This article develops a Markov chain Monte Carlo (MCMC) method for a class of models that encompasses finite and countable mixtures of densities and mixtures of experts with a variable number of mixture components. The method is shown to maximize the expected probability of acceptance for cross-dimensional moves and to minimize the asymptotic variance of sample average estimators under certain restrictions. The method can be represented as a retrospective sampling algorithm with an optimal choice of auxiliary priors and as a reversible jump algorithm with optimal proposal distributions. The method is primarily motivated by and applied to a Bayesian nonparametric model for conditional densities based on mixtures of a variable number of experts. The mixture of experts model outperforms standard parametric and nonparametric alternatives in out of sample performance comparisons in an application to Engel curve estimation. The proposed MCMC algorithm makes estimation of this model practical.

中文翻译：

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一类变维模型的最优辅助先验和可逆跳跃建议

本文为一类模型开发了马尔可夫链蒙特卡罗 (MCMC) 方法，该模型包含密度的有限和可数混合以及具有可变数量混合成分的专家混合。该方法被证明可以最大化跨维移动的预期接受概率，并在某些限制下最小化样本平均估计量的渐近方差。该方法可以表示为具有最佳辅助先验选择的回顾性采样算法和具有最佳提议分布的可逆跳跃算法。该方法主要受基于可变数量专家混合的条件密度贝叶斯非参数模型的启发和应用。在恩格尔曲线估计的应用中，专家模型的混合在样本外性能比较中优于标准参数和非参数替代方案。所提出的 MCMC 算法使该模型的估计变得实用。