Statistical Computation (eBook)

Roy C. Milton, John A. Nelder (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
474 Seiten
Elsevier Science (Verlag)
9781483258027 (ISBN)

Infos

Statistical Computation covers the proceedings of a conference held at the University of Wisconsin in Madison, Wisconsin on April 28-30, 1969. The book focuses on the methodologies, techniques, principles, and approaches involved in statistical computation. The selection first elaborates on the description of data structures for statistical computing, autocodes for the statistician, and an experimental data structure for statistical computing. Discussions focus on data-system organization, data structures, autocode requirements, data matrix, structure formulas, and structure formulas in data processing and output. The text then examines statistics and computers in relation to large data bases, statistical data language, facilities in a statistical program system for analysis of multiply-indexed data, and language design and the needs of statisticians. The book takes a look at time sharing and interactive statistics, an approach to conversational statistics, use of APL in statistics, and continuing development of a statistical system. Topics include arithmetic operations and branching statements, ASCOP system, application to statistics, semantics, pragmatics, and implementation. The selection is a valuable reference for statisticians and researchers interested in statistical computation.

Inhalt

Front Cover 1
Statistical Computation 4
Copyright Page 5
Table of Contents 12
SPEAKERS 6
PREFACE 8
PART I: KEYNOTE ADDRESS 14
CHAPTER 1. THE CHALLENGE OF STATISTICAL COMPUTATION 16
PART II: SPECIFICATIONS FOR STATISTICAL DATA STRUCTURES 24
CHAPTER 2. THE DESCRIPTION OF DATA STRUCTURES FOR STATISTICAL COMPUTING 26
0. INTRODUCTION 26
1. THE DATA MATRIX 28
2. STRUCTURE FORMULAE 34
3. STRUCTURE FORMULAE IN DATA PROCESSING 39
4. STRUCTURE FORMULAE IN OUTPUT 42
5. CONCLUSION 46
REFERENCES 47
APPENDIX 47
CHAPTER 3. AUTOCODES FOR THE STATISTICIAN 50
SUMMARY 50
1. INTRODUCTION 50
2. AUTOCODE REQUIREMENTS 54
3. CONCLUSION 72
REFERENCES 74
LANGUAGES 74
CHAPTER 4. AN EXPERIMENTAL DATA STRUCTURE FOR STATISTICAL COMPUTING 76
1. INTRODUCTION 76
2. DATA STRUCTURES 77
3. THE DATA-SYSTEM ORGANIZATION 82
4. USING THE DATA 84
5. IMPLEMENTATION 88
6. SUMMARY AND CONCLUSIONS 95
ACKNOWLEDGMENT 97
REFERENCES 97
CHAPTER 5. STATISTICS AND COMPUTERS IN RELATION TO LARGE DATA BASES 100
1. INTRODUCTION 103
2. DATA STRUCTURES, RECORDS, AND FILE ORGANIZATIONS– SOME PRELIMINARIES 107
3. LARGE DATA BASES—IMPLICATIONS AND CHALLENGES 135
4. ORGANIZATION AND MAINTENANCE OF HISTORICAL DATA 153
5. MODES OF COMPUTER USE 159
6. MODES OF DATA ANALYSIS WITH A COMPUTER 165
7. STATISTICAL COMPUTING LANGUAGES OR STATISTICAL SYSTEMS FOR LARGE DATA BASES 171
8. SELECTION AND ALLOCATION OF RESOURCES IN THE PRESENCE OF CONSTRAINTS AND UNCERTAINTY 178
ACKNOWLEDGMENTS 186
REFERENCES 186
PART III: STATISTOAL SYSTEMS AND LANGUAGES 190
CHAPTER 6. A STATISTICAL DATA LANGUAGE 192
1. INTRODUCTION 192
2. DATA TRANSMISSION 194
3. DATA STORAGE AND RETRIEVAL 200
4. STRUCTURES AND ATTRIBUTES 202
5. THE LANGUAGE: TRANSLATION AND EXTENSION 205
6. AN IMPLEMENTATION 208
7. CONCLUSION 211
REFERENCES 212
CHAPTER 7. FACILITIES IN A STATISTICAL PROGRAM SYSTEM FOR ANALYSIS OF MULTIPLY-INDEXED DATA 214
1. SOME GENERAL REMARKS ON THE DEVELOPMENT OF STATISTICAL SYSTEMS 214
2. FACILITIES FOR HANDLING MULTIPLY-INDEXED DATA 219
3. A GENERAL RECURSIVE PROCEDURE FOR THE ANALYSIS OF EXPERIMENTAL DESIGNS 229
REFERENCES 240
CHAPTER 8. LANGUAGE DESIGN AND THE NEEDS OF STATISTICIANS 242
INTRODUCTION 242
BASIC APPROACH 242
LANGUAGE CRITERIA 243
DATA STRUCTURES 243
MACROS 246
COMPATIBILITY 248
SUMMARY 248
APPENDIX 248
EXTENSIONS TO FORTRAN 252
CHAPTER 9. TIME SHARING AND INTERACTIVE STATISTICS 256
1. INTRODUCTION 256
2. THE OPERATING SYSTEM TORTOS 257
3. THE BATCH STATISTICAL PROGRAMS 265
4. THE INTERACTIVE PROGRAMS 271
5. THE FUTURE 277
CHAPTER 10. AN APPROACH TO CONVERSATIONAL STATISTICS 280
1. INTRODUCTION 280
2. BRIEF STATEMENT OF THE PROBLEM 281
3. SYNTAX 283
4. SEMANTICS 283
5. PRAGMATICS 289
6. IMPLEMENTATION 292
7. DISCUSSION 294
REFERENCES 296
CHAPTER 11. THE USE OF APL IN STATISTICS 298
THE LANGUAGE 298
APPLICATIONS TO STATISTICS 301
ACKNOWLEDGMENT 305
REFERENCES 305
CHAPTER 12. THE CONTINUING DEVELOPMENT OF A STATISTICAL SYSTEM 308
1. INTRODUCTION 308
2. THE ASCOP SYSTEM 308
3. DECLARATIONS 312
4. INSTRUCTIONS 312
5. ARITHMETIC OPERATIONS AND BRANCHING STATEMENTS 313
6. EXAMPLE ASCOP PROGRAMS 315
7. USE MADE OF THE SYSTEM 319
8. PROJECT AIMS 322
9. VERSION 3 326
10. AVAILABILITY 327
REFERENCES 328
PART IV: STATISTOAL DATA SCREENING WITH COMPUTERS 330
CHAPTER 13. ROBOT DATA SCREENING – A UBIQUITOUS AUTOMATIC SEARCH TECHNIQUE 332
TWO ALTERNATIVE POSITIONS FOR STATISTICAL INFERENCE 332
THE SPECIFIC PURPOSE OF ROBOT SCREENING 336
REQUIREMENTS FOR AUTOMATIC SEARCH TECHNIQUES AND THEIR IMPLEMENTATION IN ROBOT DATA SCREENING 337
PREDICTION CRITERIA 337
SEARCH STRATEGIES FOR FINDING RELEVANT PREDICTORS 342
SELECTION DECISION RULES 343
CONCLUSION 345
BIBLIOGRAPHY 346
PART V: TEACHING OF STATISTICS WITH COMPUTERS 348
CHAPTER 14. COMPUTER-ASSISTED INSTRUCTION IN STATISTICS 350
INTRODUCTION TO STATISTICAL INFERENCE 352
INTRODUCTION TO MULTIVARIATE ANALYSIS 354
PLANS FOR THE FUTURE 355
REFERENCES 356
Printout 1 357
Printout 2 358
Printout 3 359
CHAPTER 15. COMPUTERS IN THE TEACHING OF STATISTICS: WHERE ARE THE MAIN EFFECTS? 362
PART VI: CURRENT TECHNIQUES IN NUMERICAL ANALYSIS RELATED TO STATIS¹CAL COMPUTATON 376
CHAPTER 16. MATRIX DECOMPOSITIONS AND STATISTICAL CALCULATIONS 378
0. INTRODUCTION 379
1. CHOLESKY DECOMPOSITION 379
2. ACCURACY OF THE CHOLESKY DECOMPOSITION 380
3. SOLUTION OF LINEAR EQUATIONS 381
4. CONDITIONING OF MATRICES 383
5. ITERATIVE REFINEMENT 384
6. PARTIAL CORRELATION 385
7. LEAST SQUARES 386
8. A MATRIX DECOMPOSITION 388
9. STATISTICAL CALCULATIONS 390
10. GRAM-SCHMIDT ORTHOGONALIZATION 394
11. SENSITIVITY OF THE SOLUTION 395
12. ITERATIVE REFINEMENT FOR LEAST SQUARES PROBLEMS 398
13. SINGULAR SYSTEMS 400
14. SINGULAR VALUE DECOMPOSITION 401
15. APPLICATIONS OF THE SVD 402
16. CALCULATION OF THE SVD 405
17. CANONICAL CORRELATIONS 406
ACKNOWLEDGEMENTS 408
REFERENCES 408
CHAPTER 17. ALGORITHMS FOR DATA MAINTENANCE AND COMPUTATION OF ANALYSIS OF VARIANCE 412
1. INTRODUCTION 412
2. THE SDP OPERATOR 413
3. LARGE SCALE ANALYSIS OF VARIANCE 420
4. LARGE SCALE ANALYSIS OF COVARIANCE 421
5. SUMMARY 423
REFERENCES 424
CHAPTER 18. AN ALGORITHM FOR MULTIVARIATE ANALYSIS OF COVARIANCE (IMPLEMENTED IN AARDVARK) 426
INTRODUCTION 426
HISTORY 427
THE MULTIVARIATE ALGORITHM 429
AARDVARK MULTIVARIATE ANALYSIS 437
REFERENCES 438
CHAPTER 19. TOWARD A PRACTICAL METHOD WHICH HELPS UNCOVER THE STRUCTURE OF A SET OF MULTIVARIATE OBSERVATIONS BY FINDING THE LINEAR TRANSFORMATION WHICH OPTIMIZES A NEW "INDEX OF CONDENSATION" 440
1. INTRODUCTION 440
2. INTUITIVE CONSIDERATIONS TOWARD AN INDEX OF CONDENSATION 442
3. THE INDEX OF CONDENSATION USED IN THIS PAPER 444
4. THE EXPECTED VALUE AND THE DISTRIBUTION OF C AS A FUNCTION OF THE SAMPLE COVARIANCE MATRIX 446
5. RESULTS SO FAR WITH SYNTHETIC DATA 448
6. THE PROBLEM OF OPTIMIZING 451
REFERENCES 453
CHAPTER 20. COMPUTER OPTIMIZATION OF SECOND ORDER RESPONSE SURFACE DESIGNS 454
1. INTRODUCTION 454
2. 'OPTIMIZATION' OF THE EXPERIMENT 455
3. DESIGN OPTIMIZATION BY 'SPHERICAL PROGRAMMING' 457
4. INVARIANCE PROPERTIES OF THE OBJECTIVE FUNCTION AND IMPROVED ALGORITHM 459
5. STOCHASTIC CONTROL OF OPTIMIZATION AND EXAMPLES 464
ACKNOWLEDGMENT 474
REFERENCES 474

Produkt-Details

• Erscheint lt. Verlag: 10.5.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Technik
• ISBN-13: 9781483258027 / 9781483258027