's second approach

247

(3)

8.4 Comparison of estimators

250

(6)

8.4.1 ARE-Gauss

250

(2)

8.4.2 ARE--Laplace

252

(2)

8.4.3 Excursus on sufficiency

254

(2)

8.5 Sampling-theory testing

256

(3)

Daniel Bernoulli's problem

256

(1)

Tides of the atmosphere

257

(1)

Choice of the rejection rule

258

(1)

8.6 Reign of errors

259

(6)

8.6.1 Theory of Errors

259

(1)

8.6.2 Standardization of measures

260

(1)

8.6.3 Development of approaches

260

(1)

8.6.4 Various models

261

(1)

8.6.5 Families of random variables

262

(2)

8.6.6 True value syndrome

264

(1)

9 Breaking the barrier: out into a broader domain

265

(48)

9.1 Nature of conceptual barrier

265

(1)

9.2 'Avalanche of numbers'

266

(2)

9.3 Poisson

268

(2)

9.4 Adolphe Quetelet

270

(5)

9.4.1 Quetelet's objective

270

(1)

9.4.2 The 'Average Man'

271

(1)

9.4.3 Breaking the barrier

272

(1)

9.4.4 Social physics

273

(2)

9.4.5 Nature of Quetelet's studies

275

(1)

9.4.6 Quetelet-the organizer

275

(1)

9.5 Aftermath of the opening up

275

(7)

9.5.1 Implications for statistics

275

(3)

9.5.2 Implications for social sciences

278

(1)

Social activism

278

(1)

9.5.3 Implications for philosophy

279

(3)

Deterministic social laws

280

(1)

Physical indeterminism

281

(1)

9.6 Developments in probability

282

(2)

9.6.1 Advent of frequency probability

282

(2)

C. S. Peirce

283

(1)

9.6.2 Mathematics of probability

284

(1)

9.7 Francis Galton

284

(15)

9.7.1 Galton's conceptual departure

284

(1)

Early work

285

(1)

9.7.2 Eugenic movement

285

(5)

Distribution of abilities

286

(1)

Genealogical studies

287

(1)

Quincunx

287

(1)

Questions to be addressed

288

(2)

9.7.3 First phase-heredity

290

(3)

9.7.4 Second phase-family likeness

293

(3)

The bivariate normal model

295

(1)

9.7.5 Third phase-correlation

296

(1)

9.7.6 Nature and impact of Galton's contributions

297

(2)

9.8 Extension of Galton's work

299

(11)

9.8.1 Galton's successors

299

(1)

9.8.2 Reification of correlation

300

(2)

9.8.3 Multivariate normal

302

(2)

9.8.4 The least squares connection

304

(3)

9.8.5 Inductive inference about p

307

(3)

9.9 Statistical induction-19th century scenario

310

(3)

9.9.1 Post-Laplacian era

310

(1)

9.9.2 Behavioural approach

310

(2)

9.9.3 Abstraction of the method

312

(1)

10 Modern era: the superstructure builds up

313

(82)

10.1 Into the 20th century

313

(3)

Models and parameters

314

(1)

Types of induction

314

(2)

10.2 Model-selecting induction

316

(21)

10.2.1 Beginning

316

(1)

Frequent encounter with non-normality

316

(1)

'Reservoir of models'

317

(1)

10.2.2 Method of transformation

317

(1)

Johnson system

318

(1)

Box-Cox

318

(1)

10.2.3 Method of asymptotic expansion

318

(2)

Gram-Charlier expansion

319

(1)

Edgeworth expansion

319

(1)

10.2.4 Method of mixture

320

(1)

Two attitudes

321

(1)

Compounding

321

(1)

10.2.5 Method of formal embedding

321

(2)

Pearsonian system

322

(1)

Main drawback

322

(1)

10.2.6 Selection and fitting

323

(2)

Method of moments

323

(1)

Maximum likelihood

324

(1)

Bayesian methods

325

(1)

10.2.7 Goodness of fit

325

(5)

Nibbling at the problem

325

(1)

Pearsonian x2-simple Ho

326

(2)

Pearsonian x2-composite Ho

328

(1)

A 20th century wonder

328

(1)

Other goodness-of-fit tests

329

(1)

Case of a parametric family

330

(1)

10.2.8 Models for other occasions

330

(5)

Discrete models

331

(1)

Life testing models

331

(1)

Postulational approach

332

(2)

Non-identical variables GUM

334

(1)

Dependent variables

334

(1)

10.2.9 Information criteria

335

(2)

AIC and BIC

336

(1)

Predictive criteria

336

(1)

10.3 Model-specific induction

337

(35)

10.3.1 Beginning

337

(1)

10.3.2 'Student's' sampling theory

338

(3)

Encounter with the problem

338

(1)

'Student's' t

339

(1)

Work on r

340

(1)

10.3.3 Small-scale experiments-background

341

(3)

Agricultural experiments accumulated lore

342

(1)

'Student's' contributions

343

(1)

Comparison of treatments

343

(1)

10.3.4 Enter R. A. Fisher

344

(1)

10.3.5 Sampling distribution

344

(1)

10.3.6 Theory of estimation

345

(2)

10.3.7 Fisher's work on designs

347

(8)

Gauss and Fisher

348

(1)

Factorial designs

349

(1)

Randomization

350

(1)

Randomization analysis

351

(2)

A theoretical objection

353

(1)

An answer

353

(2)

10.3.8 Further developments-theory of inference

355

(6)

The behavioural approach

356

(1)

Behavioural-instantial divide

357

(1)

Wald

358

(1)

Subsequent developments

359

(2)

10.3.9 Further developments-multivariate analysis

361

(5)

10.3.10 Further developments design of experiments

366

(2)

10.3.11 Outliers and robustness

368

(4)

10.4 Model-free induction

372

(21)

10.4.1 Types of problem

372

(1)

10.4.2 Sampling from infinite populations

372

(14)

(a) Approximate procedures

374

(1)

Regression with stochastic predictors

374

(1)

Large sample procedures for contingency tables

375

(1)

Moments, cumulants, U-statistics

376

(1)

Cox's partial likelihood methods

377

(1)

(b) Exact procedures

378

(1)

Use of probability integral transforms

378

(1)

Inference about a quantile

379

(1)

Association in a 2 x 2 table

379

(1)

Course of development

380

(1)

Two sample location problem

381

(1)

Approximate boot-strap procedures

383

(1)

Comparison of performance

383

(1)

Question of robustness

384

(1)

Model-free Bayesian approach

385

(1)

10.4.3 Sampling from a finite population

386

(7)

Early developments

387

(1)

Neyman

388

(1)

Expansion of applications

389

(1)

Developments in theory

390

(1)

The randomization imbroglio

391

(1)

Non-sampling-theory approaches

392

(1)

10.5 Epilogue

393

(2)

References

395

(14)

Index

409

Please wait while the item is added to your bag...

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Statistical Thought A Perspective and History

Summary

Author Biography

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Statistical Thought A Perspective and History

Summary

Author Biography

Table of Contents

Supplemental Materials

Digital License