Local three-dimensional earthquake tomography by trans-dimensional Monte Carlo sampling

Trans-dimensional Markov chain Monte Carlo

In the context of sample-based computation of Bayesian posterior distributions in complex stochastic systems, this chapter discusses some of the uses for a Markov chain with a prescribed invariant distribution whose support is a union of euclidean spaces of differing dimensions. This leads into a re-formulation of the reversible jump MCMC framework for constructing such ‘trans-dimensional’ Mark...

Radial Basis Function Regression Using Trans-dimensional Sequential Monte Carlo

We consider the general problem of sampling from a sequence of distributions that is defined on a union of subspaces. We will illustrate the general approach on the problem of sequential radial basis function (RBF) regression where the number of kernels is variable and unknown. Our approach, which we term Trans-Dimensional Sequential Monte Carlo (TD-SMC), is based on a generalisation of importa...

Two and Three Dimensional Monte Carlo Simulation of Magnetite Nanoparticle Based Ferrofluids

We have simulated a magnetite nanoparticle based ferrofluid using Monte Carlo method. Two and three dimensional Monte Carlo simulations have been done using parallel computing technique. The aggregation and rearrangement of nanoparticles embedded in a liquid carrier have been studied in various particle volume fractions. Our simulation results are in complete agreement with the reported experim...

Tomography Imaging Through the Monte Carlo Sampling

Infinite-Dimensional Monte Carlo Integration

In mathematics, Monte Carlo integration is a technique for numerical integration using random numbers and a a particular Monte Carlo method numerically computes the Riemann integral. Whereas other algorithms usually evaluate the integrand at a regular grid, Monte Carlo randomly chooses points at which the integrand is evaluated. This method is particularly useful for higher-dimensional integral...