OPTIMAL AUXILIARY PRIORS AND REVERSIBLE JUMP PROPOSALS FOR A CLASS OF VARIABLE DIMENSION MODELS
针对变分量数的混合模型，提出一种马尔可夫链蒙特卡洛方法，通过最优辅助先验和提议分布提高跨维度移动的接受概率并降低估计方差，应用于条件密度的贝叶斯非参数模型，在恩格尔曲线估计中表现优于标准方法。
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.