2014/10/29 by Wenxin Jiang
Computer Science · Mathematics · #Convergence (economics) #Markov Chains and Monte Carlo Methods #Oracle #Posterior probability #Rate of convergence #Set (abstract data type) #Simple (philosophy) #Statistical Methods and Bayesian Inference #Stochastic Gradient Optimization Techniques #math.ST #msc:62-XX #stat.TH
paper · pdf · doi:10.1155/2014/469340
published in International Scholarly Research Notices 2014, 1-8 (Hindawi Publishing Corporation) · 8 pages
openalex publication_date 2014/10/29 · arxiv created 2014/11/11 · arxiv updated 2014/11/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a "penalized divergence" of the prior, which measures the ability of the prior distribution to propose a nonnegligible set of working models to approximate the true model and a "norm complexity" of the prior, which measures the complexity of the prior support, weighted by the prior probability masses. These formulas are explicit and involve no essential assumptions and are easy to apply. We apply this approach to the case with model averaging and derive some useful oracle inequalities that can optimize the performance adaptively without knowing the true model.