2021/11/05 by Miguel Fudolig, Fudolig, Miguel, Réka Howard +1
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2111.03691
openalex publication_date 2021/11/05 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
The Ball Pit Algorithm (BPA) is a novel Markov chain Monte Carlo (MCMC)\nalgorithm for sampling marginal posterior distributions developed from the path\nintegral formulation of the Bayesian analysis for Markov chains. The BPA\nyielded comparable results to the Hamiltonian Monte Carlo as implemented by the\nadaptive No U-Turn Sampler (NUTS) in sampling posterior distributions for\nsimulated data from Bernoulli and Poisson likelihoods. One major advantage of\nthe BPA is its significantly lower computational time, which was measured to be\nat least 95% faster than NUTS in analyzing single parameter models. The BPA was\nalso applied to a multi-parameter Cauchy model using real data of the height\ndifferences of cross- and self-fertilized plants. The posterior medians for the\nlocation parameter were consistent with other Bayesian sampling methods.\nAdditionally, the posterior median for the logarithm of the scale parameter\nobtained from the BPA was close to the estimated posterior median calculated\nusing the Laplace normal approximation. The computational time of the BPA\nimplementation of the Cauchy analysis is 55% faster compared to that for NUTS.\nOverall, we have found that the BPA is a highly efficient alternative to the\nHamiltonian Monte Carlo and other standard MCMC methods.\n