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Linear Methods for Regression
3.1 Introduction
A linear regression model assumes that the regression function E(Y |X) is
linear in the inputs X1 , . . . , Xp . Linear models were largely developed in
the precomputer
Articles
Increased methylation variation in epigenetic domains
across cancer types
2011 Nature America, Inc. All rights reserved.
Kasper Daniel Hansen1,2,10, Winston Timp24,10, Hctor Corrada Bravo2,5,10, Sarven Sabunciyan2,6,10,
Benjamin Langmead1,2,10,
Local Warming:
Climate Change Comes Home
Robert J. Vanderbei
November 2, 2011
Wharton Statistics
Univ. of Pennsylvania
http:/www.princeton.edu/rvdb
Introduction
There has been so much talk about global warming.
Is it real?
Is it anthropogenic?
Global warm
LOCAL WARMING
ROBERT J. VANDERBEI
Abstract. Using 55 years of daily average temperatures from a local weather station, I made a
least-absolute-deviations (LAD) regression model that accounts for three effects: seasonal variations,
the 11-year solar cycle,
c 20132014 Han Liu
Copyright
ORF350: Analysis of Big Data
Chapter 6
Inferential Analysis using Likelihood
The maximum likelihood estimator is asymptotically normal and efficient. What is the implication of this result? In this chapter we show that the as
Probability and Statistics
Overview
Han Liu
Department of Opera-ons Research and Financial Engineering
Princeton University
Thursday, February 7, 13
Last Lecture
Big Data Definition
Course Overview
Readings have been uploaded to the blackboard
syst
c 20132014 Han Liu
Copyright
ORF350: Analysis of Big Data
Chapter 7
Sufficiency Principle
When dealing with Big Data, an effective approach is to do data reduction. Data reduction
is the process of minimizing the amount of data that needs to be stored fo
Lecture 1: Overview
Han Liu
Department of Opera-ons Research and Financial Engineering
Princeton University
Wednesday, February 6, 13
Big Data
Collection of Data Sets that are
so Large and Complex
that they are difficult to process and analyze
usin
ORF350 (Fall 2013) Analysis of Big Data
Lecture: 1
Overview
Lecturer: Han Liu
Email: hanliu@princeton.edu
We provide an introductory paradigm of Big data analysis.
1
Big Data
Data Modeling: modeling data as a big matrix or big graph.
Massive data: data w
ORF 309
Solutions to Homework 11
Fall 2013
Not to be submitted
Exercise 4.2
Similarly to Example 4.4 on page 193-194, the system can be analyzed by using a Markov
chain with 8 states:
state
state
state
state
state
state
state
state
0
1
2
3
4
5
6
7
Today
R
ORF 309
Solutions to Homework 9
Fall 2013
Due on Nov. 26, 2013
Exercise 1.13
We are given that X gamma(, ) (or X (, ). That is,
Pcfw_X dx =
ex (x)1
dx,
()
x0
so using the dx notation, we can write
Pcfw_cX dx = Pcfw_cX [x, x + dx]
x x dx
,+
cc
c
e(x/c) (x/
ORF 309
Solutions to Homework 10
Fall 2013
Due on Dec. 2, 2013
Exercise 3.9
To show X is a Gaussian process, we need to show that for any n 1, t1 , , tn [0, 1],
(Xt1 , , Xtn ) is a Gaussian vector.
It is equivalent to show for any Rn , n=1 i Xti is a Gaus
ORF 309
Solutions to Homework 8
Fall 2013
Due on Nov. 20, 2013
Exercise 5.60
Let us use minutes as the units of time. Denote by N the given Poisson process with rate
. The event that two customers arrived during the rst hour is cfw_N60 = 2.
(a) The event
ORF 309
Solutions to Homework 7
Fall 2013
Due on Nov. 13, 2013
Exercise 5.4
For each i cfw_A, B, C , dene
Ti := the time it takes for the clerk to serve customer i.
In order for A to still be in the post oce after the other two have left, B must nish befo
ORF 309
Solutions to Homework 6
Fall 2013
Due on Nov. 6, 2013
Exercise 1
In this question, we will use Theorem 7 in Prof. Cnlars lecture notes on Branching Pro
cesses, which states that if 1, then = 1, while if > 1, then 0 < < 1 and is the
smallest soluti
ORF 309
Solutions to Homework 5
Fall 2013
Due on Oct. 16, 2013
Exercise 3.3
By the denition of the conditional expectation and conditional probability,
3
E[X |Y = i] =
3
j Pcfw_X = j |Y = i =
j =1
j
j =1
Pcfw_X = j, Y = i
.
Pcfw_ Y = i
Expand Pcfw_Y = i,
ORF 309
Solutions to Homework 4
Fall 2013
Due on Oct. 9, 2013
Exercise 9.4
(a) (NEW QUESTION COMPARED TO BOOK) The system corresponding to the structure function (x) = x1 max(x2 , x3 , x4 )x5 is given by the series of the following three
subsystems:
comp
ORF 309
Solutions to Homework 3
Fall 2013
Due on Oct. 2, 2013
Exercise 2.40
As usual, we model the sequence of games as a sequence of Bernoulli trials, in other words,
as a Bernoulli process. Let
1 if A wins the ith game
Xi =
, i cfw_1, 2, ..
0 if B wins
ORF 309
Solutions to Homework 2
Fall 2013
Due on Sep. 25, 2013
Exercise 2.16
Let X be the random variable describing the number of the people showing up for the specic
ight. As the airline believes that there is a 95 percent probability that someone who m
ORF 309
Solutions to Homework 1
Fall 2013
Due on Sep. 18, 2013
Exercise 1.4
Let E , F , G be three events.
a) only F occurs: F E c Gc
b) both E and F but not G: E F Gc
c) at least one event occurs: E F G
d) at least two events occur: (E F Gc ) (E F c G) (