Introduction to Statistical Decision Theory: Utility Theory and Causal Analysis provides the theoretical background to approach decision theory from a statistical perspective. It covers both traditional approaches, in terms of value theory and expected utility theory, and recent developments, in terms of causal inference. The book is specifically designed to appeal to students and researchers that intend to acquire a knowledge of statistical science based on decision theory. Features Covers approaches for making decisions under certainty, risk, and uncertainty Illustrates expected utility theory and its extensions Describes approaches to elicit the utility function Reviews classical and Bayesian approaches to statistical inference based on decision theory Discusses the role of causal analysis in statistical decision theory.
Author(s): Silvia Bacci, Bruno Chiandotto
Edition: 1st
Publisher: Chapman and Hall/CRC Press/Taylor & Francis Group
Year: 2020
Language: English
Pages: 305
Tags: Statistical Decision Theory, Utility Theory, Causal Analysis
Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Dedication......Page 6
Contents......Page 8
Authors......Page 12
Preface......Page 14
1.1 Introduction......Page 18
1.2 Decision theory......Page 19
1.3 Value theory and utility theory......Page 21
1.4 Decisions and informational background......Page 23
1.5 Statistical inference and decision theory......Page 27
1.6 The decision-making approach to statistics......Page 30
2.1 Introduction......Page 34
2.2 Random experiments, events, and probability......Page 35
2.3 Bayes' rule......Page 40
2.4 Univariate random variables......Page 42
2.5 Multivariate random variables......Page 53
2.6 The exponential family......Page 63
2.7 Descriptive statistics and statistical inference......Page 65
2.8 Sample distributions......Page 68
2.9 Classical statistical inference......Page 73
2.9.1 Optimal point estimators......Page 75
2.9.2 Point estimation methods......Page 79
2.9.3 Confidence intervals......Page 86
2.9.4 Hypothesis testing......Page 88
2.10 Bayesian statistical inference......Page 95
2.10.1 Conjugate prior distributions......Page 101
2.10.2 Uninformative prior distributions......Page 105
2.10.3 Bayesian point and interval estimation......Page 108
2.10.4 Bayesian hypothesis testing......Page 109
2.11 Multiple linear regression model......Page 111
2.11.1 The statistical model......Page 112
2.11.2 Least squares estimator and maximum likelihood estimator......Page 113
2.11.3 Hypothesis testing......Page 115
2.11.4 Bayesian regression......Page 117
2.12 Structural equation model......Page 118
3.1 Introduction......Page 126
3.2 Binary relations and preferences......Page 127
3.3 Decisions under certainty: Value theory......Page 128
3.4 Decisions under risk: Utility theory......Page 135
3.4.1 von Neumann and Morgenstern's theory......Page 137
3.4.2 Savage's theory......Page 144
3.5.1 Violation of transitivity......Page 148
3.5.2 Certainty effect......Page 150
3.5.3 Pseudo-certainty effect and isolation effect......Page 151
3.5.4 Framing effect......Page 152
3.5.5 Extreme probability effect......Page 153
3.5.6 Aversion to uncertainty......Page 154
3.6 Alternative utility theories......Page 155
3.6.1 Rank-dependent utility theory......Page 159
3.6.2 Prospect theory and cumulative prospect theory......Page 160
4.1 Introduction......Page 164
4.2 Attitude towards risk......Page 165
4.3 A measure of risk aversion......Page 172
4.4 Classical elicitation paradigm......Page 173
4.4.1 Standard gamble methods......Page 175
4.4.2 Paired gamble methods......Page 179
4.4.3 Other classical elicitation methods......Page 183
4.5 Multi-step approaches......Page 184
4.6 Partial preference information paradigm......Page 186
4.7 Combining multiple preferences......Page 189
4.8 Case study: Utility elicitation for banking foundations......Page 190
5.1 Introduction......Page 196
5.2 Structure of the decision-making process......Page 197
5.3 Decisions under uncertainty (classical decision theory)......Page 200
5.4 Decisions with sample information (classical statistical decision theory)......Page 205
5.5 Decisions with sample and prior information (Bayesian statistical decisional theory)......Page 212
5.6 Perfect information and sample information......Page 221
5.7 Case study: Seeding hurricanes......Page 231
6.1 Introduction......Page 242
6.2 Causality and statistical inference......Page 243
6.3 Causal inference......Page 247
6.3.1 Statistical causality......Page 248
6.3.2 Modern causal inference......Page 249
6.3.3 Structural equation approach to causal inference......Page 253
6.4 Causal decision theory......Page 261
6.5 Case study: Subscription fees of the RAI Radiotelevisione Italiana......Page 266
6.6 Case study: Customer satisfaction for the RAI Radiotelevisione Italiana......Page 273
References......Page 284
Index......Page 300
