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An Introduction to Decision Theory

Martin Peterson

Chapter 10

Bayesian vs. non-Bayesian decision theory - all with Video Answers

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Chapter Questions

01:30

Problem 1

Explain, by using your own words, the term 'Bayesianism'.

Manik Pulyani
Manik Pulyani
Numerade Educator
01:28

Problem 2

Your subjective degree of belief in $B$ is 0.1 and your degree of belief in $A$ given $B$ is 0.4 . You then come to believe that the unconditional probability of $A$ is 0.90 . To what degree should you believe $B$ given $A$ ? (That is, what is $p(B \mid A) ?$ ?)

Christopher Stanley
Christopher Stanley
Numerade Educator
01:52

Problem 3

Pete is a Bayesian. He tells you that he prefers $x$ to $z$, and the lottery $y p w$ to $x p w$. He thereafter asks you to advise him whether he should prefer $y$ to $z$, or $z$ to $y$, or be indifferent. What do you tell him?

Prabhakar Kumar
Prabhakar Kumar
Numerade Educator
01:00

Problem 4

Suppose that Pete in Exercise 10.3 prefers $z$ to $y$. His preferences are then incoherent. Can you advise him which of his preferences he ought to revise?

Barath Palanisamy
Barath Palanisamy
Numerade Educator

Problem 5

In the account of Bayesianism given here, we identified an epistemic and a deliberative component, respectively. But is there really any fundamental difference between choosing what to believe and choosing what to do - perhaps choosing a belief is a way of performing an act? If so, do you think it would be possible to reduce Bayesianism to a single, unified theory about rational deliberation?

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