Spring 1997 John Rust
Economics 551b 37 Hillhouse, Rm. 27
PROBLEM SET 1
Bayesian Basics
QUESTION 1
Derive optimal estimator with absolute error loss function:
QUESTION 2
Derive optimal estimator with asymmetric loss function:
This loss function penalizes underestimation more than overestimation when b>a.
QUESTION 3
Suppose Beta distribution as a prior distribution of 
:
where 
is Beta function and 
.
Derive the posterior distribution of when 
( 
) follows Bernoulli distibution
QUESTION 4
Show how the posterior distribution in Question 3 changes
different value of N given an initial
Beta prior which you can choose. You do this by choosing values
for the hyperparameters of the Beta prior distribution in question 3.
You must also choose the ``true value'' of 
to generate
the 
data.
For example, choose 
and generate
Bernoulli random variables for N=10,50,100,500.