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 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 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 | 0 | |a Entscheidung bei Unsicherheit |0 (DE-588)4070864-0 |D s |
| 689 | 0 | 1 | |a Multivariate Analyse |0 (DE-588)4040708-1 |D s |
| 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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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016316237 | ||
Datensatz im Suchindex
| _version_ | 1804137378090057728 |
|---|---|
| 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 | 2024-07-09T21:11:20Z |
| 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 DE-M347 |
| owner_facet | DE-91G DE-BY-TUM DE-11 DE-355 DE-BY-UBR DE-M347 |
| 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 Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd rswk-swf Assoziationsmaß (DE-588)4208029-0 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 Multivariate Analyse (DE-588)4040708-1 gnd Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd Assoziationsmaß (DE-588)4208029-0 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4070864-0 (DE-588)4208029-0 |
| 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 Multivariate Analyse (DE-588)4040708-1 gnd Entscheidung bei Unsicherheit (DE-588)4070864-0 gnd Assoziationsmaß (DE-588)4208029-0 gnd |
| topic_facet | Incertitude (Théorie de l'information) - Mathématiques Onzekerheid Wiskundige modellen Mathematik Uncertainty (Information theory) Mathematics Multivariate Analyse Entscheidung bei Unsicherheit Assoziationsmaß |
| 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 |