Heyo, in this post I’m going to describe how you can explore parameter spaces using MCMC in cases where you have a set of models with different numbers of parameters or more simply where you have a model with an unknown number of parameters using Reversible Jump Markov Chain Monte Carlo (RJMCMC). UNDER CONSTRUCTION

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Resources

• “Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model” - Peter Green (1995)
• “Advanced Simulation Methods || Chapter 7 - Reversible Jump MCMC” - Patrick Rebeschini (~2004 not sure)
• “Lecture 22. Reversible Jump MCMC” - N Zabaras, University of Notre Dame (2017)

Table of Contents

• Statement of the problem
• Describing the mathematics of jumping between different dimensional spaces
• Examples
  • Combined Gaussians
  • Multiple Linear Regression
• Conclusion

Statement of the problem

It is quite common that when performing inference, a statistician doesn’t know a priori how many parameters they need to describe her data or which one of a collection of models actually describes the data.

Describing the mathematics of jumping between different dimensional spaces

Examples

Combined Gaussians

Multiple Linear Regression

Conclusion

Footnotes