The Floating Random Walk and Its Application to Monte Carlo Solutions of Heat Equations

1966 ◽  
Vol 14 (2) ◽  
pp. 370-389 ◽  
Author(s):  
A. Haji-Sheikh ◽  
E. M. Sparrow
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Heat Equations

Adsorption of non-ionic surfactants on organoclays in drilling fluid investigated by molecular descriptors and Monte Carlo random walk simulations

2021 ◽  
Vol 538 ◽  
pp. 148154
Author(s):  
Dina Kania ◽  
Robiah Yunus ◽  
Rozita Omar ◽  
Suraya Abdul Rashid ◽  
Badrul Mohamed Jan ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Molecular Descriptors ◽  
Drilling Fluid ◽  
Ionic Surfactants ◽  
Monte Carlo Random Walk

scholarly journals Relaxed Random Walks at Scale

2020 ◽  
Author(s):  
Alexander A Fisher ◽  
Xiang Ji ◽  
Zhenyu Zhang ◽  
Philippe Lemey ◽  
Marc A Suchard
Keyword(s):  
Monte Carlo ◽  
Life History ◽  
Random Walk ◽  
Biological Data ◽  
Brownian Diffusion ◽  
Specific Rate ◽  
Unknown Parameters ◽  
Hamiltonian Monte Carlo ◽  
Speed Increase ◽  
Gradient Calculation

Abstract Relaxed random walk (RRW) models of trait evolution introduce branch-specific rate multipliers to modulate the variance of a standard Brownian diffusion process along a phylogeny and more accurately model overdispersed biological data. Increased taxonomic sampling challenges inference under RRWs as the number of unknown parameters grows with the number of taxa. To solve this problem, we present a scalable method to efficiently fit RRWs and infer this branch-specific variation in a Bayesian framework. We develop a Hamiltonian Monte Carlo (HMC) sampler to approximate the high-dimensional, correlated posterior that exploits a closed-form evaluation of the gradient of the trait data log-likelihood with respect to all branch-rate multipliers simultaneously. Our gradient calculation achieves computational complexity that scales only linearly with the number of taxa under study. We compare the efficiency of our HMC sampler to the previously standard univariable Metropolis–Hastings approach while studying the spatial emergence of the West Nile virus in North America in the early 2000s. Our method achieves at least a 6-fold speed increase over the univariable approach. Additionally, we demonstrate the scalability of our method by applying the RRW to study the correlation between five mammalian life history traits in a phylogenetic tree with $3650$ tips.[Bayesian inference; BEAST; Hamiltonian Monte Carlo; life history; phylodynamics, relaxed random walk.]

Sign in / Sign up

Export Citation Format

Share Document