Bayesia Lab Choice Modeling 1

Modeling Vehicle Choice and Simulating Market
Share with Bayesian Networks

A case study about predicting the U.S. market share of the Porsche Panamera
using the Bayesia Market Simulator

White Paper 2010/II

Stefan Conrady, stefan.conrady@conradyscience.com

Dr. Lionel Jouffe, jouffe@bayesia.com

December 18, 2010

Conrady Applied Science, LLC - Bayesia’s North American Partner for Sales and Consulting

Simulating Market Share with the Bayesia Market Simulator

Table of Contents

Modeling Vehicle Choice and Simulating Market Share with Bayesian Net-
works
Abstract/Executive Summary 1
Objective 1
About the Authors 2
Stefan Conrady 2
Lionel Jouffe 2
Acknowledgements 2

Introduction 2
Bayesian Networks for Choice Modeling 3

Case Study 4
Porsche Panamera 4
Common Forecasting Practices 6

Tutorial 6
Data Preparation 6
Consumer Research 6
Variable Selection 7
Set of Choice Alternatives 7
Filtered Values (Censored States) 7
Data Modeling 8
Data Import 8
Missing Values 9
Discretization 10
Variable Classes and Forbidden Arcs 12
Unsupervised Learning 13

Simulation 14
Product Scenario Baseline 14
Product Scenario Simulation 16
Substitution and Cannibalization 19
Market Scenario Simulation 20

Conrady Applied Science, LLC - www.conradyscience.com
i


Limitations 20

Outlook 20

Summary 21

Appendix 22
Utility-Based Choice Theory 22
Multinomial Logit Models 22
Stated Preference Data 23
Revealed Preference Data 23
NVES Variables 23

References 25

Contact Information 26
Conrady Applied Science, LLC 26
Bayesia SAS 26

Copyright 26

Conrady Applied Science, LLC - www.conradyscience.com
ii


This innovative approach is explained step-by-step in a
Modeling Vehicle Choice study about the introduction of the new Porsche Panam-
and Simulating Market era in the U.S. market. The results con rm that market
share simulation with Bayesian networks is feasible even
Share with Bayesian in niche markets that provide relatively few observa-
tions.
Networks
We believe that making this method and the tools acces-
sible to practitioners is an important contribution to
Abstract/Executive Summary real-world marketing. We are con dent that for many
We present a new method and the associated work ow companies this approach can yield a step-change in their
for estimating market shares of future products based forecasting ability.
exclusively on pre-introduction data, such as syndicated
studies conducted prior to product launch. Our ap- Objective
proach provides a highly practical, fast and economical This tutorial is intended for marketing practitioners, who
alternative to conducting new primary research. are exploring the use of Bayesian network for their
work. The example in this tutorial is meant to illustrate
With Bayesian networks as the framework, and by em- the capabilities of BayesiaLab with a real-world case
ploying the BayesiaLab and Bayesia Market Simulator study and actual consumer data. Beyond market re-
software packages, this approach helps market research- searchers, analysts in many elds will hopefully nd the
ers and product planners to reliably perform market proposed methodology valuable and intuitive. In this
share simulations on their desktop computers1 , which context, many of the technical steps are outlined in great
would have been entirely inconceivable in the past. detail, such as data preparation and the network learn-

Market Share Simulation Work ow with BayesiaLab and Bayesia Market Simulator

Scenario
Market Data
from Survey
De nition
from Analyst

Projection
Market Model Simulation
Modeling
Bayesian Network Bayesia Market
BayesiaLab
Simulator
Market Shares

1 BayesiaLab and Bayesia Market Simulator can run on a wide range of operating systems, including Windows, OS X,
Linux/Unix, etc.

Conrady Applied Science, LLC - www.conradyscience.com 1


ing, as they are applicable to research with BayesiaLab in Bayesian networks. BayesiaLab enjoys broad acceptance
general, regardless of the domain. in academic communities as well as in business and in-
dustry. The relevance of Bayesian networks, especially in
This paper is part of a series of tutorials, which are ex-
the context of market research, is highlighted by
ploring a broad range of real-world applications of
Bayesia’s strategic partnership with Procter & Gamble,
Bayesian networks. who has deployed BayesiaLab globally since 2007.

About the Authors Acknowledgements
Strategic Vision, Inc.2 (SVI) has generously made their
Stefan Conrady
Stefan Conrady is the co-founder and managing partner 2009 New Vehicle Experience Survey available as a data

of Conrady Applied Science, LLC, a privately held con- source for this case study. In this context, special thanks
go to Alexander Edwards, President, Automotive Divi-
sulting rm specializing in knowledge discovery and
probabilistic reasoning with Bayesian networks. In 2010, sion of Strategic Vision.

Conrady Applied Science was appointed the authorized
We would also like to thank Jeff Dotson3, John Fitzger-
sales and consulting partner of Bayesia SAS for North
ald4 and Frank Koppelman5 for their ongoing coaching
America. Stefan Conrady has many years of marketing, and their valuable comments on this paper. However, all
product planning and market research experience with
errors remain the responsibility of the authors.
Mercedes-Benz, BMW Group, Rolls-Royce Motor Cars
and Nissan. In the context of these management assign- Finally, Kenneth Train’s6 books and articles have been
ments, Stefan has been based in Europe, North America very helpful over the years as we explored the eld of
and Asia. consumer choice modeling.

Lionel Jouffe Introduction
Dr. Lionel Jouffe is co-founder and CEO of France-based
For the vast majority of businesses, market share is a key
Bayesia SAS. Lionel Jouffe holds a Ph.D. in Computer
performance indicator. Market share is used as a metric
Science and has been working in the eld of Arti cial
that allows comparing competitive performance inde-
Intelligence since the early 1990s. He and his team have
pendently from overall market size and its uctuations.
been developing BayesiaLab since 1999 and it has
emerged as the leading software package for knowledge In the product planning process, the expected market
discovery, data mining and knowledge modeling using share is critical, along with the overall market forecast,

2 www.strategicvision.com
3 Assistant Professor of Marketing, Vanderbilt University, Owen Graduate School of Management.
4 President, Fitzgerald Brunetti Productions, Inc., New York.
5 Professor Emeritus, Professor Emeritus of Civil and Environmental Engineering, Robert R. McCormick School of En-
gineering and Applied Science, Northwestern University.
6 Adjunct Professor of Economics and Public Policy, University of California, Berkeley.



as together they de ne the sales volume expectation, “oracles” that allow us to “deliberately reason about the
which, for obvious reasons, is a key element in most consequences of actions we have not yet taken.” 8
business cases.
Bayesian Networks for Choice Modeling
As a result, it is critical for decision makers to correctly Using Bayesian networks9 as the general framework for
predict the future market shares of products not yet de- modeling a domain or system has many advantages,
veloped. The task of such market share forecasts typi- which Darwiche (2010) summarizes as follows:
cally falls into marketing and market research depart-
ments, who are mostly closely involved with understand- • “Bayesian networks provide a systematic and localized
ing consumer behavior and, more speci cally, the method for structuring probabilistic information
product choices they make. about a situation into a coherent whole […]”

If we fully understood the consumer’s decision making • “Many applications can be reduced to Bayesian net-
process and observed all components of it, we could work inference, allowing one to to capitalize on Bayes-
simply generate a deterministic model for predicting ian network algorithms instead of having to invent
future consumer choices. However, we do not and it is specialized algorithms for each new application.”
obvious that many elements contributing to a consumer’s
Given the very attractive properties of Bayesian net-
purchase decision are inherently unobservable. Despite
works for representing a wide range of problem do-
our limited comprehension of the true human choice
mains, it seems appropriate applying them for choice
process, there are a number of tools that still allow mod-
modeling as well. In particular, the BayesiaLab software
eling consumer choice with what is observable, and ac-
package has made it very convenient to automatically
counting for what will remain unknowable. In this con-
machine-learn fairly large and complex Bayesian net-
text, and based on the seminal works of Nobel-laureate
works from observational data.
Daniel McFadden7, choice modeling has emerged as an
important tool in understanding and simulating con- Beyond the convenience and speed of estimating Bayes-
sumer choice. ian networks with BayesiaLab, there are three fundamen-
tal differences in modeling consumer choice with Bayes-
Such choice models serve a representation of the “real
ian networks compared to traditional discrete choice
world” and thus become, what Judea Pearl likes to call
models.10

7 Daniel McFadden received, jointly with James Heckman, the 2000 Nobel Memorial Prize in Economic Sciences;
McFadden’s share of the prize was “for his development of theory and methods for analyzing discrete choice”.
8 A recurring quote from Judea Pearl’s many lectures on causality.
9 A Bayesian network is a graphical model that represents the joint probability distribution over a set of random vari-
ables and their conditional dependencies via a directed acyclic graph (DAG). For example, a Bayesian network could
represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to
compute the probabilities of the presence of various diseases. A very concise introduction to Bayesian networks can be
found in Darwiche (2010).
10 A very brief overview about utility-based choice models is provided in the appendix.



1. Whereas utility-based choice models, such as multi- As a result we obtain a choice probability as a function
nomial logit models (MNL), will “ atten” the vector of product and consumer attributes.
of attribute utilities into a single scalar value, Bayes-
In order to obtain a product’s projected market share, we
ian networks do not inherently restrict all the di-
then need to simulate choice probabilities across all
mensions relating to choice. For example, learning a
Bayesian network on observed vehicle choices might product scenarios and across all individuals in the popu-
lation under study. For this speci c purpose Bayesia SAS
reveal that fuel economy and vehicle price are sub-
has developed the Bayesia Market Simulator, which uses
ject to tradeoff, while safety is a nonnegotiable basic
requirement for the consumer. Correctly recognizing the Bayesian networks generated by BayesiaLab. Both
tools will play a central role in this case study.
such dynamics are obviously critical for making
predictions about future consumer choices.
Case Study
2. Bayesian networks are nonparametric and therefore To illustrate the entire market share estimation process
do not require the speci cation of a functional form. with Bayesian networks, we have derived a case study
No assumptions need to made regarding the form of from the U.S. auto industry. More speci cally, we will
links between variables. Potentially nonlinear pat- model consumer choice behavior in the high-end vehicle
terns are therefore not an issue for model estimation market based on 2009 survey data. This is an interesting
or simulation. point in time, as it precedes the launch of the new Por-
sche Panamera in model year 2010 (MY 2010), which
3. Bayesian networks are inherently probabilistic and
will be the focus of our study.
as such there is no need to specify an error term. An
error would be needed in a traditional choice model Porsche Panamera
to make it non-deterministic.

4. In BayesiaLab all computations are natively discrete
and therefore no transformation functions, such as
logit or probit, are needed. Given that we are deal-
ing with discrete consumer choices, this all-discrete
approach is an advantage.

For our case study we use BayesiaLab 5.0 Professional
Edition to learn a Bayesian network from consumer
choices in the form of stated preference (SP) or revealed
After the highly successful Cayenne, a four-door luxury
preference (RP) data.11 ,12 The learned Bayesian network
SUV, the Panamera is Porsche’s second vehicle with four
allows us to compute the posterior probability distribu-
doors. Clearly in uenced by the legendary 911’s styling,
tion in each choice situation, including hypothetical
the Panamera is offers sports-car looks and performance
product alternatives (and even hypothetical consumers).
while comfortably accommodating four passengers. It

11 The properties of Stated Preference (SP) and Revealed Preference (RP) data are explained in the appendix.
12 Although we focus here exclusively on machine-learning consumer behavior, within the BayesiaLab framework we
can also utilize expert knowledge about consumer behavior. For instance, vehicle dealers and their salespeople will have
extensive knowledge about how consumer behave in the showroom. A special Knowledge Elicitation module in
BayesiaLab can formally capture such expertise and build a new Bayesian network from it or augment an existing one.
Knowledge Elicitation with BayesiaLab will be the subject of a separate tutorial to be published in the near future.



enters a segment with well-established contenders, such Beyond these traditional premium sedans, there are a
the Mercedes-Benz S-Class13 ,
the BMW 7-series14 and number of less conventional products that one can as-
the Audi A815, shown below in that order. sume to be in the Panamera’s competitive eld as well.
The coupe-like Mercedes-Benz CLS16 would probably
fall into this category.

Finally, the new Panamera may draw customers away
from Porsche’s own product offerings, such as the Cay-
enne17 , an effect that is often referred to as “product
substitution” or “product cannibalization.”

It is not our intention to speculate about potential
product interactions, but rather to attempt learning from

13 MY 2010 shown
14 MY 2009 shown
15 MY 2009 shown
16 MY 2010 shown
17 MY 2009 shown



revealed consumer behavior in a very formal way with Tutorial
Bayesian networks.
In this tutorial we will explain each step from data
In order not to prematurely restrict our consumer choice preparation to market share simulation using BayesiaLab
set, we have de ned a broad set of competitors for our and Bayesia Market Simulator, according to the follow-
purposes and included all non-domestic luxury vehicles18 ing outline:
(including Light Trucks) priced above $75,000.19
1. Data preparation (external)
What was certainly a very real task for Porsche’s product
2. BayesiaLab:
planning team in recent years, i.e. predicting the Panam-
era market share, now becomes the topic of our case a. Data import
study and tutorial. Our objective is to predict what mar-
ket share the Panamera will achieve without conducting b. Data modeling
any new research, strictly using RP data from before the
3. Baseline product scenario generation (external)
product launch.
4. Bayesia Market Simulator:
Common Forecasting Practices
Although we have no knowledge of the speci c forecast- a. Network import
ing methods at Porsche, we know from industry experi-
ence that volume and market share forecasts are often b. De nition of scenarios

determined through a long series of negotiations20 be-
c. Market share simulation
tween stakeholders, typically with an optimistic market-
ing group on one side and a skeptical CFO on the other. Notation
While expert consensus may indeed be a reasonable heu-
ristic for business planning, the lack of forecasting for- To clearly distinguish between natural language,
malisms is often justi ed by saying that forecasting is at software-speci c functions and study-speci c variable
least as much art as it is science. names, the following notation is used:

The authors believe strongly that there is great risk in • BayesiaLab and Bayesia Market Simulator functions,
relying too heavily on “art”, which is inherently non- keywords, commands, etc., are shown in bold type.
auditable, and have therefore been pursuing easily trac-
• Variable/node names are capitalized and italicized.
table, but scienti cally sound methods to support mana-
gerial decision making, especially in the context of fore- Data Preparation
casting. With this in mind, this very formal and struc-
tured forecasting exercise was consciously chosen as the Consumer Research
topic of the tutorial. This tutorial utilizes the 2009 New Vehicle Experience
Survey, a syndicated study conducted annually by Strate-
gic Vision, Inc., which surveys new vehicle buyers in the

18 We followed the SVI segmentation and included “Luxury Car”, “Premium Coupe”, “Premium Convertible/Roadster”
and “Luxury Utility” in our selection.
19 The $75,000 threshold was chosen as it marks the lower end of the Panamera price range.
20 As an interesting aside, these negotiations are usually Markovian in nature, i.e. the starting point of today’s negotia-
tion only depends on the outcome of the previous negotiation.



U.S. This study is widely used in the auto industry and it cles actual buyers did consider and which vehicles they
serves one of the primary market research tools. NVES disposed in the context of their most recent purchase.23
contains over 1,000 variables and close to 200,000 re-
As mentioned in the case study introduction, we included
spondent records. In large auto companies, hundreds of
“Luxury Car”, “Premium Coupe”, “Premium
analysts typically have access to NVES, most often
through the mTAB interface provided by Productive Ac- Convertible/Roadster” and “Luxury Utility” 24 in the
choice set and we further restricted it by excluding all
cess, Inc. (PAI).21
domestic vehicles and vehicles priced below $75,000. For
Variable Selection this segment of assumed Panamera competitors we have
Compared to traditional statistical models, Bayesian approximately 1,200 unweighted observations in the
networks require much less “care” in terms of variable 2009 NVES, which, on a weighted basis, re ect ap-
selection, as overparameterization is generally not an proximately 25,000 vehicles purchased in 2009.
issue. So, although we could easily start with all 1,000+
Filtered Values (Censored States)
variables, for expositional clarity we will initially select
Although in BayesiaLab we can be less rigorous regard-
only about 50 variables22 from the following categories,
ing the maximum number of variables, we still need to
which we assume to capture relevant characteristics of
both the consumer and the product: be conscious of the information contained in them.

For instance, we need to distinguish unobserved values
1. Vehicle/product attributes, e.g. brand, segment, num-
from non-existing values, although at rst glance both
ber of cylinders, transmission, drive type, etc.
appear to be “simple” missing values in the database.
2. Consumer demographics, e.g. age, income, gender, etc. BayesiaLab has a unique feature that allows treating
non-existing values as Filtered Values or Censored States.
3. Vehicle-related consumer attitudes, e.g. “I want to
look good when driving my vehicle”, “I want a basic,
no-frills vehicle that does the job,” etc. To explain Filtered Values we need to resort to an auto-
motive example from outside our speci c study. We as-
Set of Choice Alternatives
sume that we have two questions about trailer towing.
Beyond variable selection, we must also de ne the set of
We rst ask, “do you use your vehicle for towing?”, and
choice alternatives and assume which vehicles a potential then, “what is the towing weight?” If the response to the
Panamera customer would consider. Not only that, but
rst question is “no”, then a value for the second one
we also need to make sure that all choice alternatives for
cannot exist, which in BayesiaLab’s nomenclature is a
the Panamera’s choice alternatives are included. For in- Filtered Value or Censored State. We actually must not
stance, if we included the Porsche Cayenne in the choice
impute a value for towing weight in this case and instead
set, then the Mercedes-Benz M-Class and the BMW X5
Filtered Value code will indicate this special condition.
should be included too, and so on. One might argue that
the vehicle purchase might be an alternative to a kitchen On the other hand, a respondent may answer “yes”, but
renovation or the purchase of a boat. Expert knowledge then fail to provide a towing weight. In this case, a true
is clearly required at this point as to how far to expand value for the towing weight exists, but we cannot ob-
the choice set. Furthermore, SVI’s NVES can also help us serve it. Here it is entirely appropriate to impute a miss-
in this regard as it contains questions about what vehi-

21 www.paiwhq.com
22 A list of all variables used is given in the appendix. It should be noted that even 50 variables would create a major
computational challenge with MNL models.
23 Martin Krzywinski’s visualization tool, Circos, is highly recommended for the interpretation of cross-shopping behav-
ior: www.mkweb.bcgsc.ca/circos/
24 According to SVI’s segment de nition.



ing value, as we will explain as part of the Data Import
procedure.

To indicate Filtered Values to BayesiaLab, we will need
to apply a study-speci c logic and recode the relevant
variables in the original database. Most statistical soft-
ware package have a set of functions for this kind of
task.

For example, in STATISTICA this can be done with the
Recode function.

The table displayed in the Data Import wizard shows the
individual variables as columns and the respondent re-
cords as rows. There are a number of options available,
such as for Sampling. However, this is not necessary in
our example given the relatively small size of the data-
base.

Clicking the Next button prompts a data type analysis,
which provides BayesiaLab’s best guess regarding the
data type of each variable.

Alternatively, this recoding logic can also be expressed Furthermore, the Information box provides a brief sum-
with the following pseudo code: mary regarding the number of records, the number of
missing values, ltered states, etc.
IF towing=yes THEN towing weight=unchanged

IF towing=no THEN towing weight=FV (Filtered Value)

A simple Excel function will achieve the same and it is
assumed that the reader can implement this without fur-
ther guidance.

Although Filtered Values are very important in many
research contexts, hence the emphasis here, our case
study does not require using them.

Data Modeling

Data Import
To start the analysis with BayesiaLab, we rst import the
For this example, we will need to override the default
database, which needs to be formatted as a CSV le.25
data type for the Unique Identi er variable, as each
With Data>Open Data Source>Text File, we start the
value is a nominal record identi er rather than a numeri-
Data Import wizard, which immediately provides a
cal scale value. We can change the data type by highlight-
preview of the data le.
ing the Unique Identi er column and clicking the Row

25 CSV stands for “comma-separated values”, a common format for text-based data les. As an alternative to this im-
port format, BayesiaLab offers a JDBC connection, which is practical when accessing large databases on servers.



Identi er check box, which changes the color of the of discrete distributions, means-imputation typically also
Unique Identi er column to beige. introduces a bias. There are other, better techniques,
which typically demand signi cant computational effort
Although it is not imperative to maintain a Row Identi-
and thus often turn out like a labor-intensive standalone
er, and we could instead assign the Not Distributed
project rather than being just a preparatory step.
status to the Unique Identi er variable, it can be quite
helpful for nding individual respondent records at a Without going into too much detail at this point,
later point in the analysis. BayesiaLab can estimate all missing values given the
learned network structure using the Expectation Maxi-
As the respondent records in the NVES survey are mization (EM) algorithm. As a result, we obtain a com-
weighted, we need to select the Weight by clicking on the
plete database without “making things up.” In tradi-
Combined Base Weight variable, which will turn the
tional statistics, the equivalent would be to say that nei-
column green.
ther the mean nor the variance of the variables is af-
fected by the imputation process.

Continuing in our data import process, the next screen
provides options as to how to treat the missing values.
Clicking the small upside-down triangle next to the vari-
able names brings up a window with key statistics of the
selected variable, in this case Age Bracket.

Missing Values
In the context of data import, it is important to point out
how missing values are treated in BayesiaLab. The na-
tive, automatic processing of missing values reveals a
particular strength of BayesiaLab.

In traditional statistical analysis, the analyst has to
choose from a number of methods to handle missing
The very basic functions of ltering, i.e. case-wise dele-
values in a database, but unfortunately many of them
tion, and mean/modal value imputation are available.
have serious drawbacks. Perhaps the most common
However, at this point, we can take advantage of
method is case-wise deletion, which simply excludes re-
BayesiaLab’s advanced missing values processing algo-
cords that contain any missing values. Casually speaking, rithms. We will select Dynamic Completion, which will
this means throwing away lots of good data (the non-
continuously “ ll in” and “update” the missing values
missing values) along with the bad (the missing values).
according to the conditional distribution of the variable,
Another method is means-imputation, by which any
as de ned by the current structure of the networks.
missing value is lled in with the variable’s mean. Inevi-
However, as our network is not yet connected and hence
tably, this reduces the variance of the variable and thus
does not have a structure, BayesiaLab will draw from the
has an impact on its summary statistics, which is clearly
undesirable considering the intended analysis. In the case



marginal distribution of each variable to “tentatively”
establish placeholder values for each missing value.

A screenshot from STATISTICA, where we have done
most of the preprocessing, shows the marginal distribu-
tion of the Age Bracket variable in the form of a
histogram.26

By clicking on the Type drop-down menu, the choice of
discretization algorithms appears.

Selecting Manual will show a cumulative graph of the
The missing Age Bracket values will be drawn from this
Purchase Price distribution, and we can see that it ranges
marginal distribution and are used as placeholders, until
from $75,000 to $180,000.28
we can use the structure of the Bayesian network to rees-
timate our missing values. As Dynamic Completion im-
plies, BayesiaLab performs this on continuous basis in
the background, so at any point we would have the best
possible estimates for the missing values, given the cur-
rent network structure.

Discretization
The next step is the Discretization and Aggregation dia-
logue, which allows the analyst to determine the type of
discretization, which must be performed on all continu-
ous variables.27 We will use the Purchase Price variable
to explain the process. Highlighting a variable will show
the default discretization algorithm while the graph
panel is initially blank. We could now manually select binning thresholds by
way of point-and-click directly on the graph panel. This

26 The normal curve in the histogram is just for illustration purposes. BayesiaLab always uses the actual discrete distri-
bution, not a parametric approximation.
27 BayesiaLab requires discrete distributions for all variables.
28 $75,000 was previously selected as the lower boundary for this particular vehicle segment. $180,000 was the highest
reported price in NVES.



might be relevant, if there were government regulations
in place with speci c vehicle price thresholds.29

For our purposes, however, we want to create price cate-
gories that are meaningful in the context of our vehicle
segment and ve bins may seem like a reasonable start-
ing point.
The resulting bins appear much more suitable to describe
Clicking Generate Discretization will prompt us to select our domain.
the type of discretization and the number of desired in-
tervals. Without having a-priori knowledge about the
distribution of the Price variable, we may want to start
with the Equal Distances algorithm.

The resulting view shows the generated intervals and by
clicking on the interval boundaries we can see the per-
We will proceed similarly with the only other continuous
centage of cases falling into the adjacent intervals.
variable in the database, i.e. Age Bracket.

Note

For choosing discretization algorithms beyond this
example, the following rule of thumb may be helpful:

• For supervised learning, choose Decision Tree.

• For unsupervised learning, choose, in the order of
priority, K-Means, Equal Distances or Equal
Frequencies.

Clicking Finish completes the import process and 49
variables (columns) from our database are now shown as
blue nodes in the Graph Panel, which is the main win-
We learn from this that our bottom two intervals contain dow for network editing.
89% of the cases, whereas the top two intervals contain
just under 5% of the cases. This suggests that we may
not have enough granularity to characterize the bulk of
the market towards the bottom end of the price spec-
trum. Perhaps we also have too few cases within the top
two intervals. So we will generate a new discretization,
now with four intervals, and select KMeans as the type
this time.

29 The now-expired luxury tax for passenger cars in the U.S. would be an example for such a policy.



we are in P(Age < 45 | Number of children under 6
= 2). Hence we focus the learning algorithm on the
area of interest, i.e. product attributes vis-à-vis mar-
ket attributes.

2. We must not learn the dependencies between the
product variables themselves because they would
simply re ect today’s product offerings and their
contingencies, e.g. P(Vehicle Segment=“4-door se-
dan” | Brand=“Porsche”)=0. We do want to under-
stand what is available today, but we certainly do
not want to encode today’s product scenarios as
The six nodes on the far left column re ect product at-
constraints in the network. Instead, we want to be
tributes (green), the second-from-left column shows ten
able to introduce new scenarios, which are not
demographic attributes (yellow) and all remaining nodes
available today.
to the right represent 33 vehicle-related attitudes (red).
This initial view represents a fully unconnected Bayesian To focus learning in a speci c area, we need to take an
network. indirect approach and tell BayesiaLab “what not to
learn.” So, to prevent the algorithm from learning the
Also, to simplify our nomenclature, we will combine the
product-to-product variable relationships, we will “for-
demographic attributes (yellow) and the vehicle-related
bid” such arcs.
attitudes (red) and refer to them together as “Market”
variables (now all red). We rst create a Class by highlighting all product nodes
then right-clicking them. From the menu, we then select
Properties>Classes>Add.

Variable Classes and Forbidden Arcs
One is now tempted to immediately start with Unsuper-
vised Learning to see how all these variables relate to
each other.

However, there are two reasons why we need to intro-
duce another step at this point:

1. Our mission is to model the interactions between
When prompted for a name, we can choose something
products variables on the one side and market vari-
descriptive, so we give this new Class class the label
ables on the other, so we can see the consumer re-
“Product”.
sponse to products. For instance, we are more inter-
ested in learning P(Transmission= “Manual” | Atti-
tude = “Driving is one of my favorite things”) than



As a result, these Forbidden Arc relationships will appear
in the Forbidden Arc Editor and will remain there unless
we subsequently choose to modify them.

Having introduced this Class of node, we can now very
easily manage Forbidden Arcs. More speci cally, we
want to make all arcs within the Class Products forbid-
den. A right-click anywhere on the Graph Panel opens
up the menu from which we can select Edit Forbidden
Arcs.

We are also reminded about the presence of Forbidden
Arcs by the symbol in the lower right corner of the
screen.

Unsupervised Learning
Now that the learning constraints are in place, we con-
tinue to learn the network by selecting Learning>Asso-
ciation Discovering>EQ.30

In the Forbidden Arc Editor, we can select the Class
Product both as start and end.

The resulting network may appear somewhat unwieldy
We now repeat the above steps and also create Forbid- at rst glance, but upon closer inspection we can see that
den Arcs for the Market variables. arcs exist only between Product variables (green) and
Market variables (red), which is precisely what we in-
tended by establishing Forbidden Arcs.

30 EQ is one of the unsupervised learning algorithms implemented in BayesiaLab. Koller and Friedman (2009) provide a
comprehensive introduction to learning algorithms.



ing the baseline scenario is described in the following
section.

Product Scenario Baseline
The idea is that all available product con gurations were
manifested in the market in 2009 and thus captured in
the 2009 NVES.33

It still requires careful consideration as to how many
Product variables should be included to generate the
baseline product scenario. We want to create a type of

However, we will not analyze this structure any further, coordinate system, that allows us to identify products

but rather use it solely as a statistical device to be used in through their principal characteristics. For instance, the

the Bayesia Market Simulator. We simply need to save following attributes would uniquely de ne a “Mercedes-
Benz S550 4Matic”:
the network in its native xbl le format, so the Bayesia
Market Simulator can subsequently import it.
• Brand=“Mercedes-Benz”

Simulation • Engine Type=“V8”
With the Bayesia Market Simulator we have the ability
• Drive Type=“AWD”
to simulate “alternate worlds” for both the Product
variables as well as for the Market variables. In most • Transmission=“Automatic”
applications, however, marketing analysts will want to
primarily study new Product scenarios assuming the • Segment=“High Premium”34
Market remains invariant, meaning that consumer
• Price=“>$85,795 AND <= $99,378”
demographics and attitudes remain the same.31
Relating consumer attributes and attitudes to these indi-
It will be the task of the analyst to de ne new product
vidual product attributes, rather than to the vehicle as a
scenarios, which will need to include all products as-
whole, will then allow us to construct hypothetical
sumed to be in the marketplace for the to-be-projected
products during our simulation. To stay with the Mer-
timeframe, in our case 2010.32 As many products carry
cedes example, we could de ne a new product by setting
over from one year to the next, e.g. from model year
the engine type to “V6” and changing the price to “<
2010 to model year 2011, it is very helpful to use the
$85,795”.
currently available products as a baseline scenario, upon
which changes can be built. Quite simply, we need to It is easy to imagine how one can get the number of
take inventory of the product landscape today. In the permutations to exceed the number of consumers. For
current version of Bayesia Market Simulator this step is instance, in the High Premium segment, we could further
yet not automated, so a practical procedure for generat- differentiate between short wheelbase and long wheel-

31 The year-to-year invariance assumption of the market has been challenged by many marketing executives during the
most recent recession. In this context, many media headlines also proclaimed a paradigm shift in consumer behavior.
The authors have believed - then as well as now - that more has remained the same than has changed in terms of con-
sumer attitudes.
32 For expositional simplicity, we make no distinction between model year and calendar year.
33 In our example, we judge this to be a reasonable simpli cation, even though a small number of automobiles at the
very top end of the market, e.g. the Rolls-Royce Phantom, may not be captured in the survey.
34 Using the Strategic Vision segmentation nomenclature, “High Premium” de nes a large four-door luxury sedan.



base versions, which would increase the number of base-
line product scenarios. We want to nd a reasonable
balance between product granularity and the ratio of
consumers to product scenarios, although we cannot
provide the reader with a hard-and-fast rule.

Pricing is obviously a very important part of the product
scenario con guration and here we are confronted with This will export all variables and all records, including
the reality that no two customers pay exactly the same values from previously performed missing value imputa-
for the identical product, and the survey data makes this tions. The output will be in a semicolon-delimited text
very evident. Furthermore, there are numerous product le, which can be easily imported into Excel or any sta-
features outside our “coordinate system”, e.g. an op- tistical application, such as SPSS or STATISTICA. The
tional $6,000 high-end audio system, that would materi- purpose of loading this into an external application is to
ally affect the price point of an individual vehicle, but manipulate the database to extract the unique product
which would not move the vehicle into a different cate- combinations available in the market.
gory from a consumer’s perspective. With options, an
S550 can easily reach a price of over $100,000. Still we In Excel this can be done very quickly by deleting all
would want such a high-end S550 to be grouped with columns unrelated to the product con guration, which
the standard S550. Thus it is important to de ne reason- leaves us with just the product attributes.
able price brackets that cover the price spectrum of each
vehicle and minimize model fragmentation.

During the Data Import stage, BayesiaLab has discre-
tized all continuous numerical values, including Price,
and created discrete states. If these discrete states are
adequate considering the price positioning and price
spectrum of the vehicles under study, we can now lever-
age this existing binning for generating all current
product scenarios and select Data>Save Data.

In Excel 2010 (for Windows) and Excel 2011 (for Mac),
there is a very convenient feature, which allows to
quickly remove all duplicates, which is exactly what we
want to achieve. We want to know all the unique
product con gurations currently in the market.

In the subsequently appearing dialogue box, we need to
select Use the States’ Long Name. It is important that
Use Continuous Values is not checked, otherwise we will
lose the discretized states of the Price variable.

This leaves use with a table of approximately 100 unique
product scenario combinations available at the time of
the survey.



To make these unique product scenarios available for Upon loading we will see the principal interface of the
subsequent use in the Bayesia Market Simulator, we need Bayesia Market Simulator. On the left panel, all nodes of
to save the table as a semicolon-delimited CSV le. This the network appear as variables. We will now need to
is important to point out, as most programs will save separate all variables into Market Variables and Scenario
CSV les by default as comma-delimited les. Variables by clicking the respective arrow buttons. In our
case, the aptly named Market variables are the Market
Product Scenario Simulation Variables in BMS nomenclature and Product variables
Now that we have the Bayesian network describing the are the Scenario Variables.
overall market (as an xbl le) as well as the baseline
product scenarios (as a csv le), we can proceed to open
the Bayesia Market Simulator.

All variables must be allocated before being able to con-
tinue to Scenario Editing. This also implies that Product
variables, which are not to be included as Scenario Vari-
Clicking File>Open will prompt us to open the xbl net- ables, must be excluded from the Bayesian network le.
work le we previously generated with BayesiaLab. If necessary, we will return to BayesiaLab to make such
edits

As we are working with RP data, every record in our
database re ects one vehicle purchase, i.e. “reveals” one
choice, and therefore we need to leave the Target Vari-
able and Target State elds blank. These elds would
only be used in conjunction with SP data, which includes
a variable indicating acceptance versus rejection.

Clicking Scenario Editing opens up a new window. We
can now manually add any product scenarios we wish to
simulate. Given the potentially large number of scenar-
ios, it will typically be better to load the baseline product
scenarios, which were saved earlier.



Upon successful import, all baseline product scenarios
will appear in the Scenario Editing dialogue.

We can do that by selecting Offer>Import Offers.

We now select to open the semicolon-delimited CSV le
with the baseline product scenarios. It is very important
that the CSV le is formatted precisely as speci ed, for
instance, without any extra blank lines.

In case there are any import issues, it can be helpful to
review the CSV le in a text editor and to visually in-
spect the formatting. The analyst can now add any new product scenarios or
delete those products, which are no longer expected to
be in the market.35 By clicking Add Offer an additional
scenario will be added at the bottom of the product sce-
nario list. In the case of long product scenario lists, this
may require scrolling all the way down.

Clicking on the product attributes of any scenario
prompts drop-down menus to appear with the available

35 To maintain expositional simplicity, we have added all Panamera versions for the entire year 2010 and not changed
any other product scenarios. It should be pointed out that the V6 version of the Porsche Panamera was introduced only
in mid-2010. BMW has also launched an additional six-cylinder version of the 7-series as well as AWD variants, which
are not re ected in the simulation. Finally, Jaguar has released a new XJ in 2010, while that year marked the runout of
the old-generation Audi A8.



attribute states, e.g. RWD or AWD.36 This also allows to done by associating the original database, from which
change attributes of existing products, according to the the network was learned, or by creating a new, arti cial
analysts requirements. one that re ects the joint probability distribution of the
learned Bayesian network.

The latter can be achieved by selecting Database>Gener-
ate.

It is up to the analyst to determine the size of the data-
base to be generated. Although there is no xed rule, too
small of a database will limit the observability of prod-
ucts with a very small market share.

For our case study, we will add the following versions of
the Panamera as new product scenarios:

• Panamera (V6, RWD)
Alternatively, we can also associate the original database,
• Panamera 4 (V6, AWD) which contains the survey responses. In our case, the
original database contains 1,203 records, which is very
• Panamera S (V8, RWD) reasonable in terms of computational requirements.

• Panamera 4S (V8, AWD) Once a database is associated, clicking the Simulation
button will start the market share estimation process.
• Panamera Turbo (V8 Turbo, RWD)

To characterize all of them as large 4-door luxury se-
dans, which is the key distinction versus previous Por-
sche products, we will assign the “High Premium” at-
tribute to them.

Once this is completed, we need to obtain a database
that represents the consumer base, on which these new
product scenarios will be “tried out”. This can either be

36 RWD and AWD stands for rear-wheel drive and all-wheel drive respectively



Simulated High Premium Market Shares ($75,000+)
1%

12%
21%
Audi
BMW
3% Jaguar
Lexus
10%
Mercedes
Porsche
53%

As can be seen from the results, the Porsche Panamera’s
predicted market share appears to be compatible with
the reported running rate for calendar year 2010, which
was available at the time of writing. Unfortunately, we
With the given complexity of our network and around do not know how this compares to Porsche’s expecta-
100 product scenarios, the simulation should take no tions, but the Panamera seems to be quite successful
longer than 30 seconds on a typical desktop computer. overall.

Upon completion, the simulation results will appear in Substitution and Cannibalization
the form of a pie chart and a table. One can go back and The fully simulated database can also be saved as a
review the scenarios by clicking the Scenario Editing semicolon-delimited CSV le, which will allow reviewing
button. the choice probability for each product scenario by indi-
vidual consumer in a spreadsheet.

We can literally examine the new, simulated choices
record-by-record and see which customers have made
the switch to the Panamera. Applying conditional for-
matting to the spreadsheet can also be very helpful. The
The aggregated simulated market shares can also be cop-
above screenshot, for example, shows a selection of ac-
ied from the results table and pasted into Excel or any
other application for further editing and presentation tual Mercedes buyers, who would either consider or pick
the Porsche Panamera in this simulation. High choice
purposes. An example is provided below, showing the
probabilities are shown in shades of red, while near-zero
simulated market shares of the brands under study in the
High Premium segment. probabilities are depicted in dark blue.



It is equally interesting to examine which Porsche buyers Upon editing the market segments, the simulation can be
would pick the Panamera over their current vehicle rerun to obtain the new market share results.
choice.
Limitations
This approach can simulate product and market scenar-
ios consisting of variations of con gurations, which can
be observed with suf cient sample today. However, the
impact of entirely new technologies cannot be simulated
on this basis. As a result, projecting the market share of
the all-electric Nissan Leaf38 would not possible, whereas
estimating the share of a hypothetical three-row BMW
crossover vehicle would be feasible. In all cases, it re-
quires the analyst’s expert knowledge and judgment to
determine the adequacy and equivalency of product at-
tributes observable today.
Not surprisingly, our simulation suggests high probabili-
ties of Panamera choice for several current Cayenne Outlook
owners. One is tempted to take this a step further and There exist several natural extensions to the presented
calculate a rate of cannibalization. In this particular sur- methodology, however it would go beyond the scope of
vey, however, the sample size is too small to attempt do- this paper to present them. A brief summary shall suf ce
ing so. Otherwise, such a computation would be simple for now and we will go into greater detail in forthcom-
arithmetic. ing case studies in this series:

Market Scenario Simulation 1. Beyond learning from data, we can use expert
Although experimenting with product scenarios is ex- knowledge to create or augment Bayesian networks.
pected to be the primary use of the Bayesia Market BayesiaLab offers a Knowledge Elicitation module,
Simulator, it is also possible to change the market scenar- which formally captures expert knowledge and en-
ios. codes it in a Bayesian network. In absence of market
data, this is an excellent approach to have decision
For example, this can be used to simulate the impact of makers collectively (and formally correct) reason
policy changes. One could hypothesize that legislation about future states of the world.
would prohibit or severely penalize ownership of vehi-
cles of a certain size or of a speci c engine type in urban 2. We can extend the concept of product attributes to
areas.37 consumers’ product satisfaction ratings. This will
allow estimating the market share impact as a func-
tion of changes in consumer ratings. For instance,
an automaker could reason about the volume im-
pact from a vehicle facelift, which is expected to
raise the consumer rating of “styling”.

3. The product cannibalization or substitution rate can
be estimated based on the simulated choice behav-
ior, given that there is suf cient sample size. So, for
most mainstream products, this seems to be realistic.

37 Given the draconian restrictions on motorists in Central London, this example is presumably not very far-fetched.
38 The all-electric Leaf was launched by Nissan in the U.S. in December of 2010.



4. With the ability to study consumer choice at the
model level, we can also aggregate these results to
the segment level. Alternatively, using a less granular
approach, we can model the entire market at the
segment and brand level, which would allow study-
ing market changes at a larger scale.

5. Beyond simulating “hard” policy changes affecting
the market, e.g. excluding a product class from a
certain geography, we can also use BayesiaLab to
simulate new populations with small changes in
average consumer attitudes versus the originally
surveyed population. For instance, such an arti -
cially modi ed population could be more environ-
mentally conscious and one could apply opinions
prevalent on the West Coast to the whole country.
Bayesia Market Simulator can then generate new
market shares based on these new hypothetical
market conditions.

Summary
BayesiaLab and Bayesia Market Simulator are unique in
their ability to use Bayesian networks for choice model-
ing and market share simulation. The presented work-
ow provides a comprehensive method for simulating
market shares of future products based on their key
characteristics, without requiring new and costly ex-
periments.

As a result, BayesiaLab and Bayesia Market Simulator
allow using a vast range of existing research for market
share predictions. Given the signi cant resources many
corporations have allocated over many years to conduct-
ing consumer surveys, these BayesiaLab tools offer an
entirely new way to turn the accumulated research data
into practical market oracles.



Appendix vance how individual product and consumer attributes
relate to these unobservable utilities. However, there are
Utility-Based Choice Theory methods that allow us to estimate these unknown vari-

In today’s choice modeling practice, utility-based choice ables and, based on this knowledge, they allow us to

theory plays a dominant role. predict choice in the future. One such method is brie y
highlighted in the following.
1. The rst concept of utility-based choice theory is
that each individual chooses the alternative that Multinomial Logit Models

yields him or her the highest utility. In the domain of choice modeling, MultiNomial Logit
models (MNL) have become the workhorse of the indus-
2. The second idea refers to being able to collapse a try, but here we only want to provide a cursory overview,
vector describing attributes of choice alternatives so the reader can compare the approach presented in the
into a single scalar utility value for the chooser. For case study with current practice.
instance, a vector of attributes for one choice alter-
native, e.g. [Price, Fuel Economy, Safety Rating], MNL models provide a functional form for describing

would translate into one scalar value, e.g. [5], spe- the relationship between the utilities of alternatives and

ci c to each chooser. the probability of choice.

The following example is meant to illustrate both: For instance, using an MNL model for a choice situation
with three vehicle alternatives, Altima, Accord and
For Consumer A: Camry, the probability of choosing the Altima can be
expressed as:
• Utility of Product 1:
[Price=$25,000, Fuel Economy=25MPG, Safety Rat- exp(VAltima )
ing=4 stars] = 7 ✓
Pr(Altima) =
exp(VAltima ) + exp(VAccord ) + exp(VCamry )
[Price=$29,000, Fuel Economy=23MPG, Safety Rat- VAltima in this case stands for the utility of the Altima
ing=5 stars] = 5.5 alternative. The utilities VAltima, VAccord, and VCamry are a
function of the product attributes, e.g.
For Consumer B:
VAltima = β1 × Cost Altima + β 2 × FuelEconomyAltima + β 3 × SafetyRatingAltima
[Price=$25,000, Fuel Economy=25MPG, Safety Rat- As we can observe tangible attributes like vehicle cost,
ing=4 stars] = 4 fuel economy and safety rating, and we can also observe
who bought which vehicle, we can estimate the unknown
• Utility of Product 2: parameters. Once we have the parameters, we can simu-
[Price=$29,000, Fuel Economy=23MPG, Safety Rat- late choices based on new, hypothetical product attrib-
ing=5 stars] = 7.5 ✓ utes, such as a better fuel economy for the Altima or a
lower price for the Camry.
This concept implies that consumers make tradeoffs,
either explicitly or implicitly, and that there exists an The parameters of MNL models can be estimated both
amount x of “Fuel Economy” that is equivalent in utility from “stated preference” (SP) data, i.e. asking consumers
to an amount y of “Safety”. The reader may reasonably about what they would choose, and “revealed prefer-
object that not even a fuel economy of 100MPG would ence” (RP) data, i.e. observing what they have actually
make it acceptable to drive a vehicle that is rated very chosen. There are numerous variations and extensions
poorly on safety. to the class of MNL models and the reader is referred to
Train (2003) and Koppelman (2006) for a comprehen-
Also, we do not know a priori what the utility values are sive introduction.
nor can we measure them. Neither do we know in ad-



Stated Preference Data cal for a much broader audience. Although ELM has
Stated preference data typically comes from experiments, successfully removed the burden of manual coding,
i.e. consumer surveys or product clinics. In this context, countless iterations of speci cation and estimation re-
conjoint experiments have become a very popular choice main a very time-consuming task of the analyst.
elicitation method and a wide range of tools have been
NVES Variables
developed for this particular approach. In conjoint stud-
The following variables from the 2009 Strategic Vision
ies, consumers would typically be given a set of arti -
cially generated product choices along with their attrib- NVES were included this case study:

utes, from which preference responses are then elicited.
• UNIQUE IDENTIFIER
There are many variations of this method that all at-
tempt to address some of the inherent challenges related • Combined Base Weight
to dealing with responses to hypothetical questions.
• New Model Purchased - Make/Model/Series (Alpha
The Sawtooth software package has become de-facto Order)
industry standard for such conjoint studies.39
• New Model Purchased - Brand
Revealed Preference Data
• New Model Purchased - Region Origin
In contrast to SP data, revealed preference data is purely
derived from passive observations. As the name implies, • New Model Segment
the consumer choice is revealed by their actual behavior
rather than by their stated intent in a hypothetical situa- • Segmentation 2
tion. A key bene t is that it is typically easier and more
• Type Of Transmission
economical to obtain passive observations than to con-
duct formal experiments. A conceptual limitation of RP • Number Of Cylinders (VIN)
data relates to the fact that non-yet-existing products can
obviously not be chosen by consumers in the present • Drive Type (VIN)
market environment. Thus simulating market shares of
• Fuel Type
hypothetical products requires “assembling” them from
components and attributes of products, which are al- • Gender
ready available in the market. This inherently limits the
exploration of entirely new technologies, which have • Marital Status
little in common with the technologies they may replace.
• Age Bracket
Studies based on RP data have become very popular for
• Children Under 6
researching travel mode choice, as is also documented in
a large body of research. In market research related to • Children 6 To 12
CPG products or durable goods, using RP data is some-
what less common. • Children 13 To 17

We speculate that one of the reasons for the lack of • Total Family Pre-Tax Income
popularity outside the world of academia is the absence
• Ethnic Group
of easy-to-use software packages. Only recently, with the
release of Easy Logit Modeling (ELM)40 , specifying and • Location Of Residence
estimating multinomial logit models has become practi-

39 A wide range of tools is available from Sawtooth Software, Inc., www.sawtoothsoftware.com.
40 Easy Logit Modeling is available from ELM-Works, Inc., www.elm-works.com. ELM can estimate models based on
both RP and SP data, although we only mention it in the RP context.



• Customer Region Classi cation #1 • My choice of vehicle re ects my personality

• I Seek Variety in My Life • I want a vehicle that says a lot about my success in life
/ career
• I'm Curious and Open to Experiences
• I will switch brand for features or price
• Luxury is Not Important Unless it Has Purpose
• There are lots of different brands of vehicles that I
• I Enjoy Expressing Myself Creatively would consider buying

• I See Life as Full of Endless Possibilities
• I prefer sofa-like comfort over a cockpit-like interior

• Driving is one of my favorite things to do
• I want a vehicle that provides the quietest interior

• I really don't enjoy driving • I want to look good when driving my vehicle

• Whenever I get a chance, I love to go for a drive
• I want my vehicle to stand out in a crowd

• When I drive for fun, I mainly prefer to relax and lis-
• I would pay signi cantly more for environmentally
ten to music or talk
friendly vehicle

• I want vehicles that provide that open-air driving ex- • Price is most important to me when buying a new
perience
vehicle

• I prefer a vehicle that has the capability to outperform
• Purchase Price (100's)
others

• I prefer vehicles that provide superior straight ahead
power

• I prefer vehicles that provide superior handling and
cornering agility

• I prefer a balance of comfort and performance

• I prefer vehicles that provide the softest, most com-
fortable ride quality

• I just want the basics on my vehicle - no extras

• Value equals balance of costs, comfort & performance

• I prefer vehicles that project a tough and workmanlike
image

• Vehicles are a 'tool' or a part of the 'gear' in an active
outdoors lifestyle

• I Want to be able to tow heavy loads

• I want to be able to traverse any terrain

• I want the most versatility in my interior

• I want a basic, no frills vehicle that does the job



References

Barber, David. “Bayesian Reasoning and Machine Learn-
ing.” http://www.cs.ucl.ac.uk/staff/d.barber/brml.
———. Bayesian Reasoning and Machine Learning.
Cambridge University Press, 2011.
Darwiche, Adnan. “Bayesian networks.” Communica-
tions of the ACM 53, no. 12 (12, 2010): 80.
Koller, Daphne, and Nir Friedman. Probabilistic Graphi-
cal Models: Principles and Techniques. The MIT
Press, 2009.
Koppelman, Frank, and Chandra Bhat. “A Self Instruct-
ing Course in Mode Choice Modeling: Multinomial
and Nested Logit Models.” January 31, 2006.
Krzywinski, M., J. Schein, I. Birol, J. Connors, R.
Gascoyne, D. Horsman, S. J. Jones, and M. A.
Marra. “Circos: An information aesthetic for com-
parative genomics.” Genome Research 19, no. 9 (6,
2009): 1639-1645.
Neapolitan, Richard E., and Xia Jiang. Probabilistic
Methods for Financial and Marketing Informatics.
1st ed. Morgan Kaufmann, 2007.
Pearl, Judea. Causality: Models, Reasoning and Infer-
ence. 2nd ed. Cambridge University Press, 2009.
Spirtes, Peter, Clark Glymour, and Richard Scheines.
Causation, Prediction, and Search, Second Edition.
2nd ed. The MIT Press, 2001.
Train, Kenneth. Qualitative Choice Analysis: Theory,
Econometrics, and an Application to Automobile
Demand. 1st ed. The MIT Press, 1985.
Train, Kenneth E. Discrete Choice Methods with Simula-
tion. Cambridge University Press, 2003.



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