Agent Based Modeling, Mathematical Formalism for

Laubenbacher, Reinhard; Jarrah, Abdul Salam; Mortveit, Henning S.; Ravi, S. S.

doi:10.1007/978-0-387-30440-3_10

Cited by 14 publications

(12 citation statements)

References 69 publications

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“…Laubenbacher et al (2009) review existing formal frameworks that have the potential to model ABMs, such as cellular automata and finite dynamical systems and argue for the latter as an appropriate 20 Background mathematical framework to represent ABMs. However, the probabilistic nature of most ABMs can only be accounted for by the stochastic version -the so-called stochastic finite dynamical systems -the analysis of which »is still in its infancy« (ibid., 14).…”

Section: Markov Chain Formalization Of Agent-based Modelsmentioning

confidence: 99%

“…However, the probabilistic nature of most ABMs can only be accounted for by the stochastic version -the so-called stochastic finite dynamical systems -the analysis of which »is still in its infancy« (ibid., 14). On the other hand, Laubenbacher et al (2009) recognize that stochastic finite dynamical systems give rise to Markov chains. However, for reasons that do not become very clear in their paper, the authors argue:…”

Section: Markov Chain Formalization Of Agent-based Modelsmentioning

confidence: 99%

“…But of course, the incentive of Laubenbacher et al (2009) to further elaborate the theory of stochastic dynamical systems in order to derive rigorous results for ABMs in future is highly appreciable.…”

Section: Markov Chain Formalization Of Agent-based Modelsmentioning

confidence: 99%

“…Though it has often been recognized that ABMs may be conceived as (stochastic) dynamical systems or Markov chains Laubenbacher et al, 2009;Izquierdo et al, 2009;Page, 2012), the afore mentioned aggregation techniques developed for these systems have not yet been applied to ABMs. One of the reasons for this is that an explicit formulation of the micro process in terms of dynamical systems or Markov chains has been accomplished only in an abstract (Laubenbacher et al, 2009;Page, 2012) or approximate way.…”

Section: Bridging a Gapmentioning

confidence: 99%

“…One of the reasons for this is that an explicit formulation of the micro process in terms of dynamical systems or Markov chains has been accomplished only in an abstract (Laubenbacher et al, 2009;Page, 2012) or approximate way. The explicit formalization of the micro process as a Markov chain -the reasoning presented in this thesis will be started with it (Sec.…”

Section: Bridging a Gapmentioning

confidence: 99%

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Markov Chain Aggregation for Agent-Based Models

Banisch

2016

Understanding Complex Systems

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AcknowledgementsScience needs freedom. It needs free thought, it needs free time, it needs free talk. Philippe Blanchard is among those teachers who are deeply committed to such an understanding of science. I am very proud and grateful to be among his students.I am also very grateful to Ricardo Lima. He is probably the person who engaged most in the details of this project and should really be an honorary member of the reading committee. Thank you for always inspiring discussions and the critical reading of all parts of this work.Tanya Araújo has given me encouragement since the first day we met. She also read through all the thesis and her advises (especially during the last turbulent months) helped a lot to finalize the writing.I was once told that those people who are most busy (those that really are and do not just pretend to be) are also the people who always have time when you approach them with some question or meet them on the floor. I don't know whether this is a general rule, but it certainly applies to Dima Volchenkov. Thank you for an open ear whenever I knocked on your door.A special thanks goes to Hanne Litschewsky, our great secretary in E5. Due to Hanne, I could experience how comfortable, how helpful, yet sometimes essential it is to be supported in all the bureaucratic aspects of science.All of this would have been a lot more difficult without the unconditional support of my family. I am very thankful to my parents, my parents-in-law, and especially to my wife Nannette.Financial support of the German Federal Ministry of Education and Research (BMBF) through the project Linguistic Networks is also gratefully acknowledged (http://project.linguistic-networks.net). AbstractThis thesis introduces a Markov chain approach that allows a rigorous analysis of a class of agent-based models (ABMs). It provides a general framework of aggregation in agent-based and related computational models by making use of Markov chain aggregation and lumpability theory in order to link between the micro and the macro level of observation.The starting point is a microscopic Markov chain description of the dynamical process in complete correspondence with the dynamical behavior of the agent model, which is obtained by considering the set of all possible agent configurations as the state space of a huge Markov chain. This is referred to as micro chain, and an explicit formal representation including microscopic transition rates can be derived for a class of models by using the random mapping representation of a Markov process. The explicit micro formulation enables the application of the theory of Markov chain aggregation -namely, lumpability -in order to reduce the state space of the micro chain and relate microscopic descriptions to a macroscopic formulation of interest. Well-known conditions for lumpability make it possible to establish the cases where the macro model is still Markov, and in this case we obtain a complete picture of the dynamics including the transient stage, the most interesting phase in applications.F...

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Section: Markov Chain Formalization Of Agent-based Modelsmentioning

confidence: 99%

Section: Markov Chain Formalization Of Agent-based Modelsmentioning

confidence: 99%

Section: Markov Chain Formalization Of Agent-based Modelsmentioning

confidence: 99%

Section: Bridging a Gapmentioning

confidence: 99%

Section: Bridging a Gapmentioning

confidence: 99%

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Markov Chain Aggregation for Agent-Based Models

Banisch

2016

Understanding Complex Systems

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Background and Concepts

Banisch

2015

Understanding Complex Systems

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Memory-Based Reduced Modelling and Data-Based Estimation of Opinion Spreading

2021

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We investigate opinion dynamics based on an agent-based model and are interested in predicting the evolution of the percentages of the entire agent population that share an opinion. Since these opinion percentages can be seen as an aggregated observation of the full system state, the individual opinions of each agent, we view this in the framework of the Mori–Zwanzig projection formalism. More specifically, we show how to estimate a nonlinear autoregressive model (NAR) with memory from data given by a time series of opinion percentages, and discuss its prediction capacities for various specific topologies of the agent interaction network. We demonstrate that the inclusion of memory terms significantly improves the prediction quality on examples with different network topologies.

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Agent Based Modeling, Mathematical Formalism for

Cited by 14 publications

References 69 publications

Markov Chain Aggregation for Agent-Based Models

Markov Chain Aggregation for Agent-Based Models

Background and Concepts

Memory-Based Reduced Modelling and Data-Based Estimation of Opinion Spreading

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