OF THE DISSERTATION Markov Chain Monte Carlo Estimation Of Multi-Factor Affine Term-Structure Models by He Hu Doctoral of Philosophy in Statistics University of California, Los Angeles, 2005 Professor Jun Liu, Co-Chair Professor Yingnian Wu, Co-Chair This dissertation develops a Bayesian state-space model of the term structure of interest rates. We propose a hybrid Markov Chain Monte Carlo (MCM...

Markov chain Monte Carlo (MCMC) produces a correlated sample in order to estimate expectations with respect to a target distribution. A fundamental question is when should sampling stop so that we have good estimates of the desired quantities? The key to answering this question lies in assessing the Monte Carlo error through a multivariate Markov chain central limit theorem. However, the multiv...

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...

In this paper we introduce a class of non-linear Markov Chain Monte Carlo (MCMC) methods for simulating from a probability measure π. Non-linear Markov kernels (e.g. Del Moral (2004)) can be constructed to admit π as an invariant distribution and have typically superior mixing properties to ordinary (linear) MCMC kernels. However, such non-linear kernels often cannot be simulated exactly, so, i...

Markov random fields are used extensively in modelbased approaches to image segmentation and, under the Bayesian paradigm, are implemented through Markov chain Monte Carlo (MCMC) methods. In this paper, we describe a class of such models (the double Markov random field) for images composed of several textures, which we consider to be the natural hierarchical model for such a task. We show how s...

We present some new results on incorporating quasi-Monte Carlo rules into Markov chain Monte Carlo. First, we present some new constructions of points, fully equidistributed LFSRs, which are small enough that the entire point set can be used in a Monte Carlo calculation. Second, we introduce some antithetic and round trip sampling constructions and show that they preserve the completely uniform...

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...

Markov Chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods are the two most popular classes of algorithms used to sample from general high-dimensional probability distributions. The theoretical convergence of MCMC algorithms is ensured under weak assumptions, but their practical performance is notoriously unsatisfactory when the proposal distributions used to explore the space are...

This article discusses design ideas useful in the development of Markov chain Monte Carlo (MCMC) software. Goals of the design are to facilitate analysis of as many statistical models as possible, and to enable users to experiment with different MCMC algorithms as a research tool. These ideas have been used in YADAS, a system written in the Java language, but are also applicable in other object...

In this paper we use Markov chain Monte Carlo (MCMC) methods in order to estimate and compare GARCH models from a Bayesian perspective. We allow for possibly heavy tailed and asymmetric distributions in the error term. We use a general method proposed in the literature to introduce skewness into a continuous unimodal and symmetric distribution. For each model we compute an approximation to the ...