APPLICATIONS
309
subject to
ij
Vij
>
0.
(15.8)
Here, x is our measurement decision, W captures what we observe if we choose to
make the measurement, and y is our implementation decision. R1 is the amount of
money we have to invest. The measurement problem

MEASUREMENT POLICIES
79
for 0 < c < 1. If we explore, we would choose measurement x with probability
1/|#|. This means that in the limit, the number of times we will measure x is given
by
oo
'
n=l
'
This assures us that we will estimate each measurement x

UPDATING FOR NON-GAUSSIAN PRIORS
49
observation n + 1 belongs to category k, we increment oQ by 1 and leave the other
components of an unchanged.
2.3.5 Learning an Unknown Variance*
Our last learning model takes us back to the basic setting of one-dimensi

THE BAYESIAN VIEW
39
is better than another lineup that includes three from the same group with two
different people. If the scoring of these five people is higher than we had
expected, we would probably raise our belief about the other group, since there

AREAS OF APPLICATION
9
Who are the best hitters that you should choose for your baseball team? It is
necessary to see how a player hits in game situations, and of course these are
very noisy observations.
What plays work the best for your football team?

ORIE 3800: Information Systems and Analysis
ORIE 3800
Aug 22, 2012
Product Pricing
We would like to price airline tickets so as
to maximize revenue.
We learn about demand for a ight as we
sell tickets.
The information collected depends on how
we price eac

ORIE 3800: Information Systems and Analysis
This course will show you how to make decisions about information, and how decisions about
information affect the world at large. We will consider questions such as:
How much time should a venture capitalist sp

KNOWLEDGE GRADIENT FOR CORRELATED BELIEFS
99
Now we are trying to find the best price for our laptop. We start with an initial
guess of the sales volume we will for prices in $100 increments from 700 to
1200. We start at $1100, and sales are much lower t

PROBLEMS
129
mean 0.267 and standard deviation of 0.10. Finally assume that we are going to
approximate the observed batting average from at least*! 0 at-bats as normally
distributed with mean:
H
Wrr
where H is the number of hits and m is the number of at

THE PROBLEM OF PRIORS
119
Figure 5.8 The effect of the prior on the search process: (a) Unbiased prior, (b) Resulting
measurements, (c) Prior that is biased low. (d) A low prior produces measurements focused
around whatever point is chosen first, (e) Prio

INDIFFERENCE ZONE SELECTION
289
/4(2) = . = /X(M) = 0 a n d M(i) ^- Because the measurement noise is common
for all alternatives, we can also suppose that o^ \. The quantity Zi in (14.2)
then represents the deviation of the difference in the sample means

SEQUENTIAL PROBABILITY RATIO TEST
259
Figure 12.1 The expected risk as a function of the prior probability that Ho is true.
where L(Wk)
=
,Wkl is the likelihood ratio for a single observation. We next use
Bayes' rule to compute the posterior P Q + 1 (Wn)

BAYESIAN MODELING FOR DYNAMIC PRICING
239
is, there is a price p for which / i (p) = $2 (p) = / Substituting this price into (11.7)
gives us
q^
1
=
Qnfxn+\l-f)
qnfXn+1(l
i-x71
~ / ) 1 _ X " + 1 + (1 - qn) F " + 1 ( l - / ) 1 _ J f n + 1
qnfXn+\l-!)l-Xn+1

A BRIEF REVIEW OF LINEAR REGRESSION
189
Just as [i is a random variable (our truth), so is #, which is the truth about the effect
of each feature. We learned that we get tremendous benefits from exploiting the
covariance between two alternatives. The cova

LARGER SETS
209
drugs in the same class will be correlated. If a patient reacts adversely to sensitizers,
all drugs of this type will tend to perform poorly. In any case, however, our prior is not
able to capture all the nuances of the problem. Instead, t

OBJECTIVE FUNCTIONS
169
7.5.1 Designing Versus Controlling
We have already compared two broad settings in which optimal learning arises: offline
learning, where we conduct a series of measurements to design a process or system
under some sort of measureme

UPPER CONFIDENCE BOUNDING
149
vides tight minimax bounds on the regret for problems with continuous arms,
but these are exponential in the number of dimensions.
Response-surface bandits - There are many applications where our beliefs about the
value of di

THE KNOWLEDGE GRADIENT FOR SOME NON-GAUSSIAN DISTRIBUTIONS
109
where N+1 is the number of units of product x ordered on the next day. We assume
that iV+1 ~ Poisson (Xx). If we are looking for the largest rate, the definition of
the KG factor is once again

Information Systems and Analysis
ORIE3800 Fall 2012
Recitation 3
September 17, 2012
Question 1:
Normal distribution with unknown mean: a random sample of n students is drawn from a large
population, and their weights are measured. The average weight of th

Information Systems and Analysis
ORIE3800 Fall 2012
Recitation Solution
November 12, 2012
Question 1 Multi-armed Bandit Problem in nite number of steps
A computer receives a string of documents, where documents are coming from some distribution. Every tim

3. a.
After a single trial (1000 simulations), the following values were obtained:
^
V s=0.8767
95% Confidence Interval = [0.8696, 0.8839]
3. b.
Our strategy of finding the next option to sample was done with a ratio of mni to ni. The ratio
method was cho

ORIE 3800: Assignment 7
Instructor: Krishnamurthy Iyer
April 21, 2014
Due on: April 16, 2014, 5pm
Please submit your homework in the dropbox in Rhodes 2nd oor lobby.
1. Suppose n bidders participate in a rst price auction for an item. The common value V o

Name: Net ID:
ORIE 3800: Information Systems and Analysis
Spring 2014 Prelim Exam
0 This exam is open notes and open book, i.e., you may use any material from the ORIE
3800 Spring 2014 class, notes, recitation materials. You may not use laptops, cellp

ORIE 3800: Assignment 6
Instructor: Krishnamurthy Iyer
March 25, 2014
Due on: Mar 26, 2014, 5pm
Please submit your homework in the dropbox in Rhodes 2nd oor lobby.
1. Consider the observational learning setting: Individuals 1, 2, - - - ,N sequentially (in

ORIE 3800: Assignment 2
Instructor: Krishnamurthy Iyer
February 17, 2014
Due on: Feb 12, 2014, 5pm
Please submit your homework in the dropbox in Rhodes 2nd oor lobby.
1. Consider the riskneutral Elementary Game with the noisy signal as studied in class.
A

ORIE 3800: Assignment 5
Instructor: Krishnamurthy Iyer
March 13, 2014
Due on: Mar 19, 2014, 5pm
Please submit your homework in the dropbox in Rhodes 2nd oor lobby.
1. Consider the comparison with a standard problem with the following parameters:
(1:1
6:1