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 [u.a.]
Springer
2013
|
| Edition: | 2. ed. |
| Series: | Information Science and Statistics
22 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 382 S. graph. Darst. |
| ISBN: | 9781461451037 9781493900299 |
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MARC
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Record in the Search Index
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| adam_text | Titel: Bayesian networks and influence diagrams
Autor: Kjaerulff, Uffe
Jahr: 2013
Contents
Part I Fundamentals
1 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......................................................................................8
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..................................................................................................11
1.4 Bayesian Decision Problems..................................................................................13
1.5 When to Use Probabilistic Nets..........................................................................14
1.6 Concluding Remarks..................................................................................................15
2 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............................................................................................................................24
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
xiii
xiv Contents
2.5.3 Converging Connections......................................................................29
2.5.4 Intercausal Inference (Explaining Away)....................................30
2.5.5 The Importance of Correct Modeling of Causality..............31
2.6 Two Equivalent Irrelevance Criteria..................................................................32
2.6.1 d-Separation Criterion............................................................................33
2.6.2 Directed Global Markov Criterion..................................................35
2.7 Summary............................................................................................................................36
3 Probabilities..................................................................................................................................39
3.1 Basics..................................................................................................................................40
3.1.1 Events..............................................................................................................40
3.1.2 Axioms............................................................................................................40
3.1.3 Conditional Probability..........................................................................41
3.2 Probability Distributions for Variables............................................................43
3.2.1 Rule of Total Probability......................................................................44
3.2.2 Graphical Representation....................................................................46
3.3 Probability Potentials ................................................................................................46
3.3.1 Normalization..............................................................................................47
3.3.2 Evidence Potentials..................................................................................49
3.3.3 Potential Calculus ....................................................................................50
3.3.4 Barren Variables........................................................................................53
3.4 Fundamental Rule and Bayes Rule..................................................................54
3.4.1 Interpretation of Bayes Rule............................................................55
3.5 Bayes Factor..................................................................................................................58
3.6 Independence..................................................................................................................59
3.6.1 Independence and DAGs......................................................................60
3.7 Chain Rule........................................................................................................................62
3.8 Summary............................................................................................................................64
4 Probabilistic Networks..........................................................................................................69
4.1 Belief Update..................................................................................................................70
4.1.1 Discrete Bayesian Networks..............................................................71
4.1.2 Conditional Linear Gaussian Bayesian Networks..................75
4.2 Decision Making Under Uncertainty................................................................79
4.2.1 Discrete Influence Diagrams..............................................................80
4.2.2 Conditional LQG Influence Diagrams..........................................89
4.2.3 Limited Memory Influence Diagrams..........................................93
4.3 Object-Oriented Probabilistic Networks........................................................95
4.3.1 Chain Rule....................................................................................................100
4.3.2 Unfolded OOPNs......................................................................................100
4.3.3 Instance Trees..............................................................................................100
4.3.4 Inheritance....................................................................................................101
4.4 Dynamic Models..........................................................................................................102
4.4.1 Time-Sliced Networks Represented as OOPNs......................104
4.5 Summary............................................................................................................................105
Contents xv
5 Solving Probabilistic Networks......................................................................................Ill
5.1 Probabilistic Inference..............................................................................................112
5.1.1 Inference in Discrete Bayesian Networks..................................112
5.1.2 Inference in CLG Bayesian Networks..........................................125
5.2 Solving Decision Models........................................................................................128
5.2.1 Solving Discrete Influence Diagrams............................................128
5.2.2 Solving CLQG Influence Diagrams..............................................132
5.2.3 Relevance Reasoning..............................................................................134
5.2.4 Solving LIMIDs........................................................................................136
5.3 Solving OOPNs ............................................................................................................140
5.4 Summary............................................................................................................................140
Part II Model Construction
6 Eliciting the Model ..................................................................................................................145
6.1 When to Use Probabilistic Networks................................................................146
6.1.1 Characteristics of Probabilistic Networks..................................147
6.1.2 Some Criteria for Using Probabilistic Networks....................148
6.2 Identifying the Variables of a Model................................................................149
6.2.1 Well-Defined Variables..........................................................................149
6.2.2 Types of Variables....................................................................................152
6.3 Eliciting the Structure................................................................................................154
6.3.1 A Basic Approach....................................................................................154
6.3.2 Idioms..............................................................................................................156
6.3.3 An Example: Extended Chest Clinic Model ............................163
6.3.4 The Generic Structure of Probabilistic Networks..................173
6.4 Model Verification........................................................................................................174
6.5 Eliciting the Numbers................................................................................................176
6.5.1 Eliciting Subjective Conditional Probabilities........................177
6.5.2 Eliciting Subjective Utilities..............................................................179
6.5.3 Specifying CPTs and UTs Through Expressions..................180
6.6 Concluding Remarks..................................................................................................183
6.7 Summary............................................................................................................................185
7 Modeling Techniques..............................................................................................................191
7.1 Structure-Related Techniques................................................................................191
7.1.1 Parent Divorcing........................................................................................192
7.1.2 Temporal Transformation....................................................................196
7.1.3 Structural and Functional Uncertainty..........................................197
7.1.4 Undirected Dependence Relations..................................................201
7.1.5 Bidirectional Relations..........................................................................204
7.1.6 Naive Bayes Model..................................................................................206
7.2 Probability Distribution-Related Techniques..............................................208
7.2.1 Measurement Uncertainty....................................................................209
7.2.2 Expert Opinions ........................................................................................211
xvi Contents
7.2.3 Node Absorption........................................................................................213
7.2.4 Set Value by Intervention....................................................................214
7.2.5 Independence of Causal Influence..................................................216
7.2.6 Mixture of Gaussian Distributions..................................................221
7.3 Decision-Related Techniques........................................ 224
7.3.1 Test Decisions ............................................................................................224
7.3.2 Missing Informational Links..............................................................227
7.3.3 Missing Observations ............................................................................229
7.3.4 Hypothesis of Highest Probability..................................................231
7.3.5 Constraints on Decisions......................................................................233
7.4 Summary............................................................................................................................235
8 Data-Driven Modeling..........................................................................................................237
8.1 The Task and Basic Assumptions......................................................................238
8.1.1 Basic Assumptions..................................................................................240
8.1.2 Equivalent Models....................................................................................240
8.2 Constraint-Based Structure Learning................................................................242
8.2.1 Statistical Hypothesis Tests................................................................242
8.2.2 Structure Constraints..............................................................................245
8.2.3 PC Algorithm..............................................................................................246
8.2.4 PC* Algorithm............................................................................................251
8.2.5 NPC Algorithm..........................................................................................251
8.3 Search and Score-Based Structure Learning................................................256
8.3.1 Space of Structures..................................................................................256
8.3.2 Search Procedures....................................................................................257
8.3.3 Score Functions..........................................................................................258
8.3.4 Learning Structure Restricted Models..........................................265
8.4 Worked Example on Structure Learning........................................................271
8.4.1 PC Algorithm..............................................................................................272
8.4.2 NPC Algorithm..........................................................................................273
8.4.3 Search and Score-Based Algorithm................................................275
8.4.4 Chow-Liu Tree..........................................................................................276
8.4.5 Comparison..................................................................................................277
8.5 Batch Parameter Learning......................................................................................278
8.5.1 Expectation-Maximization Algorithm........................................279
8.5.2 Penalized EM Algorithm......................................................................281
8.6 Sequential Parameter Learning............................................................................283
8.7 Summary............................................................................................................................285
Part III Model Analysis
9 Conflict Analysis........................................................................................................................291
9.1 Evidence-Driven Conflict Analysis....................................................................292
9.1.1 Conflict Measure........................................................................................292
!
Contents xvii
9.1.2 Tracing Conflicts ......................................................................................294
9.1.3 Conflict Resolution..................................................................................295
9.2 Hypothesis-Driven Conflict Analysis..............................................................297
9.2.1 Cost-of-Omission Measure...................................................297
9.2.2 Evidence with Conflict Impact..........................................................297
9.3 Summary............................................................................................................................299
10 Sensitivity Analysis..................................................................................................................303
10.1 Evidence Sensitivity Analysis..............................................................................304
10.1.1 Distance and Cost-of-Omission Measures................................305
10.1.2 Identify Minimum and Maximum Beliefs..................................306
10.1.3 Impact of Evidence Subsets................................................................307
10.1.4 Discrimination of Competing Hypotheses................................308
10.1.5 What-If Analysis........................................................................................309
10.1.6 Impact of Findings....................................................................................309
10.2 Parameter Sensitivity Analysis............................................................................311
10.2.1 Sensitivity Function................................................................................312
10.2.2 Sensitivity Value........................................................................................314
10.2.3 Admissible Deviation ............................................................................316
10.3 Two-Way Parameter Sensitivity Analysis......................................................317
10.3.1 Sensitivity Function................................................................................317
10.4 Parameter Tuning..........................................................................................................320
10.5 Summary............................................................................................................................323
11 Value of Information Analysis..........................................................................................327
11.1 VOI Analysis in Bayesian Networks................................................................328
11.1.1 Entropy and Mutual Information....................................................328
11.1.2 Hypothesis-Driven Value of Information Analysis..............329
11.2 VOI Analysis in Influence Diagrams................................................................333
11.3 Summary............................................................................................................................336
Quick Reference to Model Construction............................................................................341
List of Examples....................................................................................................................................351
List of Figures........................................................................................................................................355
List of Tables............................................................................................................................................365
List of Symbols......................................................................................................................................369
Reference....................................................................................................................................................371
Index..............................................................................................................................................................377
|
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| spelling | Kjaerulff, Uffe Verfasser aut Bayesian networks and influence diagrams a guide to construction and analysis Uffe B. Kjærulff ; Anders L. Madsen 2. ed. New York, NY [u.a.] Springer 2013 XVII, 382 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Information Science and Statistics 22 Informatik Statistik Statistics Computer science Data mining Artifical intelligence Distibution (Probability theory) Mathematical statistics 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 Erscheint auch als Online-Ausgabe 978-1-4614-5104-4 Information Science and Statistics 22 (DE-604)BV040672748 22 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025750238&sequence=000001&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 Information Science and Statistics Informatik Statistik Statistics Computer science Data mining Artifical intelligence Distibution (Probability theory) Mathematical statistics 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_full | Bayesian networks and influence diagrams a guide to construction and analysis Uffe B. Kjærulff ; Anders L. Madsen |
| title_fullStr | Bayesian networks and influence diagrams a guide to construction and analysis Uffe B. Kjærulff ; Anders L. Madsen |
| title_full_unstemmed | Bayesian networks and influence diagrams a guide to construction and analysis Uffe B. Kjærulff ; 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 | Informatik Statistik Statistics Computer science Data mining Artifical intelligence Distibution (Probability theory) Mathematical statistics Wahrscheinlichkeitsnetz (DE-588)4138881-1 gnd Bayes-Netz (DE-588)4567228-3 gnd |
| topic_facet | Informatik Statistik Statistics Computer science Data mining Artifical intelligence Distibution (Probability theory) Mathematical statistics Wahrscheinlichkeitsnetz Bayes-Netz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025750238&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040672748 |
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