Copyright c 2013, Lang Tong. EE5640: Statistical Inference and Decision
ECE 5640: Statistical Inference and Decision
Probability Models
http:/blackboard.cornell.edu
Lang Tong
School of Electrical and Computer Engineering
Cornell University, Ithaca, NY 148
ECE 5640: Statistical Inference & Decision
Instructor: Prof. Lang Tong
Due Sep. 23, 2013
Cornell University
HW1 SolutionSheet
1 Conditional Gaussian distribution. Consider jointly Gaussian random variables
(Y, Z) N (, ) where
y
yy yz
=
, =
.
z
zy zz
(a) S
ECE 5640: Statistical Inference & Decision
Instructor: Prof. Lang Tong
Due Sep. 23, 2013
Cornell University
HW 1: Probability and Statistical Models.
1 Conditional Gaussian distribution. Consider jointly Gaussian random variables
(Y, Z) N (, ) where
yy yz
ECE 5640: Statistical Inference & Decision
Instructor: Prof. Lang Tong
Due September 30, 2013
Cornell University
HW 2: Neyman-Pearson Test
1 (Levy [1] Chapter II 2.8 ) Consider hypotheses defined by the Laplacian distributions with different variances:
1
ECE 5640 Detection & Estimation
Instructor: Prof. Lang Tong
Fall 2009
Cornell University
Prelim 1
Date: Oct 21, 2009, 8:00PM-9:30PM. PH 403.
This is a 90 min. closed-book exam. There is no need for a calculator as the exam does not involve
numerical eva
ECE 5640: Statistical Inference & Decision
Instructor: Prof. Lang Tong
Due September 30, 2013
Cornell University
HW2 SolutionSheet
1 (Levy [1] Chapter II 2.8 ) Consider hypotheses defined by the Laplacian distributions with different variances:
H0 : f0 (y
ECE 5640 Detection & Estimation
Instructor: Prof. Lang Tong
Fall 2009
Cornell University
Prelim 1
Date: Oct 21, 2009, 8:00PM-9:30PM. PH 403.
This is a 90 min. closed-book exam. There is no need for a calculator as the exam does not involve
numerical eva
c
Copyright 2013,
Lang Tong. EE5640: Statistical Inference and Decision
ECE 5640: Inference and Decisions
Multi-Stage Optimal Decision
over Finite Horizon
http:/blackboard.cornell.edu
Lang Tong
School of Electrical and Computer Engineering
Cornell Univers
ECE 5640 Homework 3
Instructor: Qing Zhao
Oce: 325 Rhodes Hall
Email: [email protected]
Due in class on September 30
1
Materials
POMDP
2
Assignment
1. Dynamic Multichannel Access: (10 points)
Consider N time-slotted channels. In each slot t, the state of
ECE 5640 Homework 2
Instructor: Qing Zhao
Oce: 325 Rhodes Hall
Email: [email protected]
Due in class on September 23
1
Materials
Formulation of MDP over a nite horizon.
Policy evaluation.
Finding the optimal policy using backward induction.
2
Assignment
ECE 5640 Homework 1
Instructor: Qing Zhao
Oce: 325 Rhodes Hall
Email: [email protected]
Due in class on September 2
1. A die is rolled repeatedly. Which of the following sequences cfw_Xn are Markov chains? Prove
n=0
your statement. For those that are, giv
ECE 5640 Homework 4
Instructor: Qing Zhao
Oce: 325 Rhodes Hall
Email: [email protected]
Due in class on October 7
1
Materials
Techniques for establishing structured optimal policies:
Interchange argument.
Threshold optimal policies.
Modularity and mono
ECE 5640 Homework 5
Instructor: Qing Zhao
Oce: 325 Rhodes Hall
Email: [email protected]
Due in class on October 21
1
Materials
MDP over Innite Horizon under Discounted Reward:
Policy evaluation.
Value iteration.
Policy iteration.
2
Assignment
1. Random
ECE 5640 Homework 6
Instructor: Qing Zhao
Oce: 325 Rhodes Hall
Email: [email protected]
Due in class on November 18
1
Materials
Negative dynamic programming.
The optimal stopping problem.
2
Assignment
1. Negative Dynamic Programming
Prove the following s
ECE 5640 Homework 7
Instructor: Qing Zhao
Oce: 325 Rhodes Hall
Email: [email protected]
Due by 5pm on December 4
1
Materials
Markov chain and Markov reward process.
MDP under average reward over an innite horizon.
2
Assignment
1. Markov chain and Markov
ECE 5640 Homework 2 Solution
Instructor: Qing Zhao
Oce: 325 Rhodes Hall
Email: [email protected]
1. An Inventory Control Problem
st stock
at units ordered
orders arrive D demand is fullled
t
t+1
(a) The MDP formulation of the problem is summarized as below
c
Copyright 2013,
Lang Tong. EE5640: Statistical Inference and Decision
ECE 5640: Statistical Inference and Decisions
Introduction to Estimation
http:/blackboard.cornell.edu
Lang Tong
School of Electrical and Computer Engineering
Cornell University, Ithac
ECE 5640: Statistical Inference & Decision
Instructor: Prof. Lang Tong
Due December 2, 2013
Cornell University
HW6 Solution Sheet
1 (Placing 3 random digits) Consider the following game. At each time, you are given
a number randomly chosen from 0, 1, , 9.
ECE 5640: Statistical Inference and Decision
http:/blackboard.cornell.edu/
Course Description: This course introduces fundamental theories and practical ideas in statistical
inference a decision. Specific topics include Neyman-Pearson, Bayes, and minimax
ECE564 Prelim
Instructor: Lang Tong
Office: 384 Rhodes Hall
Tel: 5-3900. Email: [email protected]
March 15, 2007
This is a 75 min. closed-book exam. There is no need for a calculator as the exam does not involve numerical evaluation. You are
allowed
ECE 5640: Statistical Inference & Decision
Instructor: Prof. Lang Tong
Due November 6, 2013
Cornell University
HW 4: Bayesian Estimation and Decision
1 (Chapter IV.1) Suppose that () is a random parameter with prior
1/ 1 e
() =
0
otherwise.
Given = , supp
ECE 5640 Inference and Decisions
Instructor: Prof. Lang Tong
Fall 2010
Cornell University
ECE 5640 Prelim
Date: Oct 13, 2010, 8:40AM-9:50AM. PH 307.
This is a 70 min. closed-book exam. There is no need for a calculator as the exam does not involve
numer
ECE 5640: Statistical Inference & Decision
Instructor: Prof. Lang Tong
Due October 9, 2013
Cornell University
HW 3: Bayesian and Minimax Detection
1 (Simple binary hypotheses) Consider binary hypotheses
1 y (0, 1)
2y y (0, 1)
H0 : Y f0 (y) =
vs. H1 : Y f1
ECE 5640: Statistical Inference & Decision
Instructor: Prof. Lang Tong
Due November 6, 2013
Cornell University
HW4 Solution Sheet
1 (Chapter IV.1) Suppose that () is a random parameter with prior
1/ 1 e
() =
0
otherwise.
Given = , suppose that observation
ECE 5640: Statistical Inference & Decision
Instructor: Prof. Lang Tong
Due November 18, 2013
Cornell University
HW4 Solution Sheet
1 (Gaussian mean) Consider N (0, n), and given = , Y N (, 1). Find the
Bayesian decision under the squared error cost.
Solut
ECE 5640: Statistical Inference & Decision
Instructor: Prof. Lang Tong
Due November 18, 2013
Cornell University
HW 5: Single Stage Decision
1 (Gaussian mean) Consider N (0, n), and given = , Y N (, 1). Find the
Bayesian decision under the squared error co
ECE 564 Detection & Estimation
Instructor: Prof. Lang Tong
Spring 2008
Cornell University
Prelim 1
Date: March 12, 2008, 8:30PM-10:00PM. PH 213.
This is a 90 min. closed-book exam. There is no need for a calculator as the exam does not
involve numerical
ECE 5640 Inference and Decisions
Instructor: Prof. Lang Tong
Fall 2013
Cornell University
ECE 5640 Prelim II
Date: December 4, 2013, 8:00PM-10:00PM. PH 307.
This is a 120 min. closed-book exam. No electronic devices (tablet, smart phone, calculator, lap
ECE 5640 Inference and Decisions
Instructor: Prof. Lang Tong
Fall 2013
Cornell University
ECE 5640 Prelim
Date: Oct 16, 2013, 8:40AM-9:50AM. PH 307.
This is a 70 min. closed-book exam. No electronic devices (tablet, smart phone, calculator, laptops)
are