AESCS2015_Osamu

Copyright © by Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015
Method for Getting Parameters of Agent-Based
Model using Bayesian Network:
− A Case of Medical Insurance Market −
Osamu Matsumoto
Masashi Miyazaki
Yoko Ishino
Shingo Takahashi
Waseda University
Waseda University
Yamaguchi University
Waseda University

Introduction
2
Agent-Based Social Simulation(ABSS)
! Major aspects to which ABSS contributes:
1. rigorous testing, refinement, and extension of existing theories that have proved to
be difficult to formulate and evaluate using standard mathematical tools
2. a deeper understanding of fundamental causal mechanisms in a complex system
! at least Two difficulties in ABSS:
in constructing the behavior model of agents
in identifying the internal parameters of the behavior model
For example
! When you want to buy a car,
you should consider which factor is important: price? efficiency? support system?
Some think price as important, others think another as important.
How to select factors in modeling depends on the situation of concern,
and is not uniquely determined.

! identifying the internal parameters of the behavior model
Calibration
the use of conventional knowledge or questionnaire data
! Problems:
The ways of calibration, e.g. which parameter should be calibrated first among many
parameters or how to determine the values of the parameters are performed
“empirically.”
The internal parameters such as choice probability of behavior model are hardly
identified from questionnaire data.
Introduction
3
Conventional Methods of identifying the parameters of model
Against these problems, some related works have been proposed:
! The Virtual Grounding Method [Ohori et al. , 2013]
! Bayesian network as a behavior model [Kocabas et al., 2012] [Yang, 2012]

Related Works
4
Virtual Grounding Method
The virtual grounding method can be used only when a certain model has already
constructed and accepted as a reasonable model.
! Virtual Grounding Method
a method to construct valid facsimile models in ABSS where the real world data is
not available to build the behavioral model
to estimate the parameters, using a questionnaire survey in which participants are
asked their behavior within the acceptable behavioral model with dynamically
changing parameter values.
Acceptable
behavioral
model
Real World
Agent
Sample
Space
Virtual
world data
abstract
explain Virtually act
include
Sample agent
interpret
generate
respond
regenerate
estimate
Ohori, K., Iida, M., Takahashi, S.: Virtual Grounding for Facsimile Model
Construction Where Real Data Is not Available,
SICE Journal of Control, Measurement, and System Integration, 6-2,
108/116 (2013)
General Diagram of Virtual Grounding

The construction of a BN requires four items to be established. First, a set of
nodes corresponding to the variables in the BN represents the most important factors
of a particular event being modeled. In this study, these variables are called land-use
drivers and constitute the set V. Figure 4 represents the BN-ID structure of BNAS.
Second, each node has a set of mutually exclusive states, which are the states of the
land-use drivers. Third, a set of directed links represent causal relationships between
the nodes. Fourth, each node has a set of probabilities, specifying the chance that a
node will be in a particular state given the state of its parents. For example, there is a
conditional probability associated with choosing a speciﬁc location of an agent
given the values of the land-use drivers of the location and the socioeconomic
properties of the agent. These probabilities are stored in conditional probability
tables (CPT) and quantify the strength of dependencies between connected variables
in the BN structure (Bromley et al. 2005). This study uses different BNs (NA) and in
turn different CPTs for each agent type because of their different preferences.
Individual agents are members of different agent groups (i.e., high-income
household group).
Once land-use drivers are represented as variables (nodes) and their correspond-
ing values (states), the BN structure is constructed. Although the network structure
and the CPTs can be obtained using expert knowledge, it is still a challenging
modeling task because there are many parameters to be learned especially in large
size networks. Hence, some learning algorithms must be used to ﬁnd the best
Fig. 4 BNAS model BN-ID structure
123
Related Works
5
Bayesian network as a behavior model
Provide definitely the cause-and-effect relationship of agent’s behavior
Parameterization method has not been discussed detail.
Kocabas, V., Dragicevic, S.: Bayesian networks and agent-based
modeling approach for urban land-use and population density change: a
BNAS model, Journal of Geographical Systems, 15-4, 403/426 (2012)
Bayesian network –
Influence diagram structure
! very few researches
a behavior model in which the utilities of destinations to where townspeople move are
calculated [Kocabas et al., 2012]
a behavior model which determines what means of transportation should be taken
when a natural disaster occurs [Yang, 2012]

Purposes
6
To propose a new method to obtain parameters in ABSS using Bayesian network
! developing the algorithm to identify parameters
how to construct the agent’s behavior model
how to construct Bayesian network representing the behavior model
how to identify parameters by probabilistic inferences of the Bayesian network
! the medical insurance market as a case study
apply our method to analyze
show the validity of the behavior model

Method for Getting Parameters of ABSS Model
7
Parameter determination using Bayesian network
! Steps to determine parameters
1. Constructing the agent’s behavior model
2. Creating the hypothesis of Bayesian network from the model and general knowledge
3. Performing questionnaire survey based on the hypothesis of Bayesian network
4. Constructing Bayesian network from the questionnaire data
5. Determining parameters by probabilistic inferences of the constructed Bayesian
network
! The Main Point is that it enables us to simultaneously
construct the agent’s behavior model
estimate the internal parameters within the model

Steps for Getting Parameters from Bayesian network
8
using relative evaluation criteria
(Aakaike’s Information Criterion: AIC)
The cause-and-effect may not be
naturally established in our case.
Conventional Method
AIC
• applied to group categories
Pearson's chi-square testing
• applied to all the combinations of
nodes belonging to different groups
the log-linear model
• applied to the nodes that do not
compose groups
Constructing
ABM
• describing the cause-and-effect
relationships of factors
Constructing
BN
• hypothesis based on the created ABM
• questionnaire survey based on the
hypothesis
• Structuring of BN using our original
way
Parameter
Determination
• from probabilistic inferences

A Case of Japanese Medical Insurance Market
9
The insurance industries in Japan have undergone drastic changes.
New Insurance Business Law
! The law has become effective since 1996.
! It has allowed both life insurers and nonlife
insurers mutually to enter
! In 2001, Japanese company can enter the
third sector
The third sector
ex)medical insurance
nursing insurance
Nonlife insurers
ex)automobile
insurance
fire insurance
Life insurers
ex)whole life
insurance
term assurance
since 2000
was monopolized
by foreign
company
Consumers’ attitude has changed.
We prefer the existence
security to the
expensive life insurance
against death.
Consumer
"Economic growth has slowed
- the current world economic crisis
"The labor force is shrinking
- the falling birthrate and the aging
population
Insurance product is diversified
and competition became
seriously.
Mainly Because

Related Works | Ishino (2012)
10
Using a Bayesian network constructed from actual questionnaire data to analyze ABM
Ishino’s research showed the behavior model was valid.
The behavior model using Bayesian network did not directly connect with ABSS.
Hence, we could not use ABSS as an analysis tool of the market.
Showed
the word-of-mouth communication has impact on the purchasing decision of
the medical insurance product
! Bayesian network constructed

Application to Medical Insurance Market
11
Agent-Based Model Design
Agent’s parameters.
age
life stage
threshold of life event
event
Insurance status
regular network
①When the agent’s age reaches
a certain threshold, a life event is
generated and the agent’s
life stage alters.
②The events occur
Anxiety about health
depending on the
age
word-of-mouth
consumer
the previous agent
propagates
the advice of a
salesperson
random
the mass media
advertisement
random
the insurance
renewal
fixed period
the purchase
status
event the purchase status
general
medical
insurance
cancer
insurance
specified
disease
insurance
nursing
insurance
main
contract
○% % □% ×%
special
contract
○’% ’% □’% ×’%
Constructingof
ABM
Constructing
ofBN
Parameter
Determination
③

12
Agent-Based Model Design cont’d
purchase
status
event purchase status
③An agent purchases insurance products according to the purchase probability at every life
stages and the events calculated from probabilistic inferences of the Bayesian network.
general
medical
insurance
cancer
insurance
specified
disease
insurance
nursing
insurance
main
contract
○% % □% ×%
special
contract
○’% ’% □’% ×’%
the probability of possessing each insurance product when an agent is placed
in a given situation (e.g. what life stage an agent is ,what event has occurred)
Constructingof
ABM
Constructing
ofBN
Parameter
Determination

n=800. the allocation of respondents in terms of sex and age was performed mirroring
the Japanese insurance market. (from Aug. 20 to Aug. 24 in 2014)
Constructingof
ABM
Constructing
ofBN
Parameter
Determination
! Two important factors
the current purchase status about the medical insurance
“timely state of mind” : the mood of having people think “it is time for me to
purchase the medical health insurance”
13
Creating the hypothesis of Bayesian network
the current purchase
status about the medical
insurance
timely state of mind
anxiety about health
word-of-mouth
the previous purchase
status about the
medical insurance
advertisement
the insurance renewal
life stage
“heading into the workforce”,
“getting married”, “giving a
birth to a baby”, and so on
7 nodes, 2 states
general medical, cancer,
specified disease, nursing
of main and special
8 nodes, 2 states

n=800. the allocation of respondents in terms of sex and age was performed mirroring
the Japanese insurance market. (from Aug. 20 to Aug. 24 in 2014)
Constructingof
ABM
Constructing
ofBN
Parameter
Determination
! Two important factors
the current purchase status about the medical insurance
“timely state of mind” : the mood of having people think “it is time for me to purchase
the medical health insurance”
14
Creating the hypothesis of Bayesian network
word-of-mouth
status about the
medical insurance
advertisement
7 nodes, 2 states
8 nodes, 2 states
life stage
insurance
heading into the workforce
getting married
giving a birth to a baby
sending a child to college
buying a home bringing up a child
to be independent
retiring from work
general medical
main
general medical
special
cancer maincancer special
specified disease
main
specified disease
special
nursing main
nursing special
life stage and the
purchase status possess
some factors called
a group entity.

Constructing of Bayesian network
15
summary
health
life stage
retiring
a baby
the purchase
ad.
Combination
based on
hypothesis
a group
Pearson’s
chi-square testing
Aakaike’s Information Criterion
nodes that do not
compose a group
Constructingof
ABM
Constructing
ofBN
Parameter
Determination
Conventional Method
AIC
compose groups

16
Akaike’s Information Criterion (AIC)
health
life stage
retiring
a baby
the purchase
ad.
a group
We do not have a hypothesis of the
cause-and-effect of the group.
Constructingof
ABM
Constructing
ofBN
Parameter
Determination
Conventional Method
AIC
compose groups
a part of network
So, we determined the direction of the
edge using AIC.

17
Pearson’s chi-square testing
health
life stage
retiring
a baby
the purchase
ad.
Combination
based on
hypothesis
So, we tested whether the direction of
the edge determined by the hypothesis
is significant or not.
Constructingof
ABM
Constructing
ofBN
Parameter
Determination
Conventional Method
AIC
compose groups
a part of network
The BN constructed using only AIC did
not corresponded to the behavior model. using relative evaluation criteria

18
health
life stage
retiring
a baby
the purchase
ad.
nodes that do not
compose a group
The whole construction of the BN was not
valid. So, we used this method considering
interactions between more than two nodes.
Constructingof
ABM
Constructing
ofBN
Parameter
Determination
Conventional Method
AIC
compose groups
a part of network

19
Final Bayesian network
insurance
word-of-mouth
status about the
medical insurance
advertisement
life stage
“getting married”,
“giving a birth to a
baby”, and so on
6 nodes, 2 states
general medical, cancer,
specified disease,
nursing of main and
special
8 nodes, 2 states
! the edge from “the anxiety about health” to “advertisement” was newly added.
! “heading into the workforce” was deleted.
Constructingof
ABM
Constructing
ofBN
Parameter
Determination

Resultant Bayesian network
20
life stage
status
Constructingof
ABM
Constructing
ofBN
Parameter
Determination
the previous
purchase status

Purchase Parameter Determination
21
Identifying the probability of the purchase.
Constructingof
ABM
Constructing
ofBN
Parameter
Determination
life stage event
the current
purchase
getting
married
giving a
birth to
a baby
… word-
of-
mouth
advertis
ement
… general
medical
main
general
medical
special
…
1 0 0 1 0 0 59% 52% …
1 0 0 1 1 0 55% 40% …
...
0 1 0 1 0 0 58% 53%
0 1 0 0 1 0 48% 44%
…
If an agent got married, and he received the word-of-mouth,
then he purchases the general medical main with a probability of 59%.

0
20
40
60
80
100
General Medical Main
General Medical Special
Cancer Main
Cancer Special
Specified Disease Main
Specified Disease Special
Nursing Main
Nursing Special
Insurance Products
Simulation Experiments
22
Validation of Estimated Parameter Values
PurchaseRate(%)
the questionnaire survey data
● the proposed method
average with the proposed method
● using only AIC
average with using only AIC
The results from BN identified with only AIC are overfitted to the questionnaire survey data.
BN identified with only AIC cannot be described by the behavior model.
The results from BN identified with the proposed method reproduce the trajectories of
the questionnaire survey data.

Simulation Experiments cont’d
23
Results of Scenario Analysis
! Getting parameters using Bayesian network
The purchase probabilities for other variables such as advertisement, life stage can
be calculated from BN as well.
You can use as a means to produce information that will support make a decision on
other factors in the market.
Ex. sales strategy
! Performing scenario analysis of two sales strategies
face-to-face sales strategy only
strategy combination of face-to-face sales and media advertisement

Simulation Experiments cont’d
24
Results of Scenario Analysis
15
20
25
30
35
40
45
50
55
15
20
25
30
35
40
45
50
55
PurchaseRate(%)
face-to-face sales strategy only strategy combination of face-to-face sales
and media advertisement
G.M.M Cancer S.D.M N.M
G.M.S C.S S.D.S N.S
getting married, giving a birth to a baby, sending a child to college, buying a home,
bringing up a child to be independent, retiring from work
G.M.M Cancer S.D.M N.M
G.M.S C.S S.D.S N.S
! The cancer insurance alone has little difference of the penetration ratio between the
different strategies.
! “Buying a home” is lower than other life stage.

! Using the proposed method we can simultaneously
construct the agent’s behavior model
estimate the internal parameters within the model
! Some findings in the medical insurance market
The sales activity and the media advertisement have similar effect for the cancer
insurance.
The life stage as an event of agent affects the choice of the medical insurance
product.
Conclusions
25
Future Work
We need to still develop validation method in construction of Bayesian network.
Ex. Some of the nodes connected by Pearson’s chi-square testing are still weakly valid.
New method to obtain parameters in ABSS using Bayesian network

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