When model parameters in systems biology are not available from experiments, they need to be inferred so that the resulting simulation reproduces the experimentally known phenomena. For the purpose, Bayesian statistics with Markov chain Monte Carlo (MCMC) is a useful method. Conventional MCMC needs likelihood to evaluate a posterior distribution of acceptable parameters, while the approximate B...

Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on class Layered Adaptive Importance Sampling (LAIS) scheme, which is a family adaptive importance samplers where Markov chain algorithms employed to drive an underlying multiple scheme. The modular nature LAIS ...

Abstract We study a class of adaptive Markov Chain Monte Carlo (MCMC) processes which aim at behaving as an optimal target process via a learning procedure. We show, under appropriate conditions, that the adaptive process and the optimal (nonadaptive) MCMC process share identical asymptotic properties. The special case of adaptive MCMC algorithms governed by stochastic approximation is consider...

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...