Markov chain Monte Carlo (MCMC) algorithms provide a very general recipe for estimating properties of complicated distributions. While their use has become commonplace and there is a large literature on MCMC theory and practice, MCMC users still have to contend with several challenges with each implementation of the algorithm. These challenges include determining how to construct an efficient a...

Koyna region is well-known for its triggered seismic activities since the hazardous earthquake of M = 6.3 occurred around the Koyna reservoir on 10 December 1967. Understanding the shallow distribution of resistivity pattern in such a seismically critical area is vital for mapping faults, fractures and lineaments. However, deducing true resistivity distribution from the apparent resistivity dat...

A Markov chain Monte Carlo (MCMC) simulation is proposed for probabilistic full waveform inversion (FWI) in a layered half-space. Dynamic responses on the half-space surface are estimated using thin-layer method when harmonic vertical force applied. Subsequently, posterior probability distribution function and corresponding objective formulated to minimize difference between estimations observe...

The full Bayesian method for applying neural networks to a prediction problem is to set up the prior/hyperprior structure for the net and then perform the necessary integrals. However, these integrals are not tractable analytically, and Markov Chain Monte Carlo (MCMC) methods are slow, especially if the parameter space is high-dimensional. Using Gaussian processes we can approximate the weight ...

We present a Bayesian approach to the problem of determining parameters for coalescing binary systems observed with laser interferometric detectors. By applying a Markov Chain Monte Carlo (MCMC) algorithm, specifically the Gibbs sampler, we demonstrate the potential that MCMC techniques may hold for the computation of posterior distributions of parameters of the binary system that created the g...

The full Bayesian method for applying neural networks to a prediction problem is to set up the prior/hyperprior structure for the net and then perform the necessary integrals. However, these inte-grals are not tractable analytically, and Markov Chain Monte Carlo (MCMC) methods are slow, especially if the parameter space is high-dimensional. Using Gaussian processes we can approximate the weight...

Bayesian MLP neural networks are a flexible tool in complex nonlinear problems. The approach is complicated by need to evaluate integrals over high-dimensional probability distributions. The integrals are generally approximated with Markov Chain Monte Carlo (MCMC) methods. There are several practical issues which arise when implementing MCMC. This article discusses the choice of starting values...

This paper takes the reader on a journey through history of Bayesian computation, from 18th century to present day. Beginning with one-dimensional integral first confronted by Bayes in 1763, we highlight key contributions of: Laplace, Metropolis (and, importantly, his co-authors!), Hammersley and Handscomb, Hastings, all which set foundations for computational revolution late 20th -- led, prima...