Statistical methods in bioinformatics: an introduction
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2002
|
| Ausgabe: | Corr. 3. print. |
| Schriftenreihe: | Statictics for biology and health
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 449 - 461 |
| Beschreibung: | XIX, 476 S. graph. Darst. |
| ISBN: | 0387952292 |
Internformat
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Datensatz im Suchindex
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| adam_text | WARREN J. EWENS GREGORY R. GRANT STATISTICAL METHODS IN BIOINFORMATICS:
AN INTRODUCTION WITH 30 ILLUSTRATIONS SPRINGER 2008
AGI-INFORMATION MANAGEMENT CONSULTANTS MAY BE USED FOR PERSONAL
PURPORSES ONLY OR BY LIBRARIES ASSOCIATED TO DANDELON.COM NETWORK.
CONTENTS PREFACE VI1 PROBABILITY THEORY (I): ONE RANDOM VARIABLE 1 1.1
INTRODUCTION 1 1.2 DISCRETE RANDOM VARIABLES, DEFINITIONS 3 1.2.1
PROBABILITY DISTRIBUTIONS AND PARAMETERS 3 1.2.2 INDEPENDENCE 6 1.3 SIX
IMPORTANT DISCRETE PROBABILITY DISTRIBUTIONS 7 1.3.1 ONE BERNOULLI TRIAL
7 1.3.2 THE BINOMIAL DISTRIBUTION 7 1.3.3 THE UNIFORM DISTRIBUTION 9
1.3.4 THE GEOMETRIC DISTRIBUTION 10 1.3.5 THE NEGATIVE BINOMIAL AND THE
GENERALIZED GEOMETRIC DISTRIBUTIONS 12 1.3.6 THE POISSON DISTRIBUTION 13
1.4 THE MEAN OF A DISCRETE RANDOM VARIABLE 13 1.5 THE VARIANCE OF A
DISCRETE RANDOM VARIABLE 16 1.6 GENERAL MOMENTS OF A PROBABILITY
DISTRIBUTION 18 1.7 THE PROBABILITY-GENERATING FUNCTION 19 1.8
CONTINUOUS RANDOM VARIABLES 21 1.9 THE MEAN, VARIANCE, AND MEDIAN OF A
CONTINUOUS RANDOM VARIABLE 22 1.9.1 DEFINITIONS 22 1.9.2 CHEBYSHEV S
INEQUALITY 23 XII CONTENTS 1.10 FIVE IMPORTANT CONTINUOUS DISTRIBUTIONS
24 1.10.1 THE UNIFORM DISTRIBUTION 24 1.10.2 THE NORMAL DISTRIBUTION 24
1.10.3 THE NORMAL APPROXIMATION TO A DISCRETE DISTRIBUTION 27 1.10.4 THE
EXPONENTIAL DISTRIBUTION 28 1.10.5 THE GAMMA DISTRIBUTION 31 1.10.6 THE
BETA DISTRIBUTION 32 1.11 THE MOMENT-GENERATING FUNCTION 32 1.12 EVENTS
36 1.12.1 WHAT ARE EVENTS? 36 1.12.2 COMPLEMENTS, UNIONS, AND
INTERSECTIONS 36 1.12.3 PROBABILITIES OF EVENTS 37 1.12.4 CONDITIONAL
PROBABILITIES 39 1.12.5 INDEPENDENCE OF EVENTS 41 1.13 THE MEMORYLESS
PROPERTY OF THE GEOMETRIC AND THE EXPONENTIAL DISTRIBUTIONS 42 1.14
ENTROPY AND RELATED CONCEPTS 43 1.14.1 ENTROPY 43 1.14.2 RELATIVE
ENTROPY 44 1.14.3 SCORES AND SUPPORT 45 1.15 TRANSFORMATIONS 46 1.16
EMPIRICAL METHODS 47 PROBABILITY THEORY (II): MANY RANDOM VARIABLES 55
2.1 MANY DISCRETE RANDOM VARIABLES 55 2.1.1 THE INDEPENDENT CASE 56
2.1.2 THE DEPENDENT CASE AND THE MULTINOMIAL DISTRIBUTION 57 2.1.3
PROPERTIES OF RANDOM VARIABLES FROM PGFS 57 2.2 MANY CONTINUOUS RANDOM
VARIABLES 59 2.2.1 THE INDEPENDENT CASE 59 2.2.2 THE DEPENDENT CASE 60
2.3 MOMENT-GENERATING FUNCTIONS 60 2.4 INDICATOR RANDOM VARIABLES 62
2.4.1 DEFINITIONS 62 2.4.2 EXAMPLE: SEQUENCING EST LIBRARIES 63 2.5
MARGINAL DISTRIBUTIONS 66 2.6 CONDITIONAL DISTRIBUTIONS 68 2.7 EXPECTED
VALUES 71 2.8 COVARIANCE AND CORRELATION 73 2.9 ASYMPTOTIC DISTRIBUTIONS
75 2.10 DERIVED RANDOM VARIABLES (I): SUMS, AVERAGES, AND MINIMA 75
2.10.1 SUMS AND AVERAGES 76 2.10.2 THE MINIMUM OF N RANDOM VARIABLES 79
2.11 DERIVED RANDOM VARIABLES (II): THE MAXIMUM OF N RANDOM VARIABLES 81
CONTENTS XIII 2.11.1 DISTRIBUTIONAL PROPERTIES: CONTINUOUS RANDOM
VARIABLES 81 2.11.2 DISTRIBUTIONAL PROPERTIES: DISCRETE RANDOM VARIABLES
84 2.11.3 AN ASYMPTOTIC FORMULA FOR THE DISTRIBUTION OF X MAX 87 2.11.4
BOUNDS FOR THE DISTRIBUTIONS OF THE MAXIMA OF GEOMETRIC AND
GEOMETRIC-LIKE RANDOM VARIABLES . 89 2.12 INTRODUCTION TO P- VALUES FOR
Y MAX 91 2.12.1 INTRODUCTION 91 2.12.2 P- VALUES FOR GEOMETRIC-LIKE
RANDOM VARIABLES . . 91 2.12.3 P-VALUES FOR THE GENERALIZED GEOMETRIC
DISTRIBUTION 92 2.13 LARGE OBSERVATIONS AND RARE EVENTS 94 2.14 ORDER
STATISTICS 94 2.14.1 DEFINITION 94 2.14.2 EXAMPLE: THE UNIFORM
DISTRIBUTION 96 2.14.3 THE SAMPLE MEDIAN 97 2.15 TRANSFORMATIONS 97
2.15.1 THEORY 97 2.15.2 EXAMPLE: THE UNIFORM DISTRIBUTION (CONTINUED) .
. 98 STATISTICS (I): AN INTRODUCTION TO STATISTICAL INFERENCE 105 3.1
INTRODUCTION 105 3.2 CLASSICAL AND BAYESIAN METHODS 105 3.3 CLASSICAL
ESTIMATION METHODS 107 3.3.1 UNBIASED ESTIMATION 107 3.3.2 BIASED
ESTIMATORS 109 3.4 CLASSICAL HYPOTHESIS TESTING 110 3.4.1 GENERAL
PRINCIPLES 110 3.4.2 F-VALUES 113 3.4.3 HYPOTHESIS TESTING EXAMPLES 113
3.4.4 LIKELIHOOD RATIOS, INFORMATION, AND SUPPORT . . . . 117 3.4.5
HYPOTHESIS TESTING USING X MAX AS TEST STATISTIC . . 118 3.5
NONPARAMETRIC ALTERNATIVES TO THE TWO-SAMPLE T-TEST . . . 119 3.6 THE
BAYESIAN APPROACH TO HYPOTHESIS TESTING 122 3.7 THE BAYESIAN APPROACH TO
ESTIMATION 124 3.8 MULTIPLE TESTING 125 STOCHASTIC PROCESSES (I):
POISSON PROCESSES AND MARKOV CHAINS 129 4.1 THE HOMOGENEOUS POISSON
PROCESS AND THE POISSON DISTRIBUTION 129 4.2 THE POISSON AND THE
BINOMIAL DISTRIBUTIONS 132 4.3 THE POISSON AND THE GAMMA DISTRIBUTIONS
133 4.4 INTRODUCTION TO FINITE MARKOV CHAINS 133 4.5 TRANSITION
PROBABILITIES AND THE TRANSITION PROBABILITY MATRIX 135 4.6 MARKOV
CHAINS WITH ABSORBING STATES 137 XIV CONTENTS 4.7 MARKOV CHAINS WITH NO
ABSORBING STATES 137 4.7.1 STATIONARY DISTRIBUTIONS 138 4.7.2 EXAMPLE
139 4.8 THE GRAPHICAL REPRESENTATION OF A MARKOV CHAIN 140 4.9 MODELING
141 THE ANALYSIS OF ONE DNA SEQUENCE 147 5.1 SHOTGUN SEQUENCING 147 5.2
MODELING DNA 155 5.3 MODELING SIGNALS IN DNA 156 5.3.1 INTRODUCTION 156
5.3.2 WEIGHT MATRICES: INDEPENDENCE 157 5.3.3 MARKOV DEPENDENCIES 158
5.3.4 MAXIMAL DEPENDENCE DECOMPOSITION 158 5.4 LONG REPEATS 160 5.5
R-SCANS 162 5.6 THE ANALYSIS OF PATTERNS 165 5.7 OVERLAPS COUNTED 166
5.7.1 GENERAL COMMENTS 166 5.7.2 NUMBER OF OCCURRENCES 166 5.7.3
DISTANCE BETWEEN OCCURRENCES 169 5.8 OVERLAPS NOT COUNTED 173 5.8.1
GENERAL COMMENTS 173 5.8.2 DISTANCE BETWEEN RECURRENCES 173 5.8.3 NUMBER
OF RECURRENCES 174 5.9 GENERALIZATIONS 175 5.9.1 ARBITRARY NUCLEOTIDE
PROBABILITIES 175 5.9.2 ARBITRARY WORD LENGTH 176 THE ANALYSIS OF
MULTIPLE DNA OR PROTEIN SEQUENCES 181 6.1 TWO SEQUENCES: FREQUENCY
COMPARISONS 181 6.2 ALIGNMENTS 183 6.3 SIMPLE TESTS FOR SIGNIFICANT
SIMILARITY IN AN ALIGNMENT . . . 184 6.4 ALIGNMENT ALGORITHMS FOR TWO
SEQUENCES 189 6.4.1 INTRODUCTION 189 6.4.2 GAPPED GLOBAL COMPARISONS AND
DYNAMIC PROGRAMMING ALGORITHMS 191 6.4.3 FITTING ONE SEQUENCE INTO
ANOTHER USING A LINEAR GAP MODEL 194 6.4.4 LOCAL ALIGNMENTS WITH A
LINEAR GAP MODEL 195 6.4.5 OTHER GAP MODELS 196 6.4.6 LIMITATIONS OF THE
DYNAMIC PROGRAMMING ALIGNMENT ALGORITHMS 198 6.5 PROTEIN SEQUENCES AND
SUBSTITUTION MATRICES 199 6.5.1 INTRODUCTION 199 CONTENTS XV 6.5.2
BLOSUM SUBSTITUTION MATRICES 200 6.5.3 PAM SUBSTITUTION MATRICES 205
6.5.4 A SIMPLE SYMMETRIC PAM MATRIX 210 6.6 MULTIPLE SEQUENCES 211
STOCHASTIC PROCESSES (II): RANDOM WALKS 219 7.1 INTRODUCTION 219 7.2 THE
SIMPLE RANDOM WALK 221 7.2.1 INTRODUCTION 221 7.3 THE DIFFERENCE
EQUATION APPROACH 222 7.3.1 ABSORPTION PROBABILITIES 222 7.3.2 MEAN
NUMBER OF STEPS TAKEN UNTIL THE WALK STOPS 223 7.4 THE MOMENT-GENERATING
FUNCTION APPROACH 224 7.4.1 ABSORPTION PROBABILITIES 224 7.4.2 MEAN
NUMBER OF STEPS UNTIL THE WALK STOPS .... 226 7.4.3 AN ASYMPTOTIC CASE
227 7.5 GENERAL WALKS 228 7.6 GENERAL WALKS: ASYMPTOTIC THEORY 230 7.6.1
INTRODUCTION 230 7.6.2 THE RENEWAL THEOREM 231 7.6.3 UNRESTRICTED WALKS
231 7.6.4 RESTRICTED WALKS 234 STATISTICS (II): CLASSICAL ESTIMATION AND
HYPOTHESIS TESTING 237 8.1 INTRODUCTION 237 8.2 CLASSICAL ESTIMATION
THEORY 237 8.2.1 CRITERIA FOR GOOD ESTIMATORS 237 8.2.2 MAXIMUM
LIKELIHOOD ESTIMATION 239 8.3 CLASSICAL HYPOTHESIS TESTING: SIMPLE FIXED
SAMPLE SIZE TESTS 246 8.3.1 THE LIKELIHOOD RATIO 246 8.4 CLASSICAL
HYPOTHESIS TESTING: COMPOSITE FIXED SAMPLE SIZE TESTS 249 8.4.1
INTRODUCTION 249 8.4.2 THE -2 LOG A APPROXIMATION 254 8.5 SEQUENTIAL
ANALYSIS 258 8.5.1 THE SEQUENTIAL PROBABILITY RATIO TEST 258 8.5.2 THE
POWER CURVE FOR A SEQUENTIAL TEST 261 8.5.3 THE MEAN SAMPLE SIZE 262
8.5.4 THE EFFECT OF BOUNDARY OVERLAP 264 BLAST 269 9.1 INTRODUCTION 269
9.2 THE COMPARISON OF TWO ALIGNED SEQUENCES 270 9.2.1 INTRODUCTION 270
XVI CONTENTS 9.2.2 LADDER POINTS AND EXCURSIONS 270 9.2.3 PARAMETER
CALCULATIONS 271 9.2.4 THE CHOICE OF A SCORE 273 9.2.5 BOUNDS FOR THE P-
VALUE 275 9.2.6 THE NORMALIZED AND THE BIT SCORES 276 9.2.7 THE NUMBER
OF HIGH-SCORING EXCURSIONS 278 9.2.8 THE KARLIN-ALTSCHUL SUM STATISTIC
279 9.3 THE COMPARISON OF TWO UNALIGNED SEQUENCES 281 9.3.1 INTRODUCTION
281 9.3.2 THEORETICAL AND EMPIRICAL BACKGROUND 281 9.3.3 EDGE EFFECTS
283 9.3.4 MULTIPLE TESTING 285 9.4 THE COMPARISON OF A QUERY SEQUENCE
AGAINST A DATABASE . 286 9.5 PRINTOUTS 288 9.5.1 EXAMPLE 288 9.5.2 A
MORE COMPLICATED EXAMPLE 291 9.6 MINIMUM SIGNIFICANCE LENGTHS 294 9.6.1
A CORRECT CHOICE OF N 294 9.6.2 AN INCORRECT CHOICE OF N 296 9.7 BLAST:
A PARAMETRIC OR A NONPARAMETRIC TEST? 298 9.8 RELATION TO SEQUENTIAL
ANALYSIS 298 9.9 FURTHER DEVELOPMENTS OF BLAST AND FURTHER THEORY ...
300 10 STOCHASTIC PROCESSES (III): MARKOV CHAINS 303 10.1 INTRODUCTION
303 10.2 MARKOV CHAINS WITH NO ABSORBING STATES 304 10.2.1 INTRODUCTION
304 10.2.2 CONVERGENCE TO THE STATIONARY DISTRIBUTION 304 10.2.3
STATIONARY DISTRIBUTIONS: A NUMERICAL EXAMPLE . . . 305 10.2.4
REVERSIBILITY AND DETAILED BALANCE 306 10.3 HIGHER-ORDER MARKOV
DEPENDENCE 308 10.3.1 TESTING FOR HIGHER-ORDER MARKOV DEPENDENCE . . . .
308 10.3.2 TESTING FOR A UNIFORM STATIONARY DISTRIBUTION . . . . 308
10.4 PATTERNS IN SEQUENCES WITH FIRST-ORDER MARKOV DEPENDENCE 309 10.5
MARKOV CHAIN MONTE CARLO 310 10.5.1 THE HASTINGS-METROPOLIS ALGORITHM
311 10.5.2 GIBBS SAMPLING 311 10.5.3 SIMULATED ANNEALING 314 10.6 MARKOV
CHAINS WITH ABSORBING STATES 317 10.6.1 THEORY 317 10.6.2 EXAMPLES 318
10.7 CONTINUOUS-TIME MARKOV CHAINS 321 10.7.1 DEFINITIONS 321 10.7.2
TIME-DEPENDENT SOLUTIONS 322 10.7.3 THE STATIONARY DISTRIBUTION 323
CONTENTS XVII 10.7.4 DETAILED BALANCE 323 10.7.5 EXPONENTIAL HOLDING
TIMES 323 10.7.6 THE EMBEDDED CHAIN 324 11 HIDDEN MARKOV MODELS 327 11.1
WHAT IS A HIDDEN MARKOV MODEL? 327 11.2 THREE ALGORITHMS 329 11.2.1 THE
FORWARD AND BACKWARD ALGORITHMS 329 11.2.2 THE VITERBI ALGORITHM 331
11.2.3 THE ESTIMATION ALGORITHMS 332 11.3 APPLICATIONS 335 11.3.1
MODELING PROTEIN FAMILIES 335 11.3.2 MULTIPLE SEQUENCE ALIGNMENTS 337
11.3.3 PFAM 339 11.3.4 GENE FINDING 340 12 COMPUTATIONALLY INTENSIVE
METHODS 349 12.1 INTRODUCTION 349 12.2 ESTIMATION 350 12.2.1 CLASSICAL
ESTIMATION METHODS 350 12.2.2 BOOTSTRAP ESTIMATION AND CONFIDENCE
INTERVALS . . . 351 12.3 HYPOTHESIS TESTING: THE BOOTSTRAP ALTERNATIVE
TO THE TWO-SAMPLE T-TEST 354 12.4 MULTIPLE TESTING REVISITED 356 12.4.1
INTRODUCTION 356 12.4.2 STEP-DOWN METHODS: I-TESTS 356 12.4.3 STEP-DOWN
METHODS: A PERMUTATION TEST 359 12.4.4 STEP-DOWN METHODS APPLIED TO
EXPRESSION ARRAYS . 360 13 EVOLUTIONARY MODELS 365 13.1 MODELS OF
NUCLEOTIDE SUBSTITUTION 365 13.2 DISCRETE-TIME MODELS 366 13.2.1 THE
JUKES-CANTOR MODEL 366 13.2.2 THE KIMURA MODELS 368 13.2.3 FURTHER
GENERALIZATIONS OF THE KIMURA MODELS . . . 369 13.2.4 THE FELSENSTEIN
MODEL 370 13.2.5 THE HKY MODEL 371 13.2.6 OTHER MODELS 372 13.2.7 THE
REVERSIBILITY CRITERION 372 13.2.8 THE SIMPLE SYMMETRIC PAM MODEL 373
13.3 CONTINUOUS-TIME MODELS 374 13.3.1 THE CONTINUOUS-TIME JUKES-CANTOR
MODEL 374 13.3.2 THE CONTINUOUS-TIME KIMURA MODEL 378 13.3.3 THE
CONTINUOUS-TIME FELSENSTEIN MODEL 381 13.3.4 THE CONTINUOUS-TIME HKY
MODEL 382 XVIII CONTENTS 13.3.5 THE CONTINUOUS-TIME PAM MODEL 382 14
PHYLOGENETIC TREE ESTIMATION 385 14.1 INTRODUCTION 385 14.2 DISTANCES
387 14.3 TREE RECONSTRUCTION: THE ULTRAMETRIC CASE 388 14.4 TREE
RECONSTRUCTION: NEIGHBOR-JOINING 393 14.5 SURROGATE DISTANCES 397 14.6
TREE RECONSTRUCTION: PARSIMONY 398 14.7 TREE RECONSTRUCTION: MAXIMUM
LIKELIHOOD 400 14.8 EXAMPLE 404 14.9 MODELING, ESTIMATION, AND
HYPOTHESIS TESTING 408 14.9.1 ESTIMATION AND HYPOTHESIS TESTING 408
14.9.2 BOOTSTRAPPING 410 14.9.3 AN EXAMPLE 411 14.9.4 ASSUMPTIONS AND
PROBLEMS 415 14.9.5 PHYLOGENETIC MODELS AND HYPOTHESIS TESTING . . . .
416 A BASIC NOTIONS IN BIOLOGY 423 B MATHEMATICAL FORMULAE AND RESULTS
427 B.I NUMBERS AND INTERVALS 427 B.2 SETS AND SET NOTATION 428 B.3
FACTORIALS 428 B.4 BINOMIAL COEFFICIENTS 429 B.5 THE BINOMIAL THEOREM
429 B.6 PERMUTATIONS AND COMBINATIONS 429 B.7 LIMITS 430 B.8 ASYMPTOTICS
431 B.9 STIRLING S APPROXIMATION 433 B.10 ENTROPY AS INFORMATION 433
B.LL INFINITE SERIES 434 B.12 TAYLOR SERIES 436 B. 13 UNIQUENESS OF
TAYLOR SERIES 439 B.14 LAURENT SERIES 440 B.I5 NUMERICAL SOLUTIONS OF
EQUATIONS 440 B.16 STATISTICAL DIFFERENTIALS 441 B.17 THE GAMMA FUNCTION
441 B.18 PROOFS BY INDUCTION 443 B.19 LINEAR ALGEBRA AND MATRICES 443 C
COMPUTATIONAL ASPECTS OF THE BINOMIAL AND GENERALIZED GEOMETRIC
DISTRIBUTION FUNCTIONS 445 D BLAST: SUMS OF NORMALIZED SCORES 447
REFERENCES AUTHOR INDEX INDEX CONTENTS XIX 449 463 466
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:03:53Z |
| institution | BVB |
| isbn | 0387952292 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009913782 |
| oclc_num | 48946337 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-29 |
| owner_facet | DE-19 DE-BY-UBM DE-29 |
| physical | XIX, 476 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Statictics for biology and health |
| spelling | Ewens, Warren J. Verfasser aut Statistical methods in bioinformatics an introduction Warren J. Ewens ; Gregory R. Grant Corr. 3. print. New York [u.a.] Springer 2002 XIX, 476 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statictics for biology and health Literaturverz. S. 449 - 461 Statistik Bioinformatics Statistics Statistik (DE-588)4056995-0 gnd rswk-swf Bioinformatik (DE-588)4611085-9 gnd rswk-swf Bioinformatik (DE-588)4611085-9 s Statistik (DE-588)4056995-0 s DE-604 Grant, Gregory R. Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009913782&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ewens, Warren J. Grant, Gregory R. Statistical methods in bioinformatics an introduction Statistik Bioinformatics Statistics Statistik (DE-588)4056995-0 gnd Bioinformatik (DE-588)4611085-9 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4611085-9 |
| title | Statistical methods in bioinformatics an introduction |
| title_auth | Statistical methods in bioinformatics an introduction |
| title_exact_search | Statistical methods in bioinformatics an introduction |
| title_full | Statistical methods in bioinformatics an introduction Warren J. Ewens ; Gregory R. Grant |
| title_fullStr | Statistical methods in bioinformatics an introduction Warren J. Ewens ; Gregory R. Grant |
| title_full_unstemmed | Statistical methods in bioinformatics an introduction Warren J. Ewens ; Gregory R. Grant |
| title_short | Statistical methods in bioinformatics |
| title_sort | statistical methods in bioinformatics an introduction |
| title_sub | an introduction |
| topic | Statistik Bioinformatics Statistics Statistik (DE-588)4056995-0 gnd Bioinformatik (DE-588)4611085-9 gnd |
| topic_facet | Statistik Bioinformatics Statistics Bioinformatik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009913782&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ewenswarrenj statisticalmethodsinbioinformaticsanintroduction AT grantgregoryr statisticalmethodsinbioinformaticsanintroduction |