  Non-reversible Markov chain Monte Carlo methods often outperform their
reversible counterparts in terms of asymptotic variance of ergodic averages and
mixing properties. Lifting the state-space (Chen et al., 1999; Diaconis et al.,
2000) is a generic technique for constructing such samplers. The idea is to
think of the random variables we want to generate as position variables and to
associate to them direction variables so as to design Markov chains which do
not have the diffusive behaviour often exhibited by reversible schemes. In this
paper, we explore the benefits of using such ideas in the context of Bayesian
model choice for nested models, a class of models for which the model indicator
variable is an ordinal random variable. By lifting this model indicator
variable, we obtain non-reversible jump algorithms, a non-reversible version of
the popular reversible jump algorithms introduced by Green (1995). This simple
algorithmic modification provides samplers which can empirically outperform
their reversible counterparts at no extra computational cost. The code to
reproduce all experiments is available online.
