A Novel Simulation Method for Binary Discrete Exponential Families, with Application to Social Networks
1Departments of Sociology, Statistics, and EECS, and Institute for Mathematical Behavioral Sciences; University of California, Irvine; SSPA 2145; Irvine, CA 92697-5100; buttsc@uci.edu.
The Journal of Mathematical Sociology
|November 21, 2015
Summary
We developed a novel approximate sampling method for binary discrete exponential families, offering fixed execution time and quality guarantees. This method improves upon Markov chain Monte Carlo (MCMC) for social network analysis and random graph generation.
Area of Science:
- Computational Sociology
- Statistical Modeling
- Network Science
Background:
- Stochastic models for binary data are crucial in sociology, modeling behaviors and social networks.
- Exact sampling is challenging due to data dependence, leading to approximate Markov chain Monte Carlo (MCMC) methods.
- MCMC methods have variable execution times and uncertain draw quality.
Purpose of the Study:
- To introduce a novel approximate sampling method for binary discrete exponential families.
- To provide fixed execution time and well-defined quality guarantees for sampling.
- To apply the method to random graph generation and social network simulation.
Main Methods:
- Developed a new approximate sampling procedure for binary discrete exponential families.
- Demonstrated the method's application in generating random graphs.
- Utilized geographical covariates and dyadic dependence mechanisms for social network simulation.
Main Results:
- The novel method offers fixed execution time, unlike MCMC.
- The procedure provides well-defined quality guarantees for approximate sampling.
- Successfully simulated a large-scale social network using the new method.
Conclusions:
- The proposed sampling method is a viable and advantageous alternative to MCMC for binary discrete exponential families.
- This approach enhances the simulation of complex social networks and random graphs.
- Offers improved reliability and efficiency in computational sociology research.
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