2nd Edition, Ch15, p.1

Decision theory and Bayesian Inference

Example 10.1 (Sampling Inspection, 2nd Ed., TBp. 572)

2nd Edition, Ch15, p.2

Example 10.2 (Classification, 2nd Ed., TBp. 572)

actions datadecision d1

decision dm

distribution

f(x|θ)•••

parametersprior

g(θ)

risk function Bayes riskloss function

2nd Edition, Ch15, p.3

Summary and Definitions (Decision Theory, 2nd Ed., TBp.571)

2nd Edition, Ch15, p.4

Question 10.1

Example 10.3 (Estimation, 2nd Ed., TBp. 573)

2nd Edition, Ch15, p.5

Definition 10.2 (Prior Distribution, Bayes Risk, Bayes Rule, 2nd Ed., TBp.574)

Definition 10.1 (Minimax Rule, 2nd Ed., TBp.573)

Notes (Minimax Rule)

2nd Edition, Ch15, p.6

Notes (Bayes risk)

Example 10.4 (steel section of firm stratum, 2nd Ed., TBp. 574-575)

2nd Edition, Ch15, p.7

2nd Edition, Ch15, p.8

Example 10.5 (sampling inspection, 2nd Ed., TBp. 576-577)

2nd Edition, Ch15, p.9

2nd Edition, Ch15, p.10

Definition 10.3 (Posterior Distribution and Posterior Risk, 2nd Ed., TBp.578-579)

• Posterior Analysis --- A simple method for finding Bayes rule

Reading: textbook (2nd ed.), 15.1, 15.2, 15.2.1

2nd Edition, Ch15, p.11

2nd Edition, Ch15, p.12

actions datadecision d1

decision dm

distribution

f(x|θ)••• parameters

prior

g(θ)

risk function Bayes risk

loss function

posterior

h(θ |x)

posterior risk

Theorem 10.1 (2nd Ed., TBp.579)

update

2nd Edition, Ch15, p.13

Algorithm for finding the Bayes rule (2nd Ed., TBp.579-580)

Example 10.6 (steel section (cont.), 2nd Ed., TBp. 580, LNp.6~8)

Reading: textbook (2nd ed.), 15.2.2

2nd Edition, Ch15, p.14

• Application of Decision Theory: Estimation

Q: what if a prior is available?

Theorem 10.2 (Bayes rule for Estimation under Squared Error Loss, 2nd Ed., TBp.584)

2nd Edition, Ch15, p.15

Example 10.7 (Throw a coin once, Bayes estimator, 2nd Ed., TBp. 584-585)

2nd Edition, Ch15, p.16

Theorem 10.3 (Bayes rule for Estimation under Absolute Error Loss)

Definition 10.4 (dominate, strictly dominate, admissible, 2nd Ed., TBp.585)

2nd Edition, Ch15, p.17

Theorem 10.4 (2nd Ed., TBp.586)

2nd Edition, Ch15, p.18

Notes.

Reading: textbook (2nd ed.), 15.2.4

• The Subjectivist Point of View – where the prior distributions come from?

2nd Edition, Ch15, p.19

Bayesian View of Probability (Personal Opinion) (2nd Ed., TBp. 587-588).

Evolvement of Personal Opinion (2nd Ed., TBp. 588).

2nd Edition, Ch15, p.20

Difference btw Frequentist and Bayesian Approaches – Point Estimation (TBp. 588)

Difference btw Frequentist and Bayesian Approaches – Interval Estimation (TBp. 588)

2nd Edition, Ch15, p.21

Difference btw Frequentist and Bayesian Approaches - Testing (2nd Ed., TBp. 589)

Reading: textbook (2nd ed.), 15.3

• Bayesian Inference for the Normal distribution

Theorem 10.5 (2nd Ed., TBp. 590)

2nd Edition, Ch15, p.22

2nd Edition, Ch15, p.23

Notes (2nd Ed., TBp. 590).

2nd Edition, Ch15, p.24

Theorem 10.6 (2nd Ed., TBp.590-591)

Notes (2nd Ed., TBp.591).

2nd Edition, Ch15, p.25

Example 10.8 (2nd Ed., TBp. 591-592)

• Bayesian Inference for the Binomial distribution

Reading: textbook (2nd ed.), 15.3.1

2nd Edition, Ch15, p.26

Theorem 10.7 (2nd Ed., TBp. 593-594)

Notes (2nd Ed., TBp. 594).

2nd Edition, Ch15, p.27

Example 10.9 (2nd Ed., TBp. 596)

2nd Edition, Ch15, p.28

Reading: textbook (2nd ed.), 15.3.2

Definition 10.5 (conjugate priors, 2nd Ed., TBp. 596-597)

2nd Edition, Ch15, p.29

• Application of Decision Theory: Classification

Formulation of Classification Problem (2nd Ed., TBp.581)

2nd Edition, Ch15, p.30

Theorem 10.8 (Bayes rule for Classification, 2nd Ed., TBp.581)

Example 10.10 (0-1 loss, 2nd Ed., TBp. 581-582)

2nd Edition, Ch15, p.31

Example 10.11 (waiting times between emissions, 2nd Ed., TBp. 582)

X

θ

2nd Edition, Ch15, p.32

• Application of Decision Theory: Hypothesis Testing

2nd Edition, Ch15, p.33

2nd Edition, Ch15, p.34

Theorem 10.9 (Neyman-Pearson Lemma from Bayesian viewpoint, 2nd Ed., TBp.583)

2nd Edition, Ch15, p.35

Example 10.12 (hypothesis testing of exponential distribution, 2nd Ed., TBp. 583)

Reading: textbook (2nd ed.), 15.2.3

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