Multicanonical MCMC (Multicanonical Markov Chain Monte Carlo; Multicanonical Monte Carlo) is discussed as a method of rare event sampling. Starting from a review of the generic framework of importance sampling, multicanonical MCMC is introduced, followed by applications in random matrices, random graphs, and chaotic dynamical systems. Replica exchange MCMC (also known as parallel tempering or M...

This paper proposes a novel particle filtering strategy by combining population Monte Carlo Markov chain methods with sequential Monte Carlo chain particle which we call evolving population Monte Carlo Markov Chain (EP MCMC) filtering. Iterative convergence on groups of particles (populations) is obtained using a specified kernel moving particles toward more likely regions. The proposed techniq...

A Bayesian wavelet estimation method for estimating parameters of a stationary I(d) process is represented as an useful alternative to the existing frequentist wavelet estimation methods. The effectiveness of the proposed method is demonstrated through Monte Carlo simulations. The sampling from the posterior distribution is through the Markov Chain Monte Carlo (MCMC) easily implemented in the W...

This letter considers how a number of modern Markov chain Monte Carlo (MCMC) methods can be applied for parameter estimation and inference in state-space models with point process observations. We quantified the efficiencies of these MCMC methods on synthetic data, and our results suggest that the Reimannian manifold Hamiltonian Monte Carlo method offers the best performance. We further compare...

As an important Markov chain Monte Carlo (MCMC) method, the stochastic gradient Langevin dynamics (SGLD) algorithm has achieved great success in Bayesian learning and posterior sampling. However, S...

Isolation with Migration model (IM), which jointly estimates divergence times and migration rates between two populations from DNA sequence data, can capture many phenomena when one population splits into two. The parameters inferences for IM are based on Markov Chain Monte Carlo method (MCMC). Standard implementations of MCMC are prone to fall into local optima. Metropolis Coupled MCMC [(MC)3]...

We present a novel Markov chain Monte Carlo (MCMC) algorithm that generates samples from transdimensional distributions encoding complex constraints. We use factor graphs, a type of graphical model, to encode constraints as factors. Our proposed MCMC method, called locally annealed reversible jump MCMC, exploits knowledge of how dimension changes affect the structure of the factor graph. We emp...

Among various HLM techniques, the Multivariate Hierarchical Linear Model (MHLM) is desirable to use, particularly when multivariate criterion variables are collected and the covariance structure has information valuable for data analysis. In order to reflect prior information or to obtain stable results when the sample size and the number of groups are not sufficiently large, the Bayes method h...

The increasing availability of multi-core and multi-processor architectures provides new opportunities for improving the performance of many computer simulations. Markov Chain Monte Carlo (MCMC) simulations are widely used for approximate counting problems, Bayesian inference and as a means for estimating very high-dimensional integrals. As such MCMC has found a wide variety of applications in ...