2014/05/05 by Kushal Kr. Dey, Dey, Kushal Kr, Sourabh Bhattacharya +1
Mathematics · Physics and Astronomy · #60H10 #60J05 #60J10 #60J60 #60J70 #Computation (stat.CO) #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1405.0913
openalex publication_date 2014/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Very recently, Transformation based Markov Chain Monte Carlo (TMCMC) was\nproposed by Dutta and Bhattcharya (2013) as a much efficient alternative to the\nMetropolis-Hastings algorithm, Random Walk Metropolis (RWM) algorithm,\nespecially in high dimensions. The main advantage of this algorithm is that it\nsimultaneously updates all components of a high dimensional parameter by some\nappropriate deterministic transformation of a single random variable, thereby\nreducing time complexity and enhancing the acceptance rate. The optimal scaling\nof the additive TMCMC approach has already been studied for the Gaussian\nproposal density by Dey and Bhattacharya(2013). In this paper, we discuss\ndiffusion-based optimal scaling behavior for non-Gaussian proposal densities -\nin particular, uniform, Student's t and Cauchy proposals. We also consider\ndiffusion based optimal scaling for non-Gaussian proposals when the target\ndensity is discontinuous. In the case of the Random Walk metropolis (RWM)\nalgorithm these non-regular situations have been studied by Neal and Roberts\n(2011) in terms of expected squared jumping distance (ESJD), but the diffusion\nbased approach has not been considered. Although we could not formally prove\nour diffusion result for the Cauchy proposal, simulation based results led us\nto a conjecture that the diffusion result still holds for the Cauchy case. We\ncompare our diffusion based TMCMC approach with that of ESJD based RWM approach\nfor the very challenging Cauchy proposal case, showing that our former approach\nclearly outperforms the latter.\n