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Markov Chain Monte Carlo (MCMC) is a computational approach to fundamentalproblems such as inference, integration, optimization, and simulation. Thefield has developed a broad spectrum of algorithms, varying in the way they aremotivated, the way they are applied and how efficiently they sample. Despiteall the differences, many of them share the same core principle, which we unifyas the Involutive MCMC (iMCMC) framework. Building upon this, we describe awide range of MCMC algorithms in terms of iMCMC, and formulate a number of"tricks" which one can use as design principles for developing new MCMCalgorithms. Thus, iMCMC provides a unified view of many known MCMC algorithms,which facilitates the derivation of powerful extensions. We demonstrate thelatter with two examples where we transform known reversible MCMC algorithmsinto more efficient irreversible ones.

Involutive MCMC: a Unifying Framework