Bayesian networks and influence diagrams: a guide to construction and analysis
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2008
|
| Series: | Information Science and Statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 318 S. Ill., graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387741017 9780387741000 0387741003 |
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MARC
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| 020 | |a 9780387741000 |c Gb. : ca. EUR 65.91 (freier Pr.), ca. sfr 101.00 (freier Pr.) |9 978-0-387-74100-0 | ||
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| 100 | 1 | |a Kjaerulff, Uffe |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Bayesian networks and influence diagrams |b a guide to construction and analysis |c Uffe B. Kjaerulff ; Anders L. Madsen |
| 264 | 1 | |a New York, NY |b Springer |c 2008 | |
| 300 | |a XVII, 318 S. |b Ill., graph. Darst. |c 235 mm x 155 mm | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Information Science and Statistics | |
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Expert systems (Computer science) | |
| 650 | 4 | |a Uncertainty (Information theory) | |
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Record in the Search Index
| _version_ | 1804137709325778944 |
|---|---|
| adam_text | Contents
Part I Fundamentals
Introduction
............................................... 3
1.1
Expert Systems
......................................... 3
1.1.1
Representation of Uncertainty
....................... 4
1.1.2
Normative Expert Systems
......................... 5
1.2
Rule-Based Systems
..................................... 5
1.2.1
Causality
......................................... 6
1.2.2
Uncertainty in Rule-Based Systems
.................. 7
1.2.3
Explaining Away
.................................. 7
1.3
Bayesian Networks
...................................... 8
1.3.1
Inference in Bayesian Networks
...................... 9
1.3.2
Construction of Bayesian Networks
.................. 10
1.3.3
An Example
...................................... 10
1.4
Bayesian Decision Problems
.............................. 13
1.5
When to Use Probabilistic Nets
........................... 14
1.6
Concluding Remarks
..................................... 15
Networks
.................................................. 17
2.1
Graphs
................................................. 18
2.2
Graphical Models
........................................ 20
2.2.1
Variables
......................................... 20
2.2.2
Vertices vs. Variables
.............................. 21
2.2.3
Taxonomy of Vertices/Variables
..................... 22
2.2.4
Vertex Symbols
................................... 23
2.2.5
Summary of Notation
.............................. 23
2.3
Evidence
............................................... 23
2.4
Causality
............................................... 24
2.5
Flow of Information in Causal Networks
.................... 25
2.5.1
Serial Connections
................................. 26
2.5.2
Diverging Connections
............................. 28
2.5.3
Converging Connections
............................ 29
2.5.4
The Importance of Correct Modeling of Causality
..... 30
2.6
Two Equivalent Irrelevance Criteria
........................ 31
2.
G.I d-Separation Criterion
............................. 32
2.6.2
Directed Global Markov Criterion
................... 33
2.7
Summary
............................................... 35
Probabilities
............................................... 37
3.1
Basics
.................................................. 38
3.1.1
Events
........................................... 38
3.1.2
Conditional Probability
............................ 38
3.1.3
Axioms
.......................................... 39
3.2
Probability Distributions for Variables
..................... 40
3.2.1
Rule of Total Probability
........................... 41
3.2.2
Graphical Representation
........................... 43
3.3
Probability Potentials
.................................... 44
3.3.1
Normalization
..................................... 44
3.3.2
Evidence Potentials
................................ 45
3.3.3
Potential Calculus
................................. 46
3.3.4
Barren Variables
.................................. 49
3.4
Fundamental Rule and
Bayes
Rule
........................ 50
3.4.1
Interpretation of
Bayes
Rule
....................... 51
3.5
Bayes
Factor
........................................... 53
3.6
Independence
........................................... 54
3.6.1
Independence and DAGs
........................... 56
3.7
Chain Rule
............................................. 58
3.8
Summary
............................................... 60
Probabilistic Networks
..................................... 63
4.1
Reasoning Under Uncertainty
............................. 64
4.1.1
Discrete Bayesian Networks
......................... 65
4.1.2
Conditional Linear Gaussian Bayesian Networks
....... 70
4.2
Decision Making Under Uncertainty
....................... 74
4.2.1
Discrete Influence Diagrams
........................ 75
4.2.2
Conditional LQG Influence Diagrams
................ 85
4.2.3
Limited Memory Influence Diagrams
................. 89
4.3
Object-Oriented Probabilistic Networks
.................... 91
4.3.1
Chain Rule
....................................... 96
4.3.2
Unfolded OOPNs
.................................. 96
4.3.3
Instance Trees
.................................... 97
4.3.4
Inheritance
....................................... 98
4.4
Dynamic Models
........................................ 98
4.5
Summary
............................................... 102
Solving Probabilistic Networks
............................107
5.1
Probabilistic Inference
...................................108
5.1.1
Inference in Discrete Bayesian Networks
..............108
5.1.2
Inference in CLG Bayesian Networks
.................121
5.2
Solving Decision Models
..................................124
5.2.1
Solving Discrete Influence Diagrams
.................124
5.2.2
Solving CLQG Influence Diagrams
...................129
5.2.3
Relevance Reasoning
...............................130
5.2.4
Solving LIMIDs
...................................133
5.3
Solving OOPNs
.........................................136
5.4
Siimmarv
...............................................137
Part II Model Construction
6
Eliciting the Model
........................................143
6.1
When to Use Probabilistic Networks
.......................144
6.1.1
Characteristics of Probabilistic Networks
.............145
6.1.2
Some Criteria for Using Probabilistic Networks
........145
6.2
Identifying the Variables of a Model
.......................147
6.2.1
Well-Defined Variables
.............................147
6.2.2
Types of Variables
.................................150
6.3
Eliciting the Structure
...................................152
6.3.1
A Basic Approach
.................................152
6.3.2
Idioms
...........................................154
6.4
Model Verification
.......................................159
6.5
Eliciting the Numbers
....................................163
6.5.1
Eliciting Subjective Conditional Probabilities
.........163
6.5.2
Eliciting Subjective Utilities
........................166
6.5.3
Specifying CPTs and UTs Through Expressions
.......166
6.6
Concluding Remarks
.....................................170
6.7
Summary
...............................................172
7
Modeling Techniques
......................................177
7.1
Structure Related Techniques
.............................177
7.1.1
Parent Divorcing
..................................178
7.1.2
Temporal Transformation
..........................182
7.1.3
Structural and Functional Uncertainty
...............184
7.1.4
Undirected Dependence Relations
...................188
7.1.5
Bidirectional Relations
.............................191
7.1.6
Naive
Bayes
Model
................................193
7.2
Probability Distribution Related Techniques
................196
7.2.1
Measurement Uncertainty
..........................196
7.2.2
Expert Opinions
..................................199
7.2.3
Node Absorption
..................................201
7.2.4
Set Value by Intervention
...........................202
7.2.5
Independence of Causal Influence
....................205
7.2.6
Mixture of Gaussian Distributions
...................210
7.3
Decision Related Techniques
..............................212
7.3.1
Test Decisions
....................................212
7.3.2
Missing Informational Links
........................216
7.3.3
Missing Observations
..............................218
7.3.4
Hypothesis of Highest Probability
...................220
7.3.5
Constraints on Decisions
...........................223
7.4
Summary
...............................................225
8
Data-Driven Modeling
.....................................227
8.1
The Task and Basic Assumptions
..........................228
8.2
Structure Learning From Data
............................229
8.2.1
Basic Assumptions
................................230
8.2.2
Equivalent, Models
.................................231
8.2.3
Statistical Hypothesis Tests
.........................232
8.2.4
Structure Constraints
..............................235
8.2.5
PC Algorithm
....................................235
8.2.6
PC* Algorithm
....................................241
8.2.7
NPC Algorithm
...................................241
8.3
Batch Parameter Learning From Data
......................246
8.3.1
Expectation-Maximization Algorithm
................247
8.3.2
Penalized EM Algorithm
...........................249
8.4
Sequential Parameter Learning
............................252
8.5
Summary
...............................................254
Part III Model Analysis
9
Conflict Analysis
..........................................261
9.1
Evidence Driven Conflict Analysis
.........................262
9.1.1
Conflict Measure
..................................262
9.1.2
Tracing Conflicts
..................................264
9.1.3
Conflict Resolution
................................265
9.2
Hypothesis Driven Conflict Analysis
.......................267
9.2.1
Cost-of-Omission Measure
..........................267
9.2.2
Evidence with Conflict Impact
......................267
9.3
Summary
...............................................269
10
Sensitivity Analysis
........................................273
10.1
Evidence Sensitivity Analysis
.............................274
10.1.1
Distance and Cost-of-Omission Measures
.............275
10.1.2
Identify Minimum and Maximum Beliefs
.............276
10.1.3
Impact of Evidence Subsets
.........................277
10.1.4
Discrimination
of Competing Hypotheses
.............278
10.1.5
What-If Analysis
..................................279
10.1.6
Impact of Findings
................................280
10.2
Parameter Sensitivity Analysis
............................281
10.2.1
Sensitivity Function
...............................282
10.2.2
Sensitivity Value
..................................285
10.2.3
Admissible Deviation
..............................
28G
10.3
Summary
...............................................287
11
Value of Information Analysis
.............................291
11.1
VOI
Analysis in Bayesian Networks
........................292
11.1.1
Entropy and Mutual Information
....................292
11.1.2
Hypothesis Driven Value of Information Analysis
......293
11.2
VOI
Analysis in Influence Diagrams
.......................297
11.3
Summary
...............................................300
References
.....................................................305
List of Symbols
................................................311
Index
..........................................................313
|
| adam_txt |
Contents
Part I Fundamentals
Introduction
. 3
1.1
Expert Systems
. 3
1.1.1
Representation of Uncertainty
. 4
1.1.2
Normative Expert Systems
. 5
1.2
Rule-Based Systems
. 5
1.2.1
Causality
. 6
1.2.2
Uncertainty in Rule-Based Systems
. 7
1.2.3
Explaining Away
. 7
1.3
Bayesian Networks
. 8
1.3.1
Inference in Bayesian Networks
. 9
1.3.2
Construction of Bayesian Networks
. 10
1.3.3
An Example
. 10
1.4
Bayesian Decision Problems
. 13
1.5
When to Use Probabilistic Nets
. 14
1.6
Concluding Remarks
. 15
Networks
. 17
2.1
Graphs
. 18
2.2
Graphical Models
. 20
2.2.1
Variables
. 20
2.2.2
Vertices vs. Variables
. 21
2.2.3
Taxonomy of Vertices/Variables
. 22
2.2.4
Vertex Symbols
. 23
2.2.5
Summary of Notation
. 23
2.3
Evidence
. 23
2.4
Causality
. 24
2.5
Flow of Information in Causal Networks
. 25
2.5.1
Serial Connections
. 26
2.5.2
Diverging Connections
. 28
2.5.3
Converging Connections
. 29
2.5.4
The Importance of Correct Modeling of Causality
. 30
2.6
Two Equivalent Irrelevance Criteria
. 31
2.
G.I d-Separation Criterion
. 32
2.6.2
Directed Global Markov Criterion
. 33
2.7
Summary
. 35
Probabilities
. 37
3.1
Basics
. 38
3.1.1
Events
. 38
3.1.2
Conditional Probability
. 38
3.1.3
Axioms
. 39
3.2
Probability Distributions for Variables
. 40
3.2.1
Rule of Total Probability
. 41
3.2.2
Graphical Representation
. 43
3.3
Probability Potentials
. 44
3.3.1
Normalization
. 44
3.3.2
Evidence Potentials
. 45
3.3.3
Potential Calculus
. 46
3.3.4
Barren Variables
. 49
3.4
Fundamental Rule and
Bayes'
Rule
. 50
3.4.1
Interpretation of
Bayes'
Rule
. 51
3.5
Bayes'
Factor
. 53
3.6
Independence
. 54
3.6.1
Independence and DAGs
. 56
3.7
Chain Rule
. 58
3.8
Summary
. 60
Probabilistic Networks
. 63
4.1
Reasoning Under Uncertainty
. 64
4.1.1
Discrete Bayesian Networks
. 65
4.1.2
Conditional Linear Gaussian Bayesian Networks
. 70
4.2
Decision Making Under Uncertainty
. 74
4.2.1
Discrete Influence Diagrams
. 75
4.2.2
Conditional LQG Influence Diagrams
. 85
4.2.3
Limited Memory Influence Diagrams
. 89
4.3
Object-Oriented Probabilistic Networks
. 91
4.3.1
Chain Rule
. 96
4.3.2
Unfolded OOPNs
. 96
4.3.3
Instance Trees
. 97
4.3.4
Inheritance
. 98
4.4
Dynamic Models
. 98
4.5
Summary
. 102
Solving Probabilistic Networks
.107
5.1
Probabilistic Inference
.108
5.1.1
Inference in Discrete Bayesian Networks
.108
5.1.2
Inference in CLG Bayesian Networks
.121
5.2
Solving Decision Models
.124
5.2.1
Solving Discrete Influence Diagrams
.124
5.2.2
Solving CLQG Influence Diagrams
.129
5.2.3
Relevance Reasoning
.130
5.2.4
Solving LIMIDs
.133
5.3
Solving OOPNs
.136
5.4
Siimmarv
.137
Part II Model Construction
6
Eliciting the Model
.143
6.1
When to Use Probabilistic Networks
.144
6.1.1
Characteristics of Probabilistic Networks
.145
6.1.2
Some Criteria for Using Probabilistic Networks
.145
6.2
Identifying the Variables of a Model
.147
6.2.1
Well-Defined Variables
.147
6.2.2
Types of Variables
.150
6.3
Eliciting the Structure
.152
6.3.1
A Basic Approach
.152
6.3.2 "
Idioms
.154
6.4
Model Verification
.159
6.5
Eliciting the Numbers
.163
6.5.1
Eliciting Subjective Conditional Probabilities
.163
6.5.2
Eliciting Subjective Utilities
.166
6.5.3
Specifying CPTs and UTs Through Expressions
.166
6.6
Concluding Remarks
.170
6.7
Summary
.172
7
Modeling Techniques
.177
7.1
Structure Related Techniques
.177
7.1.1
Parent Divorcing
.178
7.1.2
Temporal Transformation
.182
7.1.3
Structural and Functional Uncertainty
.184
7.1.4
Undirected Dependence Relations
.188
7.1.5
Bidirectional Relations
.191
7.1.6
Naive
Bayes
Model
.193
7.2
Probability Distribution Related Techniques
.196
7.2.1
Measurement Uncertainty
.196
7.2.2
Expert Opinions
.199
7.2.3
Node Absorption
.201
7.2.4
Set Value by Intervention
.202
7.2.5
Independence of Causal Influence
.205
7.2.6
Mixture of Gaussian Distributions
.210
7.3
Decision Related Techniques
.212
7.3.1
Test Decisions
.212
7.3.2
Missing Informational Links
.216
7.3.3
Missing Observations
.218
7.3.4
Hypothesis of Highest Probability
.220
7.3.5
Constraints on Decisions
.223
7.4
Summary
.225
8
Data-Driven Modeling
.227
8.1
The Task and Basic Assumptions
.228
8.2
Structure Learning From Data
.229
8.2.1
Basic Assumptions
.230
8.2.2
Equivalent, Models
.231
8.2.3
Statistical Hypothesis Tests
.232
8.2.4
Structure Constraints
.235
8.2.5
PC Algorithm
.235
8.2.6
PC* Algorithm
.241
8.2.7'
NPC Algorithm
.241
8.3
Batch Parameter Learning From Data
.246
8.3.1
Expectation-Maximization Algorithm
.247
8.3.2
Penalized EM Algorithm
.249
8.4
Sequential Parameter Learning
.252
8.5
Summary
.254
Part III Model Analysis
9
Conflict Analysis
.261
9.1
Evidence Driven Conflict Analysis
.262
9.1.1
Conflict Measure
.262
9.1.2
Tracing Conflicts
.264
9.1.3
Conflict Resolution
.265
9.2
Hypothesis Driven Conflict Analysis
.267
9.2.1
Cost-of-Omission Measure
.267
9.2.2
Evidence with Conflict Impact
.267
9.3
Summary
.269
10
Sensitivity Analysis
.273
10.1
Evidence Sensitivity Analysis
.274
10.1.1
Distance and Cost-of-Omission Measures
.275
10.1.2
Identify Minimum and Maximum Beliefs
.276
10.1.3
Impact of Evidence Subsets
.277
10.1.4
Discrimination
of Competing Hypotheses
.278
10.1.5
What-If Analysis
.279
10.1.6
Impact of Findings
.280
10.2
Parameter Sensitivity Analysis
.281
10.2.1
Sensitivity Function
.282
10.2.2
Sensitivity Value
.285
10.2.3
Admissible Deviation
.
28G
10.3
Summary
.287
11
Value of Information Analysis
.291
11.1
VOI
Analysis in Bayesian Networks
.292
11.1.1
Entropy and Mutual Information
.292
11.1.2
Hypothesis Driven Value of Information Analysis
.293
11.2
VOI
Analysis in Influence Diagrams
.297
11.3
Summary
.300
References
.305
List of Symbols
.311
Index
.313 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Kjaerulff, Uffe Madsen, Anders L. |
| author_facet | Kjaerulff, Uffe Madsen, Anders L. |
| author_role | aut aut |
| author_sort | Kjaerulff, Uffe |
| author_variant | u k uk a l m al alm |
| building | Verbundindex |
| bvnumber | BV023351375 |
| callnumber-first | Q - Science |
| callnumber-label | QA279 |
| callnumber-raw | QA279.5 |
| callnumber-search | QA279.5 |
| callnumber-sort | QA 3279.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 830 ST 130 |
| classification_tum | MAT 624f MAT 622f |
| ctrlnum | (OCoLC)172984352 (DE-599)DNB984927859 |
| dewey-full | 003.54 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003.54 |
| dewey-search | 003.54 |
| dewey-sort | 13.54 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV023351375 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:05:16Z |
| indexdate | 2024-07-09T21:16:36Z |
| institution | BVB |
| isbn | 9780387741017 9780387741000 0387741003 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016534984 |
| oclc_num | 172984352 |
| open_access_boolean | |
| owner | DE-384 DE-11 DE-19 DE-BY-UBM DE-91G DE-BY-TUM |
| owner_facet | DE-384 DE-11 DE-19 DE-BY-UBM DE-91G DE-BY-TUM |
| physical | XVII, 318 S. Ill., graph. Darst. 235 mm x 155 mm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series2 | Information Science and Statistics |
| spelling | Kjaerulff, Uffe Verfasser aut Bayesian networks and influence diagrams a guide to construction and analysis Uffe B. Kjaerulff ; Anders L. Madsen New York, NY Springer 2008 XVII, 318 S. Ill., graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Information Science and Statistics Bayesian statistical decision theory Expert systems (Computer science) Uncertainty (Information theory) Wahrscheinlichkeitsnetz (DE-588)4138881-1 gnd rswk-swf Bayes-Netz (DE-588)4567228-3 gnd rswk-swf Bayes-Netz (DE-588)4567228-3 s Wahrscheinlichkeitsnetz (DE-588)4138881-1 s DE-604 Madsen, Anders L. Verfasser aut Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016534984&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kjaerulff, Uffe Madsen, Anders L. Bayesian networks and influence diagrams a guide to construction and analysis Bayesian statistical decision theory Expert systems (Computer science) Uncertainty (Information theory) Wahrscheinlichkeitsnetz (DE-588)4138881-1 gnd Bayes-Netz (DE-588)4567228-3 gnd |
| subject_GND | (DE-588)4138881-1 (DE-588)4567228-3 |
| title | Bayesian networks and influence diagrams a guide to construction and analysis |
| title_auth | Bayesian networks and influence diagrams a guide to construction and analysis |
| title_exact_search | Bayesian networks and influence diagrams a guide to construction and analysis |
| title_exact_search_txtP | Bayesian networks and influence diagrams a guide to construction and analysis |
| title_full | Bayesian networks and influence diagrams a guide to construction and analysis Uffe B. Kjaerulff ; Anders L. Madsen |
| title_fullStr | Bayesian networks and influence diagrams a guide to construction and analysis Uffe B. Kjaerulff ; Anders L. Madsen |
| title_full_unstemmed | Bayesian networks and influence diagrams a guide to construction and analysis Uffe B. Kjaerulff ; Anders L. Madsen |
| title_short | Bayesian networks and influence diagrams |
| title_sort | bayesian networks and influence diagrams a guide to construction and analysis |
| title_sub | a guide to construction and analysis |
| topic | Bayesian statistical decision theory Expert systems (Computer science) Uncertainty (Information theory) Wahrscheinlichkeitsnetz (DE-588)4138881-1 gnd Bayes-Netz (DE-588)4567228-3 gnd |
| topic_facet | Bayesian statistical decision theory Expert systems (Computer science) Uncertainty (Information theory) Wahrscheinlichkeitsnetz Bayes-Netz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016534984&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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