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AESCS2015_Osamu
1.
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
2.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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.
3.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 ! 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]
4.
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Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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
5.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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]
6.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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
7.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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
8.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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
9.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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
10.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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
11.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 Application to Medical Insurance Market 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
13.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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” Application to Medical Insurance Market 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
14.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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” Application to Medical Insurance Market 14 Creating the hypothesis of Bayesian network timely state of mind anxiety about health word-of-mouth the previous purchase status about the medical insurance advertisement the insurance renewal 7 nodes, 2 states 8 nodes, 2 states life stage the current purchase status about the medical 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.
15.
Copyright © by
Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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 the log-linear model Constructingof ABM Constructing ofBN Parameter Determination using relative evaluation criteria (Aakaike’s Information Criterion: AIC) 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 The cause-and-effect may not be naturally established in our case.
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Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 Constructing of Bayesian network 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 • 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 a part of network So, we determined the direction of the edge using AIC. using relative evaluation criteria (Aakaike’s Information Criterion: AIC) The cause-and-effect may not be naturally established in our case.
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Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 Constructing of Bayesian network 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 • 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 a part of network The BN constructed using only AIC did not corresponded to the behavior model. using relative evaluation criteria (Aakaike’s Information Criterion: AIC) The cause-and-effect may not be naturally established in our case.
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Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 Constructing of Bayesian network 18 the log-linear model 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 • 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 a part of network using relative evaluation criteria (Aakaike’s Information Criterion: AIC) The cause-and-effect may not be naturally established in our case.
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Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 Application to Medical Insurance Market 19 Final 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 “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
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Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 Resultant Bayesian network 20 life stage the current purchase status Constructingof ABM Constructing ofBN Parameter Determination the previous purchase status
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Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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%.
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Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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.
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Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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
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Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 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.
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Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 ! 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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Takahashi Lab. (Osamu MATSUMOTO) All rights reserved AESCS2015 26 Thank you