Bayesian variable selection requires sampling from a posterior distribution that combines discrete model indicators with continuously varying parameters, a challenge often addressed through reversible jump Markov chain Monte Carlo (RJMCMC). Despite its generality, RJMCMC is widely regarded as difficult to design and implement correctly. We present mixtures of mutually singular (MoMS) distributions as a transparent alternative in which competing models are represented within a single fixed-dimensional parameter space partitioned into mutually singular subspaces. We show that this formulation reproduces the exact spike-and-slab interpretation of Bayesian variable selection and that, under appropriate constructions, MoMS and RJMCMC share the same Metropolis--Hastings acceptance probability. On a benchmark dataset with ten predictors, both methods recover posterior inclusion probabilities that match full enumeration, while MoMS achieves comparable or superior effective sample size per second relative to a carefully engineered RJMCMC scheme. We further illustrate the approach in a mixed-effects logistic regression for a sleep-and-memory experiment and in factor-loading selection for a multidimensional generalized partial credit model. Together, these results show that Bayesian variable selection can be carried out within standard fixed-dimensional Markov chain Monte Carlo methodology -- without regret.

翻译：贝叶斯变量选择需要从结合离散模型指标与连续变化参数的后验分布中采样，这一挑战常通过可逆跳跃马尔可夫链蒙特卡洛（RJMCMC）解决。尽管具有普适性，但RJMCMC被认为难以正确设计与实现。我们提出互异分布混合（MoMS）作为透明替代方案，其中竞争模型被表示在划分为互异子空间的单一固定维参数空间中。我们证明该公式精确复现了贝叶斯变量选择的尖峰与石板解释，并且在适当构造下，MoMS与RJMCMC共享相同的Metropolis-Hastings接受概率。在包含十个预测变量的基准数据集上，两种方法均恢复了与完全枚举匹配的后验包含概率，而MoMS相比精心设计的RJMCMC方案实现了相当或更优的每秒有效样本量。我们进一步在睡眠-记忆实验的混合效应逻辑回归及多维广义分部评分模型的因子载荷选择中展示了该方法。这些结果共同表明，贝叶斯变量选择可在标准固定维马尔可夫链蒙特卡洛方法论中执行——无需遗憾。