Tracking articulated figures in high dimensional state spaces require tractable methods for inferring posterior distributions of joint locations, angles, and occlusion parameters. Markov chain Monte Carlo (MCMC) methods are efficient sampling procedures for approximating probability distributions. We apply MCMC to the domain of people tracking and investigate a general framework for sample-appr...

Markov Chain Monte-Carlo (MCMC) is an increasingly popular method for obtaining information about distributions, especially for estimating posterior distributions in Bayesian inference. This article provides a very basic introduction to MCMC sampling. It describes what MCMC is, and what it can be used for, with simple illustrative examples. Highlighted are some of the benefits and limitations o...

We study the convergence rate of MCMC on the statistically unidentifiable nonlinear model involving the Michaelis-Menten kinetic equation. We have shown that, under certain conditions, the convergence diagnosis of Raftery and Lewis (1992) is consistent with the convergence rate argued by Brooks and Roberts (1999). Therefore, different MCMC schemes developed in linear models are further extended...

Realistic statistical models often give rise to probability distributions that are computationally difficult to use for inference. Fortunately, we now have a collection of algorithms, known as Markov chain Monte Carlo (MCMC), that has brought many of these models within our computational reach. In turn, this has lead to a staggering amount of both theoretical and applied work on MCMC. Thus we d...

Markov chain Monte Carlo (MCMC) is a popular and successful general-purpose tool for Bayesian inference. However, MCMC cannot be practically applied to large data sets because of the prohibitive cost of evaluating every likelihood term at every iteration. Here we present Firefly Monte Carlo (FlyMC) an auxiliary variable MCMC algorithm that only queries the likelihoods of a potentially small sub...

Markov chain Monte Carlo (MCMC) is one of the most popular statistical inference methods in machine learning. Recent work shows that a significant improvement of the statistical efficiency of MCMC on complex distributions can be achieved by exploiting geometric properties of the target distribution. This is known as geometric MCMC. However, many such methods, like Riemannian manifold Hamiltonia...