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Non-reversible Markov chain Monte Carlo methods often outperform theirreversible counterparts in terms of asymptotic variance of ergodic averages andmixing properties. Lifting the state-space (Chen et al., 1999; Diaconis et al.,2000) is a generic technique for constructing such samplers. The idea is tothink of the random variables we want to generate as position variables and toassociate to them direction variables so as to design Markov chains which donot have the diffusive behaviour often exhibited by reversible schemes. In thispaper, we explore the benefits of using such ideas in the context of Bayesianmodel choice for nested models, a class of models for which the model indicatorvariable is an ordinal random variable. By lifting this model indicatorvariable, we obtain non-reversible jump algorithms, a non-reversible version ofthe popular reversible jump algorithms introduced by Green (1995). This simplealgorithmic modification provides samplers which can empirically outperformtheir reversible counterparts at no extra computational cost. The code toreproduce all experiments is available online.

Non-reversible jump algorithms for Bayesian nested model selection