Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Authors
Preface
1. Statistics and decisions
1.1 Introduction
1.2 Decision theory
1.3 Value theory and utility theory
1.4 Decisions and informational background
1.5 Statistical inference and decision theory
1.6 The decision-making approach to statistics
2. Probability and statistical inference
2.1 Introduction
2.2 Random experiments, events, and probability
2.3 Bayes' rule
2.4 Univariate random variables
2.5 Multivariate random variables
2.6 The exponential family
2.7 Descriptive statistics and statistical inference
2.8 Sample distributions
2.9 Classical statistical inference
2.9.1 Optimal point estimators
2.9.2 Point estimation methods
2.9.3 Confidence intervals
2.9.4 Hypothesis testing
2.10 Bayesian statistical inference
2.10.1 Conjugate prior distributions
2.10.2 Uninformative prior distributions
2.10.3 Bayesian point and interval estimation
2.10.4 Bayesian hypothesis testing
2.11 Multiple linear regression model
2.11.1 The statistical model
2.11.2 Least squares estimator and maximum likelihood estimator
2.11.3 Hypothesis testing
2.11.4 Bayesian regression
2.12 Structural equation model
3. Utility theory
3.1 Introduction
3.2 Binary relations and preferences
3.3 Decisions under certainty: Value theory
3.4 Decisions under risk: Utility theory
3.4.1 von Neumann and Morgenstern's theory
3.4.2 Savage's theory
3.5 Empirical failures of rational behavioral axioms
3.5.1 Violation of transitivity
3.5.2 Certainty effect
3.5.3 Pseudo-certainty effect and isolation effect
3.5.4 Framing effect
3.5.5 Extreme probability effect
3.5.6 Aversion to uncertainty
3.6 Alternative utility theories
3.6.1 Rank-dependent utility theory
3.6.2 Prospect theory and cumulative prospect theory
4. Utility function elicitation
4.1 Introduction
4.2 Attitude towards risk
4.3 A measure of risk aversion
4.4 Classical elicitation paradigm
4.4.1 Standard gamble methods
4.4.2 Paired gamble methods
4.4.3 Other classical elicitation methods
4.5 Multi-step approaches
4.6 Partial preference information paradigm
4.7 Combining multiple preferences
4.8 Case study: Utility elicitation for banking foundations
5. Classical and Bayesian statistical decision theory
5.1 Introduction
5.2 Structure of the decision-making process
5.3 Decisions under uncertainty (classical decision theory)
5.4 Decisions with sample information (classical statistical decision theory)
5.5 Decisions with sample and prior information (Bayesian statistical decisional theory)
5.6 Perfect information and sample information
5.7 Case study: Seeding hurricanes
6. Statistics, causality, and decisions
6.1 Introduction
6.2 Causality and statistical inference
6.3 Causal inference
6.3.1 Statistical causality
6.3.2 Modern causal inference
6.3.3 Structural equation approach to causal inference
6.4 Causal decision theory
6.5 Case study: Subscription fees of the RAI Radiotelevisione Italiana
6.6 Case study: Customer satisfaction for the RAI Radiotelevisione Italiana
References
Index