The Foundations of Statistics

Front Cover
Courier Dover Publications, 1972 - Mathematics - 310 pages
3 Reviews
With the 1954 publication of his Foundations of Statistics, in which he proposed a basis that takes into account not only strictly objective and repetitive events, but also vagueness and interpersonal differences, Leonard J. Savage opened the greatest controversy in modern statistical thought. His theory of the foundations, connected with the personalistic interpretation of probability, challenged the then dominant frequentist school.
In the first seven chapters of his book, Professor Savage is concerned with the foundations at a relatively deep level. To explain and defend his theory of the behavior of a highly idealized person faced with uncertainty, he considers decision making, the sure-thing principle, qualitative and quantitative personal probability, the approach to certainty through experience, symmetric sequences of events, critical comments on personal probability, utility, observations as they affect the decision, and partition problems. In chapters eight through seventeen he discusses statistics proper the actual devices of the discipline from the personalistic view. He concentrates on minimax problems and on the theories of estimation and testing. Exercises are included throughout to reinforce and supplement the text. The mathematical techniques used are quite elementary, some calculus and elementary probability theory being presupposed. Understanding of all the material calls for some mathematical maturity on the part of the reader. Professor Savage had reevaluated his position somewhat during the decade and a half since the work was first published. While reaffirming the material in the first seven chapters, he had reconsidered the appropriateness of many frequentistic applications. To explain these recent developments, he added a new preface, new footnotes, and a supplementary 180-item, annotated bibliography. Because of Professor Savage's death, the revisions that he made for this edition are his final analysis of the situation.
As he says on page one, "the foundations are the most controversial parts of many, if not all, sciences." In statistics, the foundation of probability is "as controversial a subject as one could name." In 1954, the controversy was very great, and although it has quieted since, the problem has yet to be resolved. A new generation of readers who have missed Savage's analysis have here an opportunity to study firsthand what his important foundation of statistics personal probability is, and what it means to statistical thought.
  

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Contents

Postulates of a personalistic theory of decision End papers
1
PsasoNAL PnoBABILITY
27
irs on PnnsoxaL Paosaamrrr
53
UnLrrY
71
10
109
PARTITIoN PnoaLsus
116
13
132
17
139
Mixed acts in statistics
217
Ponrr ESTIMATIoN 1 Introduction
220
27
221
Criteria that have been proposed for point estimates
223
A behavioralistic review of the criteria for point estimation I
229
A behavioralistic review continued
234
A behavioralistic review concluded
244
Tnsrmo 1 Introduction
246

Srarrsrrcs
154
PaaaLLausu BETWEEN THE Mrsruax TaroRY AND ran TuaoRr
178
Tan IAIHEhlAlICS or MiNruax PaoaLaus
184
Bilinear games
186
An example of a bilinear game
189
Bilinear games exhibiting symmetry
193
Mr m x Rows 1 Introduction
200
Utility and the minimax rule
201
Almost subminimax acts
203
The minimax rule does not generate a simple ordering
205
0 T0 OnsnnvxrroNs 1 Introduction
208
Suficient statistics
212
The approach to certainty
214
Sequential probability ratio procedues
215
Randomization
216
A theory of testing
247
Testing in practice
252
IrrrznvaL EsrlmanoN AND RELATED Torres 1 Estimates of the accuracy of estimates
257
Interval estimation and confidence intervals
259
Tolerance intervals
262
cnn VALUE
263
Convex FUNcrIoNS
266
aLu
270
43
271
Bmuocaarnrc SoreLzmsrvr
283
TzcnmcaL SYMBoLS
299
Arrrnoa Irmax
301
Gasaan Isosx
305
Copyright

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