scholarly journals Markov Chain Aggregation for Agent-Based Models

2016 ◽  
Author(s):  
Sven Banisch
Keyword(s):  
Markov Chain ◽  
Agent Based Models ◽  
Agent Based

scholarly journals Filling the Gaps: Vacancy Chains and Agent-Based Models

2020 ◽  
Author(s):  
Radu Andrei Pârvulescu
Keyword(s):  
Markov Chain ◽  
Socialist Country ◽  
Social Revolution ◽  
Agent Based Models ◽  
Agent Based ◽  
Equilibrium Dynamics ◽  
Chain Analysis ◽  
Vacancy Chains ◽  
The Impact ◽  
Scholarly Attention

Vacancy-chain analysis (VCA), a method for tracing the flows of resources such as jobs or housing, has faded from scholarly attention. This is unfortunate, because VCA is often superior to markets, auctions, or games, the more popular metaphors-cum-models of resource allocation. This paper aims to revive VCA by casting it in terms of agent-based models (ABMs). I first review and note the limitations of the Markov-chain version VCA (or MC-VCA), and then introduce an agent-based approach to vacancy chain systems, the ABM-VCA, which features the innovation of treating both resources/positions and opportunities as agents. I show that ABM-VCA can replicate MC-VCA (since the former is an MCMC estimator of the latter) and then illustrate the usefulness of ABM-VCA to empirically study off-equilibrium dynamics by using it to assessing the impact of social revolution on the judiciary of a post-socialist country. I conclude by noting the methodological possibilities opened up by ABM-VCA, such as the potential to simulating fields and ecologies. A Python implementation of ABM-VCA is available at https://github.com/r-parvulescu/abm-vca.

scholarly journals Case Studies for a Markov Chain Approach to Analyze Agent-Based Models

2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Florian Kitzler ◽  
Martin Bicher
Keyword(s):  
Social Sciences ◽  
Markov Chain ◽  
Case Studies ◽  
Care Management ◽  
Dynamic Models ◽  
Agent Based Models ◽  
Agent Based ◽  
Heterogeneous Structures ◽  
High Flexibility ◽  
Opinion Dynamic

Agent-Based Models have become a widely used tool in social sciences, health care management and other disciplines to describe complex systems from a bottom-up perspective. Some reasons for that are the easy understanding of Agent-Based Models, the high flexibility and the possibility to describe heterogeneous structures. Nevertheless problems occur when it comes to analyzing Agent-Based Models. This paper shows how to describe Agent-Based Models in a macroscopic way as Markov Chains, using the random map representation. The focus is on the implementation of this method for chosen examples of a Random Walk and Opinion Dynamic Models. It is also shown how to use Markov Chain tools to analyze these models. Our case studies imply that this method can be a powerful tool when it comes to analyzing Agent-Based Models although some further research in practice is still necessary.

scholarly journals MARKOV CHAIN AGGREGATION FOR SIMPLE AGENT-BASED MODELS ON SYMMETRIC NETWORKS: THE VOTER MODEL

2015 ◽  
Vol 18 (03n04) ◽  
pp. 1550011 ◽  
Author(s):  
SVEN BANISCH ◽  
RICARDO LIMA
Keyword(s):  
Markov Chain ◽  
Symmetry Group ◽  
General Framework ◽  
Voter Model ◽  
Dynamical Process ◽  
Agent Based Models ◽  
Agent Based ◽  
Heterogeneous Interaction ◽  
Dynamical Properties ◽  
Symmetric Networks

For Agent-based models, in particular the Voter Model (VM), a general framework of aggregation is developed which exploits the symmetries of the agent network G. Depending on the symmetry group Aut ω(N) of the weighted agent network, certain ensembles of agent configurations can be interchanged without affecting the dynamical properties of the VM. These configurations can be aggregated into the same macro state and the dynamical process projected onto these states is, contrary to the general case, still a Markov chain. The method facilitates the analysis of the relation between microscopic processes and a their aggregation to a macroscopic level of description and informs about the complexity of a system introduced by heterogeneous interaction relations. In some cases the macro chain is solvable.

scholarly journals Bayesian Estimation of Agent-Based Models via Adaptive Particle Markov Chain Monte Carlo

2021 ◽  
Author(s):  
Thomas Lux
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Estimation ◽  
Goodness Of Fit ◽  
Approximation Error ◽  
Agent Based Models ◽  
Proposal Distribution ◽  
Acceptance Probability ◽  
Agent Based

AbstractOver the last decade, agent-based models in economics have reached a state of maturity that brought the tasks of statistical inference and goodness-of-fit of such models on the agenda of the research community. While most available papers have pursued a frequentist approach adopting either likelihood-based algorithms or simulated moment estimators, here we explore Bayesian estimation using a Markov chain Monte Carlo approach (MCMC). One major problem in the design of MCMC estimators is finding a parametrization that leads to a reasonable acceptance probability for new draws from the proposal density. With agent-based models the appropriate choice of the proposal density and its parameters becomes even more complex since such models often require a numerical approximation of the likelihood. This brings in additional factors affecting the acceptance rate as it will also depend on the approximation error of the likelihood. In this paper, we take advantage of a number of recent innovations in MCMC: We combine Particle Filter Markov Chain Monte Carlo as proposed by Andrieu et al. (J R Stat Soc B 72(Part 3):269–342, 2010) with adaptive choice of the proposal distribution and delayed rejection in order to identify an appropriate design of the MCMC estimator. We illustrate the methodology using two well-known behavioral asset pricing models.

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