Application of the von Mises–Fisher distribution to Random Walk on Spheres method for solving high-dimensional diffusion–advection–reaction equations

2018 ◽  
Vol 138 ◽  
pp. 137-142 ◽  
Author(s):  
Karl K. Sabelfeld
Keyword(s):  
Random Walk ◽  
High Dimensional ◽  
Fisher Distribution ◽  
Dimensional Diffusion ◽  
Von Mises ◽  
Reaction Equations

A global random walk on spheres algorithm for transient heat equation and some extensions

2019 ◽  
Vol 25 (1) ◽  
pp. 85-96 ◽  
Author(s):  
Karl K. Sabelfeld
Keyword(s):  
Random Walk ◽  
Heat Equation ◽  
Symmetry Property ◽  
Forthcoming Paper ◽  
Diffusion Reaction ◽  
Advection Diffusion ◽  
The Green Function ◽  
Walk On Spheres Algorithm ◽  
Reaction Equations ◽  
Advection Diffusion Reaction Equations

AbstractWe suggest in this paper a global Random Walk on Spheres (gRWS) method for solving transient boundary value problems, which, in contrast to the classical RWS method, calculates the solution in any desired family ofmprescribed points. The method uses onlyNtrajectories in contrast tomNtrajectories in the conventional RWS algorithm. The idea is based on the symmetry property of the Green function and a double randomization approach. We present the gRWS method for the heat equation with arbitrary initial and boundary conditions, and the Laplace equation. Detailed description is given for 3D problems; the 2D problems can be treated analogously. Further extensions to advection-diffusion-reaction equations will be presented in a forthcoming paper.

scholarly journals Clustering Directions Based on the Estimation of a Mixture of Von Mises-Fisher Distributions

2017 ◽  
Vol 08 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Adelaide Figueiredo
Keyword(s):  
Statistical Analysis ◽  
Simulation Study ◽  
Directional Data ◽  
Fisher Distribution ◽  
Spherical Data ◽  
Model Unit ◽  
Type Algorithm ◽  
Estimation Maximization Algorithm ◽  
Von Mises ◽  
Unit Vectors

Background:In the statistical analysis of directional data, the von Mises-Fisher distribution plays an important role to model unit vectors. The estimation of the parameters of a mixture of von Mises-Fisher distributions can be done through the Estimation-Maximization algorithm.Objective:In this paper we propose a dynamic clusters type algorithm based on the estimation of the parameters of a mixture of von Mises-Fisher distributions for clustering directions, and we compare this algorithm with the Estimation-Maximization algorithm. We also define the between-groups and within-groups variability measures to compare the solutions obtained with the algorithms through these measures.Results:The comparison of the clusters obtained with both algorithms is provided for a simulation study based on samples generated from a mixture of two Fisher distributions and for an illustrative example with spherical data.

scholarly journals A novel approach for pre-filtering event sources using the von Mises–Fisher distribution

2020 ◽  
Vol 365 (3) ◽  
Author(s):  
D. Costantin ◽  
G. Menardi ◽  
A. R. Brazzale ◽  
D. Bastieri ◽  
J. H. Fan
Keyword(s):  
Fisher Distribution ◽  
Novel Approach ◽  
Von Mises

scholarly journals Optimal Scaling of the Random Walk Metropolis: General Criteria for the 0.234 Acceptance Rule

2013 ◽  
Vol 50 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Chris Sherlock
Keyword(s):  
Random Walk ◽  
Joint Distribution ◽  
Practical Problem ◽  
Sufficient Conditions ◽  
Optimal Scaling ◽  
Acceptance Rate ◽  
High Dimensional ◽  
Random Walk Metropolis ◽  
Functional Forms ◽  
Monte Carlo Implementation

Scaling of proposals for Metropolis algorithms is an important practical problem in Markov chain Monte Carlo implementation. Analyses of the random walk Metropolis for high-dimensional targets with specific functional forms have shown that in many cases the optimal scaling is achieved when the acceptance rate is approximately 0.234, but that there are exceptions. We present a general set of sufficient conditions which are invariant to orthonormal transformation of the coordinate axes and which ensure that the limiting optimal acceptance rate is 0.234. The criteria are shown to hold for the joint distribution of successive elements of a stationary pth-order multivariate Markov process.

Sign in / Sign up

Export Citation Format

Share Document