Bayes Factors for Detecting Social Group Changes
MIT Lincoln Laboratory Lexington United States
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The AI Software Architectures and Algorithms Group at MIT Lincoln Laboratory has used Bayes factors or Bayes t-tests to measure the similarity between pairs of datasets that can be modelled as draws from Poisson, binomial, or multinomial distributions. More recently, similar Bayes factors or t-tests have been obtained to determine whether a group has merged with or split from another group. It is again assumed that the available data samples can be modeled with Poisson, binomial, or multinomial distributions. A motivation for this report is that it has often been difficult to find desired Bayes factors in the academic literature. This report is intended to provide a repository of the analytical derivations that lead to the Bayes factors for similarity, merger, or splits for Poisson, binomial, and multinomial distributions. Simulation results are presented to clarify the strengths and weaknesses of the derived Bayes factors. Analysis results from the Reddit social networking site are used to demonstrate the utility of the Poisson similarity and merger Bayes factors for real-world applications.
- Statistics and Probability
- Information Science