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
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 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 #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
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
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 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: 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 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 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 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
2GR, 2UG
Homework #3
Spring 2016
A. Stepanov
(due Friday, March 4, 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.
HPS 2.4
STAT 430 Applied Bayesian Analysis Fall 2015
Homework 2
Please submit your assignment on paper. Make sure your answers are completely justied and
clear enough to read! When you use a computer, please include your code and output.
1. [5 pts] Cowles, Proble
STAT 430
1GR, 1UG
Theorem
Spring 2017
A. Stepanov
Examples for 02/16/2017
Let be a stationary distribution.
If x is transient or null recurrent, then ( x ) = 0.
Theorem
An irreducible positive recurrent Markov chain has a unique stationary
distribution ,
STAT 430
1GR, 1UG
Spring 2017
A. Stepanov
Examples for 02/02/2017
Birth and death Markov chain:
qx
P ( x, y ) = r x
p
x
q0 = 0
y = x 1
y=x
y = x +1
0xd
pd = 0
0
1
2
3
4
d2
d1
d
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
p2
r3
0
3
p1
r2
q3
0
2
p0
r1
q2
0
1
r0
q1
p3
STAT 430
1GR, 1UG
Spring 2017
A. Stepanov
Homework #1
(due Friday, February 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.
In s
STAT 430
1GR, 1UG
Examples for 02/07/2017
Spring 2017
A. Stepanov
Branching chain:
Consider particles (e.g., bacteria) that can generate new particles of the same type. The initial set
of particles is referred to as the 0th generation. Particles generated
STAT 430
1GR, 1UG
Examples for 02/09/2017
Spring 2017
A. Stepanov
If ( x ), x S, are nonnegative numbers summing to one, and if
( x ) P ( x, y )
= ( y ),
y S,
xS
then is called a stationary distribution. That is, a stationary distribution is a probabilit
STAT 430
1GR, 1UG
Spring 2017
A. Stepanov
Homework #2
(due Friday, February 17, 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.
In
STAT 430
1GR, 1UG
Spring 2017
A. Stepanov
Homework #1
(due Friday, February 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.
In s
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
1GR, 1UG
Homework #4
Spring 2017
A. Stepanov
(due Friday, March 17, 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.
Alex a
STAT 430
1GR, 1UG
Spring 2017
A. Stepanov
Extra Credit
03/02/2017
( 3 points )
1.
The state space cfw_ 1, 2, 3, 4, 5 2 is a square
with 25 = 5 5 cells. A drunk person starting
from ( 1, 1 ) tries to reach a house at ( 5, 5 ).
The person moves one cell up
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
Homework 0
STAT 430, Spring 2017
Due: Friday, January 27 by 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
Homework 4
STAT 430, Spring 2017
Due: Friday, February 24 by 11:59 PM
Please see the homework instructions document for detailed instructions and some grading notes. Failure to
follow instructions will result in point reductions.
Exercise 1
[10 points] We
Homework 1
STAT 430, Spring 2017
Due: Friday, February 3 by 11:59 PM
Please see the homework instructions document for detailed instructions and some grading notes. Failure to
follow instructions will result in point reductions.
Exercise 1
[12 points] Thi
Homework 6
STAT 430, Spring 2017
Due: Friday, March 17 by 11:59 PM
Please see the homework instructions document for detailed instructions and some grading notes. Failure to
follow instructions will result in point reductions.
Exercise 1
[10 points] For t
Homework 3
STAT 430, Spring 2017
Due: Friday, February 17 by 11:59 PM
Please see the homework instructions document for detailed instructions and some grading notes. Failure to
follow instructions will result in point reductions.
For this homework we retu