Data analysis in high energy physics: a practical guide to statistical methods
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| Language: | English |
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Weinheim
Wiley-VCH
2013
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XX, 419 S. graph. Darst. |
| ISBN: | 9783527410583 9783527653416 |
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| 245 | 1 | 0 | |a Data analysis in high energy physics |b a practical guide to statistical methods |c ed. by Olaf Behnke ... |
| 264 | 1 | |a Weinheim |b Wiley-VCH |c 2013 | |
| 300 | |a XX, 419 S. |b graph. Darst. | ||
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| adam_text | IMAGE 1
CONTENTS
PREFACE XV
LIST O F CONTRIBUTORS X I X
1 FUNDAMENTAL CONCEPTS 1
ROGER BARLOW
1.1 INTRODUCTION 1
1.2 PROBABILITY DENSITY FUNCTIONS 2
1.2.1 EXPECTATION VALUES 2
1.2.2 MOMENTS 3
1.2.2.1 VARIANCE 3
1.2.2.2 SKEW A N D KURTOSIS 3 1.2.2.3 COVARIANCE A N D CORRELATION 4
1.2.2.4 MARGINALISATION A N D PROJECTION 4 1.2.2.5 OTHER PROPERTIES 5
1.2.3 ASSOCIATED FUNCTIONS 5
1.3 THEORETICAL DISTRIBUTIONS 5
1.3.1 THE GAUSSIAN DISTRIBUTION 6
1.3.2 T H E POISSON DISTRIBUTION 8
1.3.3 THE BINOMIAL DISTRIBUTION 9
1.3.4 OTHER DISTRIBUTIONS 10
1.3.4.1 T H E UNIFORM DISTRIBUTION 10 1.3.4.2 THE CAUCHY, OR
BREIT-WIGNER, OR LORENTZIAN DISTRIBUTION 10 1.3.4.3 T H E LANDAU
DISTRIBUTION 11 1.3.4.4 T H E NEGATIVE BINOMIAL DISTRIBUTION 12 1.3.4.5
STUDENT S T DISTRIBUTION 12 1.3.4.6 THE % 2 DISTRIBUTION 14 1.3.4.7 THE
LOG-NORMAL DISTRIBUTION 15 1.3.4.8 THE WEIBULL DISTRIBUTION 15 1.4
PROBABILITY 16
1.4.1 MATHEMATICAL DEFINITION O F PROBABILITY 17 1.4.2 CLASSICAL
DEFINITION O F PROBABILITY 17 1.4.3 FREQUENTIST DEFINITION O F
PROBABILITY 17 1.4.4 BAYESIAN DEFINITION O F PROBABILITY 18
HTTP://D-NB.INFO/103000272X
IMAGE 2
V I | CONTENTS
1.4.4.1 BAYES THEOREM 19
1.5 INFERENCE A N D MEASUREMENT 20
1.5.1 LIKELIHOOD 20
1.5.2 FREQUENTIST INFERENCE 20
1.5.3 BAYESIAN INFERENCE 21
1.5.3.1 USE O F DIFFERENT PRIORS 22
1.5.3.2 JEFFREYS PRIORS 23 1.5.3.3 THE CORRECT PRIOR? 24 1.6 EXERCISES
24
REFERENCES 25
2 PARAMETER ESTIMATION 2 7
OLAF BEHNKE AND LORENZO MONETA 2.1 PARAMETER ESTIMATION I N HIGH ENERGY
PHYSICS: INTRODUCTORY WORDS 2 7 2.2 PARAMETER ESTIMATION: DEFINITION A N
D PROPERTIES 2 7 2.3 THE METHOD O F MAXIMUM LIKELIHOOD 29
2.3.1 MAXIMUM-LIKELIHOOD SOLUTION 30 2.3.2 PROPERTIES O F THE
MAXIMUM-LIKELIHOOD ESTIMATOR 31 2.3.3 MAXIMUM LIKELIHOOD A N D BAYESIAN
STATISTICS 31 2.3.3.1 AVERAGING O F MEASUREMENTS WITH GAUSSIAN ERRORS 3
2 2.3.4 VARIANCE O F THE MAXIMUM-LIKELIHOOD ESTIMATOR 33 2.3.4.1
CONFIDENCE REGION EVALUATION WITH % 2 FUNCTION QUANTILES 37
2.3.4.2 PROFILE LIKELIHOOD 37 2.3.5 MINIMUM-VARIANCE BOUND A N D
EXPERIMENT DESIGN 38 2.4 THE METHOD O F LEAST SQUARES 40
2.4.1 LINEAR LEAST-SQUARES METHOD 42 2.4.1.1 AVERAGING O F MEASUREMENTS
WITH GAUSSIAN ERRORS 43 2.4.1.2 AVERAGING CORRELATED MEASUREMENTS 44
2.4.1.3 STRAIGHT-LINE FIT 46 2.4.2 NON-LINEAR LEAST-SQUARES FITS 48
2.4.2.1 NON-LINEAR LEAST SQUARES: MASS-PEAK FIT (SIGNAL POSITION) 50
2.5 MAXIMUM-LIKELIHOOD FITS: UNBINNED, BINNED, STANDARD A N D EXTENDED
LIKELIHOOD 52 2.5.1 UNBINNED MAXIMUM-LIKELIHOOD FITS 52 2.5.1.1 UNBINNED
MLE: FITTING FRACTIONS O F PROCESSES 54
2.5.2 EXTENDED MAXIMUM LIKELIHOOD 5 5 2.5.2.1 UNBINNED EXTENDED MLE:
FITTING RATES O F PROCESSES 56 2.5.2.2 UNBINNED EXTENDED MLE: FITTING A
SIGNAL WITH POSITION-DEPENDENT NORMALISATION 5 7
2.5.3 BINNED MAXIMUM-LIKELIHOOD FITS 59 2.5.4 LEAST-SQUARES FIT TO A
HISTOGRAM 60 2.5.4.1 BINNED MASS-PEAK FIT: PRACTICAL CONSIDERATIONS 61
2.5.5 SPECIAL TOPIC: AVERAGING DATA WITH INCONSISTENCIES 63
2.6 BAYESIAN PARAMETER ESTIMATION 6 7
2.7 EXERCISES 69
REFERENCES 72
IMAGE 3
CONTENTS | V I I
3 HYPOTHESIS TESTING 75
GREGORY SCHOTT
3.1 BASIC CONCEPTS 75
3.1.1 STATISTICAL HYPOTHESES 75
3.1.2 TEST STATISTIC 76
3.1.3 CRITICAL REGION 7 7
3.1.4 TYPE I AND TYPE II ERRORS 79
3.1.5 SUMMARY: THE TESTING PROCESS 80 3.2 CHOOSING THE TEST STATISTIC 80
3.3 CHOICE O F THE CRITICAL REGION 82
3.4 DETERMINING TEST STATISTIC DISTRIBUTIONS 82
3.5 P- VALUES 83
3.5.1 SIGNIFICANCE LEVELS 84
3.5.2 INCLUSION O F SYSTEMATIC UNCERTAINTIES 86 3.5.3 COMBINING TESTS 87
3.5.4 LOOK-ELSEWHERE EFFECT 88 3.6 INVERSION O F HYPOTHESIS TESTS 89
3.7 BAYESIAN APPROACH TO HYPOTHESIS TESTING 92 3.8 GOODNESS-OF-FIT TESTS
92
3.8.1 PEARSON S X 2 TEST 93
3.8.2 RUN TEST 96
3.8.3 X 2 TEST WITH UNBINNED MEASUREMENTS 98 3.8.4 TEST USING THE
MAXIMUM-LIKELIHOOD ESTIMATE 98 3.8.5 KOLMOGOROV-SMIRNOV TEST 99 3.8.6
SMIRNOV-CRAMER-VON MISES TEST 101 3.8.7 TWO-SAMPLE TESTS 101 3.9
CONCLUSION 102
3.10 EXERCISES 102
REFERENCES 104
4 INTERVAL ESTIMATION 107
LUC DEMORTIER
4.1 INTRODUCTION 107
4.2 CHARACTERISATION O F INTERVAL CONSTRUCTIONS 108 4.3 FREQUENTIST
METHODS 110
4.3.1 NEYMAN S CONSTRUCTION 110 4.3.1.1 INGREDIENT 1: THE ESTIMATOR 111
4.3.1.2 INGREDIENT 2: THE REFERENCE ENSEMBLE 112
4.3.1.3 INGREDIENT 3: T H E ORDERING RULE 113 4.3.1.4 INGREDIENT 4: THE
CONFIDENCE LEVEL 115 4.3.2 TEST INVERSION 116
4.3.3 PIVOTING 118
4.3.3.1 GAUSSIAN MEANS A N D STANDARD DEVIATIONS 118 4.3.3.2 EXPONENTIAL
LIFETIMES 120 4.3.3.3 BINOMIAL EFFICIENCIES 120
IMAGE 4
V I I I | CONTENTS
4.3.3.4 POISSON MEANS 122
4.3.4 ASYMPTOTIC APPROXIMATIONS 123 4.3.5 BOOTSTRAPPING 124
4.3.5.1 T H E BOOTSTRAP-T INTERVAL 125 4.3.5.2 PERCENTILE INTERVALS 127
4.3.5.3 BOOTSTRAP CALIBRATION 128 4.3.6 NUISANCE PARAMETERS 128
4.4 BAYESIAN METHODS 133
4.4.1 BINOMIAL EFFICIENCIES 137 4.4.2 POISSON MEANS 138
4.5 GRAPHICAL COMPARISON O F INTERVAL CONSTRUCTIONS 140 4.6 T H E ROLE O
F INTERVALS I N SEARCH PROCEDURES 142
4.6.1 COVERAGE 143
4.6.2 SENSITIVITY 144
4.7 FINAL REMARKS A N D RECOMMENDATIONS 146
4.8 EXERCISES 146
REFERENCES 150
5 CLASSIFICATION 153
HELGE VOSS
5.1 INTRODUCTION TO MULTIVARIATE CLASSIFICATION 153 5.2 CLASSIFICATION
FROM A STATISTICAL PERSPECTIVE 155 5.2.1
RECEIVER-OPERATING-CHARACTERISTIC CURVE A N D THE NEYMAN-PEARSON LEMMA
157 5.2.1.1 NEYMAN-PEARSON LEMMA 158 5.2.2 SUPERVISED MACHINE LEARNING
159 5.2.3 BIAS-VARIANCE TRADE-OFF 159 5.2.4 CROSS-VALIDATION 161 5.3
MULTIVARIATE CLASSIFICATION TECHNIQUES 162
5.3.1 LIKELIHOOD (NAIVE BAYES CLASSIFIER) 162 5.3.2 FC-NEAREST NEIGHBOUR
A N D MULTI-DIMENSIONAL LIKELIHOOD 163 5.3.3 FISHER LINEAR DISCRIMINANT
165 5.3.4 ARTIFICIAL NEURAL NETWORKS - FEED-FORWARD MULTI-LAYER
PERCEPTIONS 168 5.3.5 SUPPORT VECTOR MACHINES 172 5.3.6 (BOOSTED)
DECISION TREES 178
5.3.7 BOOSTING A N D BAGGING 179
5.3.7.1 BOOSTING 179
5.3.7.2 ADAPTIVE BOOST (ADABOOST) 180 5.3.7.3 BAGGING 181
5.4 GENERAL REMARKS 182
5.4.1 PRE-PROCESSING 182
5.5 DEALING WITH SYSTEMATIC UNCERTAINTIES 183 5.6 EXERCISES 184
REFERENCES 186
IMAGE 5
CONTENTS | I X
6 UNFOLDING 187
VOLKER BLOHEL
6.1 INVERSE PROBLEMS 187
6.1.1 DIRECT A N D INVERSE PROCESSES 187
6.1.2 DISCRETISATION A N D LINEAR SOLUTION 289 6.1.3 UNFOLDING
POISSON-DISTRIBUTED DATA 192 6.1.4 CONVOLUTION A N D DECONVOLUTION 193
6.1.5 PARAMETRISED UNFOLDING 195 6.2 SOLUTION WITH ORTHOGONALISATION 196
6.2.1 SINGULAR VALUE A N D EIGENVALUE DECOMPOSITION 196 6.2.2 UNFOLDING
USING THE LEAST SQUARES METHOD 199 6.2.2.1 LEAST-SQUARES METHOD USING
THE SVD 199 6.2.2.2 NULL SPACE A N D TRUNCATED SVD 199 6.2.2.3
TRUNCATION A N D POSITIVE CORRELATIONS 202 6.2.3 FOLDING VERSUS
UNFOLDING 202 6.3 REGULARISATION METHODS 203
6.3.1 NORM A N D DERIVATIVE REGULARISATION 203 6.3.1.1 REGULARISATION
203 6.3.1.2 NORM REGULARISATION 204 6.3.1.3 REGULARISATION BASED O N
DERIVATIVES 206 6.3.1.4 DETERMINATION/SELECTION O F THE REGULARISATION
PARAMETER 207 6.4 THE DISCRETE COSINE TRANSFORMATION A N D PROJECTION
METHODS 209 6.4.1 DISCRETE COSINE TRANSFORMATION 210 6.4.2 PROJECTION
METHODS 211
6.4.3 LOW-PASS REGULARISATION 212 6.5 ITERATIVE UNFOLDING 213
6.6 UNFOLDING PROBLEMS I N PARTICLE PHYSICS 215
6.6.1 PARTICLE PHYSICS EXPERIMENTS 215 6.6.2 UNFOLDING SMOOTH
DISTRIBUTIONS 218 6.6.3 UNFOLDING NON-SMOOTH DISTRIBUTIONS 219 6.6.4
PRESENTATION O F REGULARISATION RESULTS 220 6.7 PROGRAMS USED FOR
UNFOLDING I N HIGH ENERGY PHYSICS 221 6.8 EXERCISE 223
REFERENCES 223
7 CONSTRAINED FITS 227
BENNO LIST
7.1 INTRODUCTION 227
7.2 SOLUTION BY ELIMINATION 230
7.2.1 STATISTICAL INTERPRETATION 231 7.3 THE METHOD O F LAGRANGE
MULTIPLIERS 232
7.3.1 LAGRANGE MULTIPLIERS 233 7.3.2 UNMEASURED PARAMETERS 236
7.4 THE LAGRANGE MULTIPLIER PROBLEM WITH LINEAR CONSTRAINTS AND
QUADRATIC OBJECTIVE FUNCTION 237
IMAGE 6
X | CONTENTS
7.4.1 ERROR PROPAGATION 239
7.4.2 ERROR PROPAGATION IN THE PRESENCE O F UNMEASURED QUANTITIES 241
7.5 ITERATIVE SOLUTION O F THE LAGRANGE MULTIPLIER PROBLEM 244 7.5.1
CHOOSING A DIRECTION 245
7.5.1.1 COPING WITH A RANK-DEFICIENT MATRIX M 248 7.5.1.2 NORMALISATION
O F PARAMETERS A N D CONSTRAINT FUNCTIONS 249 7.5.2 CONTROLLING THE STEP
LENGTH 250
7.5.2.1 MERIT FUNCTION 251 7.5.2.2 LINE SEARCHES 252 7.5.2.3 STOPPING
CONDITIONS 253 7.5.2.4 PRACTICAL CHOICE O F THE STEP LENGTH 254
7.5.2.5 T H E MARATOS EFFECT 255 7.5.3 DETECTING CONVERGENCE 256 7.5.3.1
STOPPING THE ITERATIONS 257 7.5.3.2 VERIFYING CONVERGENCE 258 7.5.4
FINDING INITIAL VALUES 258
7.5.5 ERROR CALCULATION 259
7.6 FURTHER READING A N D WEB RESOURCES 259
7.7 EXERCISES 260
REFERENCES 261
8 HOW TO DEAL WITH SYSTEMATIC UNCERTAINTIES 263
RAINER WANKE
8.1 INTRODUCTION 263
8.2 WHAT ARE SYSTEMATIC UNCERTAINTIES? 264
8.3 DETECTION O F POSSIBLE SYSTEMATIC UNCERTAINTIES 265 8.3.1 TOP-DOWN
APPROACH 265 8.3.2 BOTTOM-UP APPROACH 266
8.3.3 EXAMPLES FOR DETECTING SYSTEMATICS 267 8.3.3.1 BACKGROUND
SYSTEMATICS 267 8.3.3.2 DETECTOR ACCEPTANCES 268 8.3.3.3 SPLITTING DATA
INTO INDEPENDENT SUBSETS 269
8.3.3.4 EVALUATING T H E RESULT I N INTERVALS O F A N ANALYSIS PARAMETER
270 8.3.3.5 ANALYSIS SOFTWARE A N D FIT ROUTINES 271 8.4 ESTIMATION O F
SYSTEMATIC UNCERTAINTIES 272
8.4.1 SOME SIMPLE CASES 273
8.4.1.1 EXTERNAL INPUT PARAMETERS 273 8.4.1.2 TOLERANCES 273 8.4.1.3
SMALL SYSTEMATICS 273 8.4.2 EDUCATED GUESSES 273
8.4.2.1 BACKGROUND ESTIMATION 274 8.4.2.2 DETECTOR RESOLUTIONS 275
8.4.2.3 THEORY UNCERTAINTIES 276 8.4.2.4 DISCREPANCIES BETWEEN DATA A N
D SIMULATION 277
8.4.2.5 ANALYSES WITH SMALL STATISTICS 278
IMAGE 7
CONTENTS I X I
8.4.3 CUT VARIATIONS 279
8.4.3.1 CUT VARIATIONS IN MULTI-DIMENSIONAL ANALYSES 283 8.4.4
COMBINATION O F SYSTEMATIC UNCERTAINTIES 285 8.4.4.1 COMBINATION O F
COVARIANCE MATRICES 287 8.5 HOW TO AVOID SYSTEMATIC UNCERTAINTIES 288
8.5.1 CHOICE O F SELECTION CRITERIA 288 8.5.2 AVOIDING BIASES 289
8.5.2.1 DO N O T EXPECT A CERTAIN RESULT 289 8.5.2.2 DO N O T LOOK AT
SIGNAL EVENTS 291 8.5.3 BLIND ANALYSES 292
8.6 CONCLUSION 293
8.7 EXERCISE 295
REFERENCES 296
9 THEORY UNCERTAINTIES 297
MARKUS DIEHL
9.1 OVERVIEW 297
9.2 FACTORISATION: A CORNERSTONE O F CALCULATIONS I N QCD 298 9.2.1 THE
PERTURBATIVE EXPANSION A N D UNCERTAINTIES FROM HIGHER ORDERS 301
9.2.1.1 THE RENORMALISATION SCALE 301 9.2.1.2 THE FACTORISATION SCALE
305 9.2.1.3 COMBINING DIFFERENT ORDERS 307 9.2.1.4 MULTI-SCALE PROBLEMS
A N D RESUMMATION METHODS 307 9.3 POWER CORRECTIONS 308
9.3.1 OPERATOR PRODUCT EXPANSION 308 9.3.2 POWER CORRECTIONS I N CROSS
SECTIONS 309 9.4 THE FINAL STATE 310
9.4.1 UNDERLYING EVENT A N D MULTI-PARTON INTERACTIONS 310 9.4.2 FROM
PARTONS TO HADRONS 311
9.4.3 MONTE CARLO EVENT GENERATORS 313 9.5 FROM HADRONS TO PARTONS 314
9.5.1 PARAMETRIC PDF UNCERTAINTIES 318 9.5.1.1 THE HESSIAN MATRIX 319
9.5.1.2 LAGRANGE MULTIPLIERS 321 9.5.1.3 THE NNPDF APPROACH 321 9.5.2 A
COMPARISON O F RECENT PDF SETS 322
9.6 EXERCISES 324
REFERENCES 326
10 STATISTICAL METHODS COMMONLY USED IN HIGH ENERGY PHYSICS 329 CARSTEN
HENSEL AND KEVIN KRONINGER 10.1 INTRODUCTION 329
10.2 ESTIMATING EFFICIENCIES 329
10.2.1 MOTIVATION 330
10.2.2 TRIGGER EFFICIENCIES A N D THEIR ESTIMATES 330 10.2.3 THE
COUNTING METHOD 331
IMAGE 8
X I I | CONTENTS
10.2.4 THE TAG-AND-PROBE METHOD 332
10.2.5 THE BOOTSTRAP METHOD 332 10.2.6 CALCULATING UNCERTAINTIES O N
TRIGGER EFFICIENCIES 333 10.3 ESTIMATING THE CONTRIBUTIONS O F PROCESSES
TO A DATASET: THE MATRIX METHOD 334
10.3.1 ESTIMATING THE BACKGROUND CONTRIBUTIONS TO A DATA SAMPLE 334
10.3.2 EXTENSION TO DISTRIBUTIONS 336 10.3.3 LIMITATIONS O F THE MATRIX
METHOD 337 10.4 ESTIMATING PARAMETERS BY COMPARING SHAPES O F
DISTRIBUTIONS:
T H E TEMPLATE METHOD 337 10.4.1 TEMPLATE SHAPES 340
10.4.2 INCLUDING PRIOR KNOWLEDGE 340 10.4.3 INCLUDING EFFICIENCIES 341
10.4.4 INCLUDING SYSTEMATIC UNCERTAINTIES 341 10.4.5 SYSTEMATIC
UNCERTAINTIES DUE TO THE FITTING PROCEDURE 343
10.4.6 ALTERNATIVE FITTING METHODS A N D CHOICE O F PARAMETERS 344
10.4.7 EXTENSION TO MULTIPLE CHANNELS A N D MULTI-DIMENSIONAL TEMPLATES
344 10.5 ENSEMBLE TESTS 345
10.5.1 GENERATION O F ENSEMBLES 346 10.5.2 RESULTS O F ENSEMBLE TESTS
347 10.6 T H E EXPERIMENTER S ROLE A N D DATA BLINDING 351 10.6.1 THE
EXPERIMENTER S PRECONCEPTION 352
10.6.2 VARIANTS O F BLIND ANALYSES 352 10.7 EXERCISES 354
REFERENCES 356
11 ANALYSIS WALK-THROUGHS 357
AART HEIJBOER AND IVO VAN VULPEN 11.1 INTRODUCTION 357
11.2 SEARCH FOR A Z BOSON DECAYING INTO MUONS 357
11.2.1 COUNTING EXPERIMENT 358 11.2.1.1 QUANTIFYING THE SENSITIVITY:
P-VALUES A N D SIGNIFICANCE 358 11.2.1.2 OPTIMISING THE MASS WINDOW 360
11.2.1.3 ESTIMATING T H E BACKGROUND FROM DATA USING SIDEBANDS 360
11.2.1.4 SCANNING OVER T H E FULL D I M U O N MASS RANGE: T H E
LOOK-ELSEWHERE
EFFECT 361
11.2.2 PROFILE LIKELIHOOD RATIO ANALYSIS 362 11.2.2.1 PROFILE LIKELIHOOD
TEST STATISTIC 362 11.2.2.2 PROPERTIES O F THE TEST STATISTIC
DISTRIBUTIONS FOR THE FE-ONLY A N D S + B HYPOTHESES 363
11.2.2.3 RULES FOR DISCOVERY A N D EXCLUSION 364 11.2.2.4 RESULTS FROM
DATA 366 11.2.2.5 PROBING THE SENSITIVITY LIMITS: ENHANCED LUMINOSITY A
N D SIGNAL CROSS SECTIONS 366
11.2.2.6 SCANNING THE FULL MASS REGION 367
IMAGE 9
CONTENTS | X I I I
11.3 MEASUREMENT 369
11.3.1 INTRODUCTION 369
11.3.2 UNBINNED LIKELIHOOD 370 11.3.2.1 LIKELIHOOD INGREDIENTS 371
11.3.3 EXTRACTING A MEASUREMENT IN THE PRESENCE O F NUISANCE PARAMETERS
372 11.3.4 MASS MEASUREMENT 373
11.3.5 TESTING FOR BIAS A N D COVERAGE 373 11.3.6 SYSTEMATIC
UNCERTAINTIES 374 11.3.7 CONSTRAINTS A N D COMBINING MEASUREMENTS 375
11.4 EXERCISES 377
REFERENCES 379
12 APPLICATIONS IN ASTRONOMY 381
HARRISON B. PROSPER 12.1 INTRODUCTION 381
12.2 A SURVEY O F APPLICATIONS 382
12.2.1 THE O N / O F F PROBLEM 383 12.2.1.1 A BAYESIAN APPROACH 385
12.2.1.2 CONCLUSION 390 12.2.2 IMAGE RECONSTRUCTION 390
12.2.2.1 O F MONKEYS A N D KANGAROOS 391 12.2.2.2 MAXIMUM ENTROPY METHOD
I N PRACTICE 393 12.2.3 FITTING COSMOLOGICAL PARAMETERS 394 12.2.3.1
COSMOLOGY I N A NUTSHELL 394 12.2.3.2 STATISTICAL ANALYSIS O F
SUPERNOVAE DATA 397 12.2.3.3 MODEL COMPLEXITY 399 12.3 NESTED SAMPLING
401
12.4 OUTLOOK A N D CONCLUSIONS 404
12.5 EXERCISES 405
REFERENCES 405
THE AUTHORS 409
INDEX 413
|
| any_adam_object | 1 |
| author_GND | (DE-588)115780521 |
| building | Verbundindex |
| bvnumber | BV040899208 |
| classification_rvk | SK 950 UN 7300 UO 1000 |
| ctrlnum | (OCoLC)854333673 (DE-599)BVBBV040899208 |
| dewey-full | 539.760151953 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 539 - Modern physics |
| dewey-raw | 539.760151953 |
| dewey-search | 539.760151953 |
| dewey-sort | 3539.760151953 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV040899208 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:34:54Z |
| institution | BVB |
| isbn | 9783527410583 9783527653416 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025878718 |
| oclc_num | 854333673 |
| open_access_boolean | |
| owner | DE-11 DE-20 DE-703 DE-29T DE-19 DE-BY-UBM |
| owner_facet | DE-11 DE-20 DE-703 DE-29T DE-19 DE-BY-UBM |
| physical | XX, 419 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Wiley-VCH |
| record_format | marc |
| spelling | Data analysis in high energy physics a practical guide to statistical methods ed. by Olaf Behnke ... Weinheim Wiley-VCH 2013 XX, 419 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Hochenergiephysik (DE-588)4127286-9 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Hochenergiephysik (DE-588)4127286-9 s Datenanalyse (DE-588)4123037-1 s DE-604 Behnke, Olaf 1964- Sonstige (DE-588)115780521 oth Erscheint auch als Online-Ausgabe, EPUB 978-3-527-65343-0 Erscheint auch als Online-Ausgabe, MOBI 978-3-527-65342-3 Erscheint auch als Online-Ausgabe, PDF 978-3-527-65344-7 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025878718&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Data analysis in high energy physics a practical guide to statistical methods Hochenergiephysik (DE-588)4127286-9 gnd Datenanalyse (DE-588)4123037-1 gnd |
| subject_GND | (DE-588)4127286-9 (DE-588)4123037-1 |
| title | Data analysis in high energy physics a practical guide to statistical methods |
| title_auth | Data analysis in high energy physics a practical guide to statistical methods |
| title_exact_search | Data analysis in high energy physics a practical guide to statistical methods |
| title_full | Data analysis in high energy physics a practical guide to statistical methods ed. by Olaf Behnke ... |
| title_fullStr | Data analysis in high energy physics a practical guide to statistical methods ed. by Olaf Behnke ... |
| title_full_unstemmed | Data analysis in high energy physics a practical guide to statistical methods ed. by Olaf Behnke ... |
| title_short | Data analysis in high energy physics |
| title_sort | data analysis in high energy physics a practical guide to statistical methods |
| title_sub | a practical guide to statistical methods |
| topic | Hochenergiephysik (DE-588)4127286-9 gnd Datenanalyse (DE-588)4123037-1 gnd |
| topic_facet | Hochenergiephysik Datenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025878718&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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