ISyE8843
Brani Vidakovic
Friday 9/10/04 Name:
Quiz 3
Select one problem!
Weighted Square Error Loss. We have seen that under squared error loss the Bayes rule [minimizer of
Bayes risk r(, ) or equival
ISyE8843
Brani Vidakovic
Friday 9/17/04 Name:
Quiz 4
Choose one problem
1
1. Assume X | is exponential E (1/) with density f (x|) = ex/ , x 0. Let F be the cdf corresponding
to f. Assume a prior on ,
ISyE8843
Brani Vidakovic
Friday 29/10/04 Name:
Quiz 7
Wallace-Freeman MML Estimator. Recall that the Minimum Message Length (MML) estimate, based
on X1 , . . . , Xn f (x|) is dened as
n
argmin [ log (
Answer for Quiz 7 (Ni Wang)
Answer: First, lets calculate the Fisher information for from the Negative Binomial N B (m, )
distribution.
log f (x|) = m log + x log(1 ) + const
x
m
log f (x|) =
+
2
( 1
ISyE8843
Brani Vidakovic
Friday 29/10/04 Name:
Quiz 7
Wallace-Freeman MML Estimator. Recall that the Minimum Message Length (MML) estimate, based
on X1 , . . . , Xn f (x|) is dened as
n
argmin [ log (
ISyE8843
Brani Vidakovic
Friday 9/17/04 Name:
Quiz 4
Choose one problem
1
1. Assume X | is exponential E (1/) with density f (x|) = ex/ , x 0. Let F be the cdf corresponding
to f. Assume a prior on ,
ISyE8843
Brani Vidakovic
Friday 9/10/04 Name:
Quiz 3
Select one problem!
Weighted Square Error Loss. We have seen that under squared error loss the Bayes rule [minimizer of
Bayes risk r(, ) or equival
ISyE8843
Brani Vidakovic
Labor Day Name:
Take Home Quiz 2
Mushrooms. The unhappy outcome of uninformed mushroom-picking is poisoning. In many cases such
poisoning is due to ignorance or a supercial ap
I SyE8843
Brani Vidakovic
Fliday, 8/27 / 04 Name:
1. Lifetime. A lifetime X of a particular m achine i s m odeled b y a n e xponential d istribution w ith u nknown
parameter 0.
onbasis
:
If theparamet
MIDTERM EXAM (ISYE8843 FALL 2004)
Chengyuan Ma
School of Electrical and Computer Engineering
Georgia Institute of Technology
Atlanta, GA 30332, USA
[email protected]
1. SOLUTION TO PROBLEM 1
th
ISyE8843
Brani Vidakovic
Labor Day Name:
Take Home Quiz 2
Mushrooms. The unhappy outcome of uninformed mushroom-picking is poisoning. In many cases such
poisoning is due to ignorance or a supercial ap
I SyE8843
Brani Vidakovic
Fliday, 8/27 / 04 Name:
1. Lifetime. A lifetime X of a particular m achine i s m odeled b y a n e xponential d istribution w ith u nknown
parameter 0.
onbasis
:
If theparamet
MIDTERM EXAM (ISYE8843 FALL 2004)
Chengyuan Ma
School of Electrical and Computer Engineering
Georgia Institute of Technology
Atlanta, GA 30332, USA
[email protected]
1. SOLUTION TO PROBLEM 1
th
ISYE 8843 Final Exam
Hongmei Chen
1. Bayesian Wavelet Shrinkage. This open ended question is essentially
asking to select a data set with noise present in it (a noisy signal, function, or
noisy image)
ISYE8843 Final
Jinyu Li
1. Question 1
I use Bayesian Wavelet Shrinkage to denoise. I choose a simple signal as following:
t=linspace(0,1,1024);
sig = (sin(5*pi*t)+2.0*cos(10*pi*t)+3.0*sin(15*pi*t).*ex
FINAL EXAM (ISYE8843 FALL 2004)
Chengyuan Ma
School of Electrical and Computer Engineering
Georgia Institute of Technology
Atlanta, GA 30332, USA
[email protected]
1. BAYESIAN WAVELET SHRINKAGE
Final Exam
Ni Wang
1
Bayesian Wavelet Shrinkage
Figure 1 shows the famous blocky function from Donoho and Johnstone (1994). Figure 2 shows the
plot of noisy function when random noise is added to the
FINAL EXAM
ISyE 8843: Bayesian Statistics
Brani Vidakovic
due before noon, Thursday 12/9/2004.
Name
1. Bayesian Wavelet Shrinkage. This open ended question is essentially asking to select a data set w
ISyE 8843 Bayes Statistics
Fall 2004
Midterm
Version 2.0
James D. Delaney
October 27, 2004
Problem 1: Nematodes
The Nematode data is an example of an unbalanced one-way layout. Assuming the one-way AN
MIDTERM EXAM
ISyE 8843: Bayesian Statistics
Brani Vidakovic
Friday, 10/15/2004.
Name
1. Nematodes. Some varieties of nematodes (roundworms that live in the soil and are frequently so small
they are in
Midterm Exam
ISyE8843
Abhyuday Mandal
22 October, 2004
1
Problem 1
The model is yij = i + ij ,
i = 1, . . . , k ; j = 1, . . . , ni , where k = 3, n1 = 9, n2 = 11 and n3 = 14. Among
the nine parameter
Bayesian Data Analysis, Midterm I
Bugra Gedik
[email protected]
October 23, 2004
Q1)
I have used Gibs sampler to solve this problem. 5,000 iterations with burn-in value of 1,000 is used. The result
ISyE 8843, Mid-term Exam
Tirthankar Dasgupta
1
Problem 1
We have the model
yij = i +
ij ,
i = 1, . . . , k ; j = 1, . . . , ni
where k = 3, n1 = 9, n2 = 11, n3 = 14.
We thus have nine parameters of in
ISyE 8843, Mid-term Exam
Tirthankar Dasgupta
1
Problem 1
We have the model
yij = i +
ij ,
i = 1, . . . , k ; j = 1, . . . , ni
where k = 3, n1 = 9, n2 = 11, n3 = 14.
We thus have nine parameters of in
Bayesian Data Analysis, Midterm I
Bugra Gedik
[email protected]
October 23, 2004
Q1)
I have used Gibs sampler to solve this problem. 5,000 iterations with burn-in value of 1,000 is used. The result
ISyE8843A, Brani Vidakovic
1
Handout 5
Priors
A prior is a sword and Achilles heel of Bayesian statistics. Priors are carriers of prior information that is
coherently incorporated via Bayes theorem to
ISyE8843A, Brani Vidakovic
1
Handout 4
Decision Theoretic Setup: Loss, Posterior Risk, Bayes Action
Let A be action space and a A be an action. For example, in estimation problems, A is the set of rea
ISyE8843A, Brani Vidakovic
1
Handout 3
Ingredients of Bayesian Inference
The model for a typical observation X conditional on unknown parameter is f (x|). As a function of ,
f (x|) = () is called lik
ISyE8843A, Brani Vidakovic
Handout 1
1
Probability, Conditional Probability and Bayes Formula
The intuition of chance and probability develops at very early ages.1 However, a formal, precise definitio