An invariant approach to statistical analysis of shapes: interdisciplinary statistics
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2001
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| Schriftenreihe: | Interdisciplinary statistics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 308 S. Ill., graph. Darst. |
| ISBN: | 0849303192 |
Internformat
MARC
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| 245 | 1 | 0 | |a An invariant approach to statistical analysis of shapes |b interdisciplinary statistics |c Subhash R. Lele ; Joan T. Richtsmeier |
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Datensatz im Suchindex
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| adam_text | AN INVARIANT APPROACH
TO
STATISTICAL
ANALYSIS OF SHAPES
Interdisciplinary Statistics
Subhash R Lele
Department of Mathematical Sciences
University of Alberta
Edmonton, Canada
Joan T Richtsmeier
Department of Anthropology
The Pennsylvania State University
University Park, Pennsylvania, USA
CHAPMAN amp; HALL/CRC
Boca Raton London New York Washington, D C
Contents
1 Introduction 1
11A brief history of morphometrics 3
1 2 Foundations for the study of biological forms 5
1 3 Description of the data sets 7
2 Morphometric Data 15
2 1 Types of morphometric data 15
2 2 Landmark homology and correspondence 24
2 3 Collection of landmark coordinates 27
2 4 Reliability of landmark coordinate data 36
2 5 Summary 43
Part 2: Statistical and Mathematical Preliminaries
for Landmark Coordinate Data 44
2 6 Introduction to matrix algebra 44
2 7 Matrix representation of landmark coordinate data 48
2 8 Statistical model and inference for the
measurement error study 52
3 Statistical Models for Landmark Coordinate Data 61
3 1 Statistical models 62
3 2 Models for intra-group variability 63
3 3 Effect of nuisance parameters 69
3 4 Invariance and elimination of nuisance parameters 72
35A definition of form 73
3 6 Coordinate system-free representation of form 75
3 7 The abilty to estimate the mean form and variance 76
3 8 Analysis of example data sets 78
3 9 Some comments on EDMA vs
other morphometric methods 92
3 10 Summary 96
Part 2: Statistical Theory for the Analysis of a
Single Population 97
3 11 The perturbation model 97
3 12 Invariance and elimination of nuisance parameters 98
3 13 Estimation of parameters 102
3 14 Computational algorithms 112
4 Statistical Methods for Comparison of Forms 123
4 1 Introduction 123
4 2 Limiting factors in morphometrics 124
4 3 Comparing two forms: introduction to the problem 126
4 4 Superimposition-based approaches 128
4 5 Transformational grids and deformation-based
approaches 132
4 6 The relationship between mathematical and
scientific invariance 135
4 7 An invariant approach:
Euclidean Distance Matrix Analysis (EDMA) 142
4 8 Statistical analysis of form and shape
difference using EDMA 153
4 9 Statistical hypothesis testing for shape difference 158
4 10 Methods for exploring the form difference matrix 166
4 11 A graphical tool for the detection of
influential landmarks 171
4 12 Analysis of example data sets: mouse mandibles 173
4 13 Summary 195
Part 2: Statistical Theory for the Comparison of Two Forms 197
4 14 Deformation approach to form difference 198
4 15 Superimposition methods for comparison of forms 200
4 16 Matrix transformations, invariance,
and identifiability issues 202
4 17 Form comparisons based on distances 206
4 18 Form space based on Euclidean Distance
Matrix representation 207
4 19 Statistical properties of the estimators of mean
form, mean form difference, and mean shape
difference matrices 209
4 20 Computational algorithms 210
5 The Study of Growth 215
5 1 Limiting factors in studying growth using
morphometric approaches 218
5 2 Longitudinal vs cross-sectional data 218
5 3 Assigning age and forming age-related groups 220
5 4 EDMA applied to the study of growth 222
5 5 Growth measured as relative form difference 223
5 6 Estimation of growth using EDMA 224
5 7 Statistical analysis of form and shape
difference due to growth 226
5 8 Growth difference matrix analysis: comparing
patterns of growth using growth matrices 229
5 9 Analysis of example data sets: differences
in facial growth 230
5 10 Producing hypothetical morphologies from
forms and growth patterns 239
5 11 Summary 244
6 Classification and Clustering Applications 245
6 1 Classification Analysis 246
6 2 Methods of classification 247
6 3 Dissimilarity measures for landmark
coordinate data 249
64A classification example 251
6 5 Cluster analysis ~ 255
6 6 Clustering analysis example 256
6 7 Summary 261
7 Further Applications of EDMA 263
7 1 The study of asymmetry 263
7 2 Comparisons of molecular structures 270
7 3 Detection of phylogenetic signals 279
7 4 Summary 284
Postlude 285
References 287
Index 301
|
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| language | English |
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| spelling | Lele, Subhash R. Verfasser aut An invariant approach to statistical analysis of shapes interdisciplinary statistics Subhash R. Lele ; Joan T. Richtsmeier Boca Raton [u.a.] Chapman & Hall/CRC 2001 308 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Interdisciplinary statistics series Anatomie (DE-588)4001895-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Anatomie (DE-588)4001895-7 s Statistik (DE-588)4056995-0 s DE-604 Richtsmeier, Joan T. Verfasser aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009423997&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lele, Subhash R. Richtsmeier, Joan T. An invariant approach to statistical analysis of shapes interdisciplinary statistics Anatomie (DE-588)4001895-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4001895-7 (DE-588)4056995-0 |
| title | An invariant approach to statistical analysis of shapes interdisciplinary statistics |
| title_auth | An invariant approach to statistical analysis of shapes interdisciplinary statistics |
| title_exact_search | An invariant approach to statistical analysis of shapes interdisciplinary statistics |
| title_full | An invariant approach to statistical analysis of shapes interdisciplinary statistics Subhash R. Lele ; Joan T. Richtsmeier |
| title_fullStr | An invariant approach to statistical analysis of shapes interdisciplinary statistics Subhash R. Lele ; Joan T. Richtsmeier |
| title_full_unstemmed | An invariant approach to statistical analysis of shapes interdisciplinary statistics Subhash R. Lele ; Joan T. Richtsmeier |
| title_short | An invariant approach to statistical analysis of shapes |
| title_sort | an invariant approach to statistical analysis of shapes interdisciplinary statistics |
| title_sub | interdisciplinary statistics |
| topic | Anatomie (DE-588)4001895-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Anatomie Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009423997&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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