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Turning Simulation into Estimation: Generalized Exchange Algorithms for Exponential Family Models.

Maarten Marsman1, Gunter Maris1,2, Timo Bechger2

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The Single Variable Exchange algorithm improves statistical model estimation by drawing from posterior distributions. This method enhances Markov chain convergence and autocorrelation, requiring only model simulation capabilities.

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Area of Science:

  • Statistical modeling
  • Computational statistics
  • Bayesian inference

Background:

  • Estimating statistical models often requires complex computational methods.
  • The Single Variable Exchange algorithm offers a novel approach to posterior distribution sampling.

Purpose of the Study:

  • To present the Single Variable Exchange algorithm as a mixture of Metropolis transition kernels.
  • To propose strategies for automatically selecting efficient transition kernels.
  • To demonstrate significant improvements in Markov chain convergence and autocorrelation.

Main Methods:

  • Framing the Exchange algorithm as a mixture of Metropolis transition kernels.
  • Developing strategies for automatic selection of efficient transition kernels.
  • Applying the method to statistical models in the Exponential Family, using educational measurement examples.

Main Results:

  • Achieved significant improvements in convergence rate of the Markov chain.
  • Demonstrated reduced autocorrelation in the Markov chain.
  • Showcased the algorithm's effectiveness without needing more than simulation capabilities.

Conclusions:

  • The enhanced Single Variable Exchange algorithm provides efficient posterior estimation for simulated models.
  • The proposed strategies automatically select efficient kernels, improving computational performance.
  • This method offers a valuable tool for statistical modeling, particularly in the Exponential Family.