Decision Theory

Index

Note: The entries in italics denote figures

a posteriori probabilities 23–4

Actions 40–1

multistage problems 230, 231, 233

NM theory 42

Savage’s theory 81

Adaptive design 245

Admissibility, decision rules 155–73, 284

Allais, M. 48

Allais paradox

NM theory 48–50

Savage’s theory 91–2, 94

Anscombe–Aumann representation theorem 103–5

Anscombe–Aumann theory 98–108

Anscombe, F. J. 98, 99

Archimedean axiom

NM theory (NM3) 44, 45, 51–2

alternative version 50

Ramsey’s theory (R8) 79

Savage’s theory (S6) 89–90

Arrow–Pratt measure 61

see also Local risk aversion (risk-aversion functions)

Associative means 38–9

Aumann, R. J. 98, 99

Axioms

Anscombe–Aumann theory 100–1, 102, 103–8

NM theory 43–5, 48, 51–2

probability theory 19, 20, 22

Ramsey’s theory 78–9

Savage’s theory 82–4, 85, 86–7, 89–90

Backwards induction 223, 224, 225, 230, 238, 249, 330

Bather, J. 240

Bayes actions 116–17, 118–19

Bayes estimators 149, 160, 164, 181–2, 183, 187

Bayes factors 135–6, 213, 219

Bayesian decision theory (Chernoff quote) 6

Bayesian information criteria (BICs) 213

Bayes risks 121, 126, 132, 145–6

Bayes rules 21, 23, 121–2, 125, 126, 129–31

admissibility 155–6, 159–60, 164–5

relationship to expected utility principle 122

relationship to minimax rules 144, 146, 150

uses

binary classification problems 139

coherent forecasters 206

information analysis 277

interval estimation 144

multistage problems 227, 228, 232

obtaining estimators 181, 185, 187

point estimation 140, 141

sample size determination 292–3