Uncertainty analysis with high dimensional dependence modelling:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Wiley
2006
|
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Inhaltsverzeichnis |
| Beschreibung: | VIII, 284 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9780470863060 0470863064 |
Internformat
MARC
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| 020 | |a 9780470863060 |9 978-0-470-86306-0 | ||
| 020 | |a 0470863064 |c alk. paper |9 0-470-86306-4 | ||
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| 100 | 1 | |a Kurowicka, Dorota |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Uncertainty analysis with high dimensional dependence modelling |c Dorota Kurowicka and Roger Cooke |
| 264 | 1 | |a Chichester |b Wiley |c 2006 | |
| 300 | |a VIII, 284 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and statistics | |
| 650 | 4 | |a Incertitude (Théorie de l'information) - Mathématiques | |
| 650 | 7 | |a Onzekerheid |2 gtt | |
| 650 | 7 | |a Wiskundige modellen |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Uncertainty (Information theory) |x Mathematics | |
| 650 | 0 | 7 | |a Assoziationsmaß |0 (DE-588)4208029-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Multivariate Analyse |0 (DE-588)4040708-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Entscheidung bei Unsicherheit |0 (DE-588)4070864-0 |2 gnd |9 rswk-swf |
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| 689 | 0 | 2 | |a Assoziationsmaß |0 (DE-588)4208029-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Cooke, Roger |e Verfasser |4 aut | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0643/2005057712-d.html |3 Publisher description | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-016316237 | |
Datensatz im Suchindex
| _version_ | 1826189493455028224 |
|---|---|
| adam_text |
Contents
Preface
ix
1
Introduction
1
1.1
Wags
and Bogsats
. 1
1.2
Uncertainty analysis and decision support: a recent example
. 4
1.3
Outline of the book
. 9
2
Assessing Uncertainty on Model Input
13
2.1
Introduction
. 13
2.2
Structured expert judgment in outline
. 14
2.3
Assessing distributions of continuous univariate uncertain quantities
15
2.4
Assessing dependencies
. 16
2.5
Unicorn
. 20
2.6
Unicorn projects
. 20
3
Bivariate Dependence
25
3.1
Introduction
. 25
3.2
Measures of dependence
. 26
3.2.1
Product moment correlation
. 26
3.2.2
Rank correlation
. 30
3.2.3
Kendall's
tau. 32
3.3
Partial, conditional and multiple correlations
. 32
3.4
Copulae
. 34
3.4.1
Fréchet
copula
. 36
3.4.2
Diagonal band copula
. 37
3.4.3
Generalized diagonal band copula
. 41
3.4.4
Elliptical copula
. 42
3.4.5
Archimedean copulae
. 45
3.4.6
Minimum information copula
. 47
3.4.7
Comparison of copulae
. 49
3.5
Bivariate normal distribution
. 50
3.5.1
Basic properties
. 50
3.6
Multivariate extensions
. 51
3.6.1
Multivariate dependence measures
. 51
vi
CONTENTS
3.6.2
Multivariate
copulae. 53
3.6.3
Multivariate
normal
distribution.
53
3.7
Conclusions
. 54
3.8
Unicorn
projects
. 55
3.9
Exercises
. 61
3.10
Supplement
. 67
4
High-dimensional Dependence Modelling
81
4.1
Introduction
. 81
4.2
Joint normal transform
. 82
4.3
Dependence trees
. 86
4.3.1
Trees
. 86
4.3.2
Dependence trees with copulae
. 86
4.3.3
Example: Investment
. 90
4.4
Dependence vines
. 92
4.4.1
Vines
. 92
4.4.2
Bivariate- and copula-vine specifications
. 96
4.4.3
Example: Investment continued
. 98
4.4.4
Partial correlation vines
. 99
4.4.5
Normal vines
. 101
4.4.6
Relationship between conditional rank and partial correla¬
tions on a regular vine
. 101
4.5
Vines and positive definiteness
. 105
4.5.1
Checking positive definiteness
. 105
4.5.2
Repairing violations of positive definiteness
. 107
4.5.3
The completion problem
. 109
4.6
Conclusions
.
Ill
4.7
Unicorn projects
.
Ill
4.8
Exercises
. 115
4.9
Supplement
. 116
4.9.1
Proofs
. 116
4.9.2
Results for Section
4.4.6. 127
4.9.3
Example of fourvariate correlation matrices
. 129
4.9.4
Results for Section
4.5.2. 130
5
Other Graphical Models
131
5.1
Introduction
. 131
5.2
Bayesian belief nets
. 131
5.2.1
Discrete bbn's
. 132
5.2.2
Continuous bbn's
. 133
5.3
Independence graphs
. 141
5.4
Model inference
. 142
5.4.1
Inference for bbn's
. 143
5.4.2
Inference for independence graphs
. 144
5.4.3
Inference for vines
. 145
CONTENTS
vii
5.5
Conclusions
. 150
5.6
Unicom
projects .
150
5.7
Supplement
. 157
6
Sampling Methods
159
6.1
Introduction
. 159
6.2
(Pseudo-)
random sampling
. 160
6.3
Reduced variance sampling
. 161
6.3.1
Quasi-random sampling
. 161
6.3.2
Stratified sampling
. 164
6.3.3
Latin hypercube sampling
. 166
6.4
Sampling trees, vines and continuous bbn's
. 168
6.4.1
Sampling a tree
. 168
6.4.2
Sampling a regular vine
. 169
6.4.3
Density approach to sampling regular vine
. 174
6.4.4
Sampling a continuous bbn
. 174
6.5
Conclusions
. 180
6.6
Unicorn projects
. 180
6.7
Exercise
. 184
7
Visualization
185
7.1
Introduction
. 185
7.2
A simple problem
. 186
7.3
Tornado graphs
. 186
7.4
Radar graphs
. 187
7.5
Scatter plots, matrix and overlay scatter plots
. 188
7.6
Cobweb plots
. 191
7.7
Cobweb plots local sensitivity: dike ring reliability
. 195
7.8
Radar plots for importance; internal dosimetry
. 199
7.9
Conclusions
. 201
7.10
Unicorn projects
. 201
7.11
Exercises
. 203
8
Probabilistic Sensitivity Measures
205
8.1
Introduction
. 205
8.2
Screening techniques
. 205
8.2.1
Morris' method
. 205
8.2.2
Design of experiments
. 208
8.3
Global sensitivity measures
. 214
8.3.1
Correlation ratio
. 215
8.3.2
Sobol
indices
. 219
8.4
Local sensitivity measures
. 222
8.4.1
First order reliability method
. 222
8.4.2
Local probabilistic sensitivity measure
. 223
8.4.3
Computing iEf^o)
. 225
viii
CONTENTS
8.5
Conclusions
. 227
8.6
Unicorn
projects
. 228
8.7
Exercises
. 230
8.8
Supplement
. 236
8.8.1
Proofs
. 236
9
Probabilistic Inversion
239
9.1
Introduction
. 239
9.2
Existing algorithms for probabilistic inversion
. 240
9.2.1
Conditional sampling
. 240
9.2.2
PARFUM
. 242
9.2.3
Hora-
Young and PREJUDICE algorithms
. 243
9.3
Iterative algorithms
. 243
9.3.1
Iterative proportional fitting
. 244
9.3.2
Iterative
PARFUM
. 245
9.4
Sample re-weighting
. 246
9.4.1
Notation
. 246
9.4.2
Optimization approaches
. 247
9.4.3
IPF and
PARFUM
for sample re-weighting probabilistic
inversion
. 248
9.5
Applications
. 249
9.5.1
Dispersion coefficients
. 249
9.5.2
Chicken processing line
. 252
9.6
Convolution constraints with prescribed margins
. 253
9.7
Conclusions
. 255
9.8
Unicorn projects
. 256
9.9
Supplement
. 258
9.9.1
Proofs
. 258
9.9.2
IPF and
PARFUM
. 263
10
Uncertainty and the UN Compensation Commission
269
10.1
Introduction
. 269
10.2
Claims based on uncertainty
. 270
10.3
Who pays for uncertainty
. 272
Bibliography
273
Index
281 |
| adam_txt |
Contents
Preface
ix
1
Introduction
1
1.1
Wags
and Bogsats
. 1
1.2
Uncertainty analysis and decision support: a recent example
. 4
1.3
Outline of the book
. 9
2
Assessing Uncertainty on Model Input
13
2.1
Introduction
. 13
2.2
Structured expert judgment in outline
. 14
2.3
Assessing distributions of continuous univariate uncertain quantities
15
2.4
Assessing dependencies
. 16
2.5
Unicorn
. 20
2.6
Unicorn projects
. 20
3
Bivariate Dependence
25
3.1
Introduction
. 25
3.2
Measures of dependence
. 26
3.2.1
Product moment correlation
. 26
3.2.2
Rank correlation
. 30
3.2.3
Kendall's
tau. 32
3.3
Partial, conditional and multiple correlations
. 32
3.4
Copulae
. 34
3.4.1
Fréchet
copula
. 36
3.4.2
Diagonal band copula
. 37
3.4.3
Generalized diagonal band copula
. 41
3.4.4
Elliptical copula
. 42
3.4.5
Archimedean copulae
. 45
3.4.6
Minimum information copula
. 47
3.4.7
Comparison of copulae
. 49
3.5
Bivariate normal distribution
. 50
3.5.1
Basic properties
. 50
3.6
Multivariate extensions
. 51
3.6.1
Multivariate dependence measures
. 51
vi
CONTENTS
3.6.2
Multivariate
copulae. 53
3.6.3
Multivariate
normal
distribution.
53
3.7
Conclusions
. 54
3.8
Unicorn
projects
. 55
3.9
Exercises
. 61
3.10
Supplement
. 67
4
High-dimensional Dependence Modelling
81
4.1
Introduction
. 81
4.2
Joint normal transform
. 82
4.3
Dependence trees
. 86
4.3.1
Trees
. 86
4.3.2
Dependence trees with copulae
. 86
4.3.3
Example: Investment
. 90
4.4
Dependence vines
. 92
4.4.1
Vines
. 92
4.4.2
Bivariate- and copula-vine specifications
. 96
4.4.3
Example: Investment continued
. 98
4.4.4
Partial correlation vines
. 99
4.4.5
Normal vines
. 101
4.4.6
Relationship between conditional rank and partial correla¬
tions on a regular vine
. 101
4.5
Vines and positive definiteness
. 105
4.5.1
Checking positive definiteness
. 105
4.5.2
Repairing violations of positive definiteness
. 107
4.5.3
The completion problem
. 109
4.6
Conclusions
.
Ill
4.7
Unicorn projects
.
Ill
4.8
Exercises
. 115
4.9
Supplement
. 116
4.9.1
Proofs
. 116
4.9.2
Results for Section
4.4.6. 127
4.9.3
Example of fourvariate correlation matrices
. 129
4.9.4
Results for Section
4.5.2. 130
5
Other Graphical Models
131
5.1
Introduction
. 131
5.2
Bayesian belief nets
. 131
5.2.1
Discrete bbn's
. 132
5.2.2
Continuous bbn's
. 133
5.3
Independence graphs
. 141
5.4
Model inference
. 142
5.4.1
Inference for bbn's
. 143
5.4.2
Inference for independence graphs
. 144
5.4.3
Inference for vines
. 145
CONTENTS
vii
5.5
Conclusions
. 150
5.6
Unicom
projects .
150
5.7
Supplement
. 157
6
Sampling Methods
159
6.1
Introduction
. 159
6.2
(Pseudo-)
random sampling
. 160
6.3
Reduced variance sampling
. 161
6.3.1
Quasi-random sampling
. 161
6.3.2
Stratified sampling
. 164
6.3.3
Latin hypercube sampling
. 166
6.4
Sampling trees, vines and continuous bbn's
. 168
6.4.1
Sampling a tree
. 168
6.4.2
Sampling a regular vine
. 169
6.4.3
Density approach to sampling regular vine
. 174
6.4.4
Sampling a continuous bbn
. 174
6.5
Conclusions
. 180
6.6
Unicorn projects
. 180
6.7
Exercise
. 184
7
Visualization
185
7.1
Introduction
. 185
7.2
A simple problem
. 186
7.3
Tornado graphs
. 186
7.4
Radar graphs
. 187
7.5
Scatter plots, matrix and overlay scatter plots
. 188
7.6
Cobweb plots
. 191
7.7
Cobweb plots local sensitivity: dike ring reliability
. 195
7.8
Radar plots for importance; internal dosimetry
. 199
7.9
Conclusions
. 201
7.10
Unicorn projects
. 201
7.11
Exercises
. 203
8
Probabilistic Sensitivity Measures
205
8.1
Introduction
. 205
8.2
Screening techniques
. 205
8.2.1
Morris' method
. 205
8.2.2
Design of experiments
. 208
8.3
Global sensitivity measures
. 214
8.3.1
Correlation ratio
. 215
8.3.2
Sobol
indices
. 219
8.4
Local sensitivity measures
. 222
8.4.1
First order reliability method
. 222
8.4.2
Local probabilistic sensitivity measure
. 223
8.4.3
Computing iEf^o)
. 225
viii
CONTENTS
8.5
Conclusions
. 227
8.6
Unicorn
projects
. 228
8.7
Exercises
. 230
8.8
Supplement
. 236
8.8.1
Proofs
. 236
9
Probabilistic Inversion
239
9.1
Introduction
. 239
9.2
Existing algorithms for probabilistic inversion
. 240
9.2.1
Conditional sampling
. 240
9.2.2
PARFUM
. 242
9.2.3
Hora-
Young and PREJUDICE algorithms
. 243
9.3
Iterative algorithms
. 243
9.3.1
Iterative proportional fitting
. 244
9.3.2
Iterative
PARFUM
. 245
9.4
Sample re-weighting
. 246
9.4.1
Notation
. 246
9.4.2
Optimization approaches
. 247
9.4.3
IPF and
PARFUM
for sample re-weighting probabilistic
inversion
. 248
9.5
Applications
. 249
9.5.1
Dispersion coefficients
. 249
9.5.2
Chicken processing line
. 252
9.6
Convolution constraints with prescribed margins
. 253
9.7
Conclusions
. 255
9.8
Unicorn projects
. 256
9.9
Supplement
. 258
9.9.1
Proofs
. 258
9.9.2
IPF and
PARFUM
. 263
10
Uncertainty and the UN Compensation Commission
269
10.1
Introduction
. 269
10.2
Claims based on uncertainty
. 270
10.3
Who pays for uncertainty
. 272
Bibliography
273
Index
281 |
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| id | DE-604.BV023113683 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:49:13Z |
| indexdate | 2025-03-10T07:00:16Z |
| institution | BVB |
| isbn | 9780470863060 0470863064 |
| language | English |
| lccn | 2005057712 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016316237 |
| oclc_num | 62342240 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-11 DE-355 DE-BY-UBR |
| owner_facet | DE-91G DE-BY-TUM DE-11 DE-355 DE-BY-UBR |
| physical | VIII, 284 S. Ill., graph. Darst. 24 cm |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Kurowicka, Dorota Verfasser aut Uncertainty analysis with high dimensional dependence modelling Dorota Kurowicka and Roger Cooke Chichester Wiley 2006 VIII, 284 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Incertitude (Théorie de l'information) - Mathématiques Onzekerheid gtt Wiskundige modellen gtt Mathematik Uncertainty (Information theory) Mathematics Assoziationsmaß (DE-588)4208029-0 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd rswk-swf Entscheidung bei Unsicherheit (DE-588)4070864-0 s Multivariate Analyse (DE-588)4040708-1 s Assoziationsmaß (DE-588)4208029-0 s DE-604 Cooke, Roger Verfasser aut http://www.loc.gov/catdir/enhancements/fy0643/2005057712-d.html Publisher description Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016316237&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kurowicka, Dorota Cooke, Roger Uncertainty analysis with high dimensional dependence modelling Incertitude (Théorie de l'information) - Mathématiques Onzekerheid gtt Wiskundige modellen gtt Mathematik Uncertainty (Information theory) Mathematics Assoziationsmaß (DE-588)4208029-0 gnd Multivariate Analyse (DE-588)4040708-1 gnd Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd |
| subject_GND | (DE-588)4208029-0 (DE-588)4040708-1 (DE-588)4070864-0 |
| title | Uncertainty analysis with high dimensional dependence modelling |
| title_auth | Uncertainty analysis with high dimensional dependence modelling |
| title_exact_search | Uncertainty analysis with high dimensional dependence modelling |
| title_exact_search_txtP | Uncertainty analysis with high dimensional dependence modelling |
| title_full | Uncertainty analysis with high dimensional dependence modelling Dorota Kurowicka and Roger Cooke |
| title_fullStr | Uncertainty analysis with high dimensional dependence modelling Dorota Kurowicka and Roger Cooke |
| title_full_unstemmed | Uncertainty analysis with high dimensional dependence modelling Dorota Kurowicka and Roger Cooke |
| title_short | Uncertainty analysis with high dimensional dependence modelling |
| title_sort | uncertainty analysis with high dimensional dependence modelling |
| topic | Incertitude (Théorie de l'information) - Mathématiques Onzekerheid gtt Wiskundige modellen gtt Mathematik Uncertainty (Information theory) Mathematics Assoziationsmaß (DE-588)4208029-0 gnd Multivariate Analyse (DE-588)4040708-1 gnd Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd |
| topic_facet | Incertitude (Théorie de l'information) - Mathématiques Onzekerheid Wiskundige modellen Mathematik Uncertainty (Information theory) Mathematics Assoziationsmaß Multivariate Analyse Entscheidung bei Unsicherheit |
| url | http://www.loc.gov/catdir/enhancements/fy0643/2005057712-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016316237&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kurowickadorota uncertaintyanalysiswithhighdimensionaldependencemodelling AT cookeroger uncertaintyanalysiswithhighdimensionaldependencemodelling |