Inferência em grafos aleatórios exponenciais através do ABC
Exponential random graph models are parametric statistical methods for probability distributions of network structures trough the analyses of configurations based on the presense (or absence) of edges,such as k-stars and triangles. These configurations are weigthed by model parameters. These models...
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| Tipo de documento: | dissertação |
| Estado: | Versão publicada |
| Data de publicação: | 2016 |
| País: | Brasil |
| Recursos: | Universidade Federal de Minas Gerais (UFMG) |
| Repositório: | Repositório Institucional da UFMG |
| Idioma: | português |
| OAI Identifier: | oai:repositorio.ufmg.br:1843/BUBD-AA2EWA |
| Acesso em linha: | http://hdl.handle.net/1843/BUBD-AA2EWA |
| Access Level: | Acceso aberto |
| Palavra-chave: | ABC ERGMs Bergm Grafos Aleatórios Exponenciaias MCMC Método de projeção aleatória Processo estocastico eoria dos grafos Estatistica Graficos aleatorios |
| Resumo: | Exponential random graph models are parametric statistical methods for probability distributions of network structures trough the analyses of configurations based on the presense (or absence) of edges,such as k-stars and triangles. These configurations are weigthed by model parameters. These models are principled statistical approach to model social networks, but they are also applied in physics and biology. They are theory driven in such a way that their use require the researcher to consider the complexity of why edges (social, biological or whatever) are formed. The focus of this work is to present a comparative study between two parameter estimation methods for the ERGMs models not taking into account the theories behind the edges formation. The methods considered were the one proposed by Caimo and Friel 2011, a Bayesian method based on Markov Chain Monte Carlo (MCMC), and the Approximate Bayesian Computation (ABC) method proposed by Del Moral et al. 2012, Beaumont et al. 2009, Drovandi and Pettitt 2011 eLenormand et al 2012. The results shows that the ABC method, specially the one proposed by Lenormand, surpassed the Bayesian one considering both the goodness-of-fit and performance. Despite the fact that this study was restricted to a limited number of parameters, based on the experiments done so far, we are strongly convinced that the ABC approach, proposed by Lenormand et al 2012, is consistently better than the Bayesian method proposed by Caimo and Friel 2011. |
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