Related papers: An effective introduction to the Markov Chain Mont…
Particle Markov Chain Monte Carlo (PMCMC) is a general computational approach to Bayesian inference for general state space models. Our article scales up PMCMC in terms of the number of observations and parameters by generating the…
Using Markov chain Monte Carlo to sample from posterior distributions was the key innovation which made Bayesian data analysis practical. Notoriously, however, MCMC is hard to tune, hard to diagnose, and hard to parallelize. This…
The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient…
We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of energy, and the resultant…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
The goal of this work is to formally abstract a Markov process evolving in discrete time over a general state space as a finite-state Markov chain, with the objective of precisely approximating its state probability distribution in time,…
This paper studies a non-random-walk Markov Chain Monte Carlo method, namely the Hamiltonian Monte Carlo (HMC) method in the context of Subset Simulation used for structural reliability analysis. The HMC method relies on a deterministic…
The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the…
The Metropolis algorithm is a Markov chain Monte Carlo (MCMC) algorithm used to simulate from parameter distributions of interest, such as generalized linear model parameters. The "Metropolis step" is a keystone concept that underlies…
The recently-introduced self-learning Monte Carlo method is a general-purpose numerical method that speeds up Monte Carlo simulations by training an effective model to propose uncorrelated configurations in the Markov chain. We implement…
We introduce the concept of a Markov influence system (MIS) and analyze its dynamics. An MIS models a random walk in a graph whose edges and transition probabilities change endogenously as a function of the current distribution. This…
We consider the recently introduced Transformation-based Markov Chain Monte Carlo (TMCMC) (Dutta and Bhattacharya (2014)), a methodology that is designed to update all the parameters simultaneously using some simple deterministic…
Numerical Generalized Randomized Hamiltonian Monte Carlo is introduced, as a robust, easy to use and computationally fast alternative to conventional Markov chain Monte Carlo methods for continuous target distributions. A wide class of…
This paper addresses the problem of Monte Carlo approximation of posterior probability distributions. In particular, we have considered a recently proposed technique known as population Monte Carlo (PMC), which is based on an iterative…
We present an efficient Monte Carlo algorithm for determining the density of states which is based on the statistics of transition probabilities between states. By measuring the infinite temperature transition probabilities--that is, the…
Population Monte Carlo (PMC) sampling methods are powerful tools for approximating distributions of static unknowns given a set of observations. These methods are iterative in nature: at each step they generate samples from a proposal…
A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…
Smoothing in state-space models amounts to computing the conditional distribution of the latent state trajectory, given observations, or expectations of functionals of the state trajectory with respect to this distributions. For models that…
This paper gives a method for computing distributions associated with patterns in the state sequence of a hidden Markov model, conditional on observing all or part of the observation sequence. Probabilities are computed for very general…
This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo…