STAT 430
2GR, 2UG
Spring 2016
A. Stepanov
Homework #2
(due Friday, February 19, by 4:00 p.m.)
Please include your name ( with your last name underlined ),
and your NetID at the top of the first page.
No credit will be given without supporting work.
1.
A m
STAT 430
2GR, 2UG
Homework #1
Spring 2016
A. Stepanov
(due Friday, February 5, by 4:00 p.m.)
Please include your name ( with your last name underlined ),
and your NetID at the top of the first page.
1.
HPS 1.7
P( X0 = x0 | X1 = x1, , Xn = xn ) =
P ( X 0 =
STAT 430: Applied Bayesian Statistics Homework 1 Solutions
Subhadeep Paul
September 14, 2015
1
Problem 1.2
The following table summarizes Bayes rule to obtain the posterior probability of having
breast cancer given a negative result of the mammogram. Note
STAT 430 Applied Bayesian Analysis Fall 2015
Homework 3
Please submit your assignment on paper. Make sure your answers are completely justied and
clear enough to read! If you use a computer, please include your code and output.
1. [5 pts] Cowles, Problem
STAT 430
2GR, 2UG
Spring 2016
A. Stepanov
Homework #4
(due Friday, March 18, by 4:00 p.m.)
Please include your name ( with your last name underlined ),
and your NetID at the top of the first page.
No credit will be given without supporting work.
Let p < 1
STAT 430
2GR, 2UG
Spring 2016
A. Stepanov
Homework #2
(due Friday, February 19, by 4:00 p.m.)
Please include your name ( with your last name underlined ),
and your NetID at the top of the first page.
No credit will be given without supporting work.
1.
A m
STAT 430 Applied Bayesian Analysis Fall 2015
Homework 1
Please submit your assignment on paper. Make sure your answers are complete and clear enough
to read!
1. [6 pts] Cowles, Problem 1.2
2. [9 pts] Cowles, Problem 2.4
3. GRADUATE STUDENTS ONLY
[5 pts] A
STAT 430: Applied Bayesian Statistics Homework 3
Solutions
Subhadeep Paul
October 12, 2015
1
Problem 5.4
We have to nd the joint distribution of y1 , y2 .yn , the n observations. We write it as
P (y1 , y2 , .yn |) to emphasize that the density is conditi
STAT 430
2GR, 2UG
Homework #6
Spring 2016
A. Stepanov
(due Wednesday, April 20, by 4:00 p.m.)
Please include your name ( with your last name underlined ),
and your NetID at the top of the first page.
No credit will be given without supporting work.
1.
The
STAT 430 — Applied Bayesian Analysis -— Spring 2014
Quiz
March 12, 2013
Full Name: K 8.1
a This is a 50 minute exam. There are 5 problems for everyone, and one additional problem
for graduate students only.
a The exam is worth a total of 33 points for u
STAT 430 Applied Bayesian Analysis Spring 2014
Quiz
March 12, 2013
Full Name:
This is a 50 minute exam. There are 5 problems for everyone, and one additional problem
for graduate students only.
The exam is worth a total of 33 points for undergraduates a
STAT 430: Applied Bayesian Statistics Homework 4
Solutions
Subhadeep Paul
March 19, 2014
1
Problem 7.1
Refer to the candy weight data in problem 6.2. There are 20 observations with mean
y = 50 and Sample variance s2 = 18.31. (Note of caution: The R funct
STAT 430 Applied Bayesian Analysis Fall 2015
Homework 5
Please submit your assignment on paper. Make sure your answers are completely justied and
clear enough to read! Any computer code and output should be included.
1. [6 pts] From the survey discussed i
STAT 430
1GR, 1UG
Spring 2017
A. Stepanov
Examples for 01/17/2017
Multiplication Rule:
P( A B ) = P( A ) P( B | A )
P(B | A) =
since
P (A B)
P (A )
Similarly,
P( A B C ) = P( A) P( B | A ) P( C | A B )
P(A B C) = P(A)
since
P (A B) P (A B C )
P (A )
P (A
STAT 430 Applied Bayesian Analysis Fall 2015
Homework 6
Please submit your assignment on paper. Make sure your answers are completely justied and
clear enough to read! Any computer code and output should be included.
1. [4 pts] Suppose Y1 and Y2 are condi
STAT 430: Applied Bayesian Statistics Homework 5
Solutions
Subhadeep Paul
April 11, 2014
1
Problem 1
The class room survey data follows binomial distribution with n = 48 and unknown
parameter . The prior density on is the Jereys prior
1 1
Beta( , ) /
2
STAT 430: Homework 2 Solutions
Subhadeep Paul
September 28, 2015
Problem 3.1
1. For the beta density with parameters = 2 and = 7, the mean is
1
1
mode is +2 = 7 .
+
= 1 , and the
3
2. The R function qbeta(0.5,2,7) gives the median of the density as 0.2011
STAT 430
1GR, 1UG
Spring 2017
A. Stepanov
Homework #3
(due Friday, March 3, by 3:00 p.m.)
Please include your name ( with your last name underlined ),
and your NetID at the top of the first page.
No credit will be given without supporting work.
1.
Let 0 <
STAT 430
Spring 2017
Version A
Name
Total
/70
ANSWERS
NetID
Exam 1
Be sure to Show all your work; your
partial credit might depend on it.
Put your nal answers at the end of
your work, and mark them clearly.
No credit will be gi
STAT 430
Spring 2017
Version B
Page
Earned
Name
Total
/70
ANSWERS
NetID
Exam 1
Be sure to show all your work; your
partial credit might depend on it.
Put your nal answers at the end of
your work, and mark them clearly.
No credit will be
STAT 430
1GR, 1UG
1.
Spring 2017
A. Stepanov
Examples for 02/28/2017
Let T 1 , T 2 , , T k be independent Exponential random variables.
1
Suppose E ( T i ) =
, i = 1, 2, , k.
i
t
That is, f T ( t ) = i e i , t > 0, i = 1, 2, , k.
i
Denote T min = min ( T
STAT 430
1GR, 1UG
Spring 2017
A. Stepanov
Examples for 01/31/2017
Suppose we have m + k states m absorbing states and k transient states.
Rearrange the states so that the first m states are absorbing and the last k states are transient.
Then
m
k
m
I mm
O
STAT 430
1GR, 1UG
1.
Spring 2017
A. Stepanov
Practice Problems 1
A medical researcher is studying the risk of heart attack in men. She first divides men
into three weight categories: thin, normal, and overweight. By studying the male
ancestors, sons, and
STAT 430
1GR, 1UG
1.
P =
Spring 2017
A. Stepanov
Practice Problems 3
Consider the Markov chain on cfw_ 0, 1, 2, 3 having transition matrix
0
1
2
3
0
0.1
0.2
0.2
0.5
1
0.3
0.4
0
0.3
2
0.4
0
0.4
0.2
3
0.3
0
0.2
0.5
a)
If the chain starts in state 2, find t
STAT 430
1GR, 1UG
Spring 2017
A. Stepanov
Examples for 01/26/2017
Let C be an irreducible closed set of recurrent states.
C ( x ) = P x ( T C < ),
x S.
( probability that the Markov chain that starts in x would be absorbed into C )
C ( x ) = 1,
x C.
C
STAT 430
1GR, 1UG
1.
Spring 2017
A. Stepanov
Practice Problems 2
A medical researcher is studying the risk of heart attack in men. She first divides men
into three weight categories: thin, normal, and overweight. By studying the male
ancestors, sons, and
STAT 430
1GR, 1UG
Spring 2017
A. Stepanov
Homework #5
(due Friday, March 31, by 3:00 p.m.)
Please include your name ( with your last name underlined ),
and your NetID at the top of the first page.
No credit will be given without supporting work.
1.
Aaron
Homework 00
STAT 430, Fall 2017
Due: Friday, September 8, 11:59 PM
Please see the homework policy document for detailed instructions and some grading notes. Failure to follow
instructions will result in point reductions.
The purpose of this homework is to