Regularized estimation and model selection in compartment models:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
München
Verl. Dr. Hut
2013
|
| Edition: | 1. Aufl. |
| Series: | Statistik
|
| Subjects: | |
| Online Access: | Inhaltstext https://nbn-resolving.org/urn:nbn:de:bvb:19-157673 Volltext Inhaltsverzeichnis |
| Physical Description: | XVI, 142 S. Ill., graph. Darst. 210 mm x 148 mm, 272 g |
| ISBN: | 9783843910385 3843910383 |
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| 245 | 1 | 0 | |a Regularized estimation and model selection in compartment models |c Julia C. Sommer |
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Record in the Search Index
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IMAGE 1
CONTENTS
LIST O F ABBREVIATIONS X V
1 INTRODUCTION 1
2 COMPARTMENT MODELS 5
2.1 APPLICATIONS 5
2.2 COMPARTMENT MODELS: ASSUMPTIONS AND MODEL EQUATIONS 6
2.3 ON INFERENCE AND PARAMETER IDENTIFIABILITY IN COMPARTMENT MODELS 11
3 INTRODUCTION T O THE ANALYSIS O F DCE-MRI 19
3.1 DCE-MRI: PHYSICAL AND PHYSIOLOGICAL BACKGROUND 19
3.2 COMPARTMENT MODELS FOR DCE-MRI 23
3.2.1 ONE TISSUE COMPARTMENT MODEL (ICOMP): TOFTS AND EXTENDED TOFTS
MODEL 23
3.2.2 TWO TISSUE AND MULTI TISSUE COMPARTMENT MODEL (2COMP AND QCOMP) 27
3.3 DCE-MRI DATA FROM A BREAST CANCER STUDY 32
4 BAYESIAN INDEPENDENT ESTIMATION PER VOXEL 35
4.1 METHODS 36
4.1.1 BAYESIAN ICOMP MODEL VOXEL WISE 36
4.1.2 BAYESIAN 2COMP MODEL VOXELWISE 37
4.1.3 IMPLEMENTATION 37
4.1.4 MEASURE OF MODEL FIT AND COMPLEXITY 38
4.1.5 REDUNDANCY ISSUES IN THE INDEPENDENT VOXELWISE MODEL 40
4.1.6 SIMULATION AND DATA 41
4.2 RESULTS 41
4.2.1 SIMULATION RESULTS 41
4.2.2 DCE-MRI BREAST CANCER STUDY 45
4.3 CONCLUSIONS 50
5 BAYESIAN SPATIAL REGULARIZATION 5 1
5.1 METHODS 52
5.1.1 BAYESIAN 2COMP MODEL VOXELWISE 52
HTTP://D-NB.INFO/1036471101
IMAGE 2
C O N T E N T S
5.1.2 SPATIAL BAYESIAN 2COMP MODEL 53
5.1.3 IMPLEMENTATION 54
5.1.4 MEASURE OF MODEL COMPLEXITY 55
5.2 SIMULATION STUDY 55
5.2.1 SIMULATION SETUP 55
5.2.2 RESULTS 56
5.3 DCE-MRI BREAST CANCER STUDY 62
5.4 CONCLUSION AND DISCUSSION 66
6 SPATIALLY PENALIZED ML-ESTIMATION AND MODEL SELECTION 6 9
6.1 INTRODUCTION 69
6.2 METHODS 71
6.2.1 MULTI TISSUE COMPARTMENT MODEL 71
6.2.2 VOXELWISE REGULARIZED ESTIMATION 71
6.2.3 SPATIALLY REGULARIZED ESTIMATION 73
6.3 SIMULATION STUDY 75
6.3.1 SIMULATION SETUP 75
6.3.2 RESULTS 75
6.4 DCE-MRI BREAST CANCER STUDY 80
6.5 CONCLUSION AND DISCUSSION 84
7 BAYESIAN MODEL SELECTION WITH REVERSIBLE J U M P M C M C 8 5
7.1 INTRODUCTION 85
7.2 METHODS 87
7.2.1 COMPARTMENT MODEL 87
7.2.2 BAYESIAN NONLINEAR REGRESSION MODEL 87
7.2.3 REGULARIZING PRIOR ON EXPONENTIAL RATES 88
7.2.4 RJMCMC ON NUMBER OF COMPARTMENTS 89
7.2.5 SAMPLING 91
7.3 SIMULATION STUDY 92
7.3.1 SIMULATION RESULTS USING A UNIFORM PRIOR ON THE EXPONENTIAL RATES
. . 93 7.3.2 SIMULATION RESULTS USING A REGULARIZING PRIOR ON THE
EXPONENTIAL RATES 96 7.4 APPLICATION: ANALYSIS OF MOLECULAR BINDING IN A
FRAP EXPERIMENT 98 7.4.1 BIOLOGICAL BACKGROUND, EXPERIMENTAL SETUP AND
MOTIVATION 98
7.4.2 RESULTS 100
7.4.3 SENSITIVITY ANALYSIS 100
7.5 CONCLUSION AND DISCUSSION 107
8 SUMMARY AND DISCUSSION 109
A CALCULATING REDUNDANCY IN SUMS O F (CONVOLVED) EXPONENTIALS 115
A.L CONVOLVED EXPONENTIALS 115
A. 1.1 BI-EXPONENTIAL INPUT FUNCTION 115
IMAGE 3
C O N T E N T S XIII
A.1.2 CONSTANT INPUT FUNCTION 116
A.2 REDUNDANCY MEASURE IN SUM OF EXPONENTIALS 116
A.3 REDUNDANCY MEASURE IN SUM OF CONVOLVED EXPONENTIALS 119
A.3.1 CALCULATION OF INTEGRALS 121
B DETAILS IN REVERSIBLE JUMP M C M C BIRTH AND DEATH TRANSFORMATIONS 129
B.L DETERMINANTS OF JACOBIAN MATRICES FOR BIRTH AND DEATH
TRANSFORMATIONS . . 129 B.2 DERIVATION OF BIRTH AND DEATH TRANSFORMATION
130
BIBLIOGRAPHY 133 |
| any_adam_object | 1 |
| author | Sommer, Julia C. |
| author_facet | Sommer, Julia C. |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.544 |
| dewey-search | 519.544 |
| dewey-sort | 3519.544 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. Aufl. |
| format | Thesis Book |
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| spelling | Sommer, Julia C. Verfasser aut Regularized estimation and model selection in compartment models Julia C. Sommer 1. Aufl. München Verl. Dr. Hut 2013 XVI, 142 S. Ill., graph. Darst. 210 mm x 148 mm, 272 g txt rdacontent n rdamedia nc rdacarrier Statistik Zugl.: München, Univ., Diss., 2013 Parameterschätzung (DE-588)4044614-1 gnd rswk-swf Kompartimentmodell (DE-588)4588313-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kompartimentmodell (DE-588)4588313-0 s Parameterschätzung (DE-588)4044614-1 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:19-157673 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4371980&prov=M&dok_var=1&dok_ext=htm Verlag kostenfrei Inhaltstext https://nbn-resolving.org/urn:nbn:de:bvb:19-157673 Resolving-System http://edoc.ub.uni-muenchen.de/15767/ Verlag kostenfrei Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026117666&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sommer, Julia C. Regularized estimation and model selection in compartment models Parameterschätzung (DE-588)4044614-1 gnd Kompartimentmodell (DE-588)4588313-0 gnd |
| subject_GND | (DE-588)4044614-1 (DE-588)4588313-0 (DE-588)4113937-9 |
| title | Regularized estimation and model selection in compartment models |
| title_auth | Regularized estimation and model selection in compartment models |
| title_exact_search | Regularized estimation and model selection in compartment models |
| title_full | Regularized estimation and model selection in compartment models Julia C. Sommer |
| title_fullStr | Regularized estimation and model selection in compartment models Julia C. Sommer |
| title_full_unstemmed | Regularized estimation and model selection in compartment models Julia C. Sommer |
| title_short | Regularized estimation and model selection in compartment models |
| title_sort | regularized estimation and model selection in compartment models |
| topic | Parameterschätzung (DE-588)4044614-1 gnd Kompartimentmodell (DE-588)4588313-0 gnd |
| topic_facet | Parameterschätzung Kompartimentmodell Hochschulschrift |
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