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Index
Cover
WILEY SERIES IN PROBABILITY AND STATISTICS
Title Page
Copyright
Introduction
A brief outline of this book
Guide to the reader
Contributors
Acknowledgements
Chapter 1: Desirability
1.1 Introduction
1.2 Reasoning about and with sets of desirable gambles
1.3 Deriving and combining sets of desirable gambles
1.4 Partial preference orders
1.5 Maximally committal sets of strictly desirable gambles
1.6 Relationships with other, nonequivalent models
1.7 Further reading
Acknowledgements
Chapter 2: Lower previsions
2.1 Introduction
2.2 Coherent lower previsions
2.3 Conditional lower previsions
2.4 Further reading
Acknowledgements
Chapter 3: Structural judgements
3.1 Introduction
3.2 Irrelevance and independence
3.3 Invariance
3.4 Exchangeability
3.5 Further reading
Acknowledgements
Chapter 4: Special cases
4.1 Introduction
4.2 Capacities and n-monotonicity
4.3 2-monotone capacities
4.4 Probability intervals on singletons
4.5 ∞-monotone capacities
4.6 Possibility distributions, p-boxes, clouds and related models
4.7 Neighbourhood models
4.8 Summary
Chapter 5: Other uncertainty theories based on capacities
5.1 Imprecise probability = modal logic + probability
5.2 From imprecise probabilities to belief functions and possibility theory
5.3 Discrepancies between uncertainty theories
5.4 Further reading
Chapter 6: Game-theoretic probability
6.1 Introduction
6.2 A law of large numbers
6.3 A general forecasting protocol
6.4 The axiom of continuity
6.5 Doob's argument
6.6 Limit theorems of probability
6.7 Lévy's zero-one law
6.8 The axiom of continuity revisited
6.9 Further reading
Acknowledgements
Chapter 7: Statistical inference
7.1 Background and introduction
7.2 Imprecision in statistics, some general sources and motives
7.3 Some basic concepts of statistical models relying on imprecise probabilities
7.4 Generalized Bayesian inference
7.5 Frequentist statistics with imprecise probabilities
7.6 Nonparametric predictive inference
7.7 A brief sketch of some further approaches and aspects
7.8 Data imprecision, partial identification
7.9 Some general further reading
7.10 Some general challenges
Acknowledgements
Chapter 8: Decision making
8.1 Non-sequential decision problems
8.2 Sequential decision problems
8.3 Examples and applications
Chapter 9: Probabilistic graphical models
9.1 Introduction
9.2 Credal sets
9.5 Computing with credal networks
9.6 Further reading
Acknowledgements
Chapter 10: Classification
10.1 Introduction
10.2 Naive Bayes
10.3 Naive credal classifier (NCC)
10.4 Extensions and developments of the naive credal classifier
10.5 Tree-based credal classifiers
10.6 Metrics, experiments and software
10.7 Scoring the conditional probability of the class
Acknowledgements
Chapter 11: Stochastic processes
11.1 The classical characterization of stochastic processes
11.2 Event-driven random processes
11.3 Imprecise Markov chains
11.4 Limit behaviour of imprecise Markov chains
11.5 Further reading
Chapter 12: Financial risk measurement
12.1 Introduction
12.2 Imprecise previsions and betting
12.3 Imprecise previsions and risk measurement
12.4 Further reading
Chapter 13: Engineering
13.1 Introduction
13.2 Probabilistic dimensioning in a simple example
13.3 Random set modelling of the output variability
13.4 Sensitivity analysis
13.5 Hybrid models
13.6 Reliability analysis and decision making in engineering
13.7 Further reading
Chapter 14: Reliability and risk
14.1 Introduction
14.2 Stress-strength reliability
14.3 Statistical inference in reliability and risk
14.4 Nonparametric predictive inference in reliability and risk
14.5 Discussion and research challenges
Chapter 15: Elicitation
15.1 Methods and issues
15.2 Evaluating imprecise probability judgements
15.3 Factors affecting elicitation
15.4 Matching methods with purposes
15.5 Further reading
Chapter 16: Computation
16.1 Introduction
16.2 Natural extension
16.3 Decision making
References
Author index
Subject index
WILEY SERIES IN PROBABILITY AND STATISTICS
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