A Markov chain Monte Carlo (MCMC) method and a bootstrap method were compared in the estimation of standard errors of item response theory (IRT) true score equating. Three test form relationships were examined: parallel, tauequivalent, and congeneric. Data were simulated based on Reading Comprehension and Vocabulary tests of the Iowa Tests of Basic Skills1. For parallel and congeneric test form...

The evolution of DNA sequences can be described by discrete state continuous time Markov processes on a phylogenetic tree. We consider neighbor-dependent evolutionary models where the instantaneous rate of substitution at a site depends on the states of the neighboring sites. Neighbor-dependent substitution models are analytically intractable and must be analyzed using either approximate or sim...

We propose a novel approximate inference framework that approximates a target distribution by amortising the dynamics of a user-selected Markov chain Monte Carlo (MCMC) sampler. The idea is to initialise MCMC using samples from an approximation network, apply the MCMC operator to improve these samples, and finally use the samples to update the approximation network thereby improving its quality...

We examine the performance of a strategy for Markov chain Monte Carlo (MCMC) developed by simulating a discrete approximation to a stochastic differential equation (SDE). We refer to the approach as diffusion MCMC. A variety of motivations for the approach are reviewed in the context of Bayesian analysis. In particular, implementation of diffusion MCMC is very simple to set-up, even in the pres...

These notes are intended to provide the reader with knowledge of basic concepts of Markov chain Monte Carlo (MCMC) and hopefully also some intuition about how MCMC works. For more thorough accounts of MCMC the reader is referred to e.g. Gilks et al. (1996), Gamerman (1997), or Robert and Casella (1999). Suppose that we are interested in generating samples from a target probability distribution ...

Adaptive Markov Chain Monte Carlo (MCMC) algorithms attempt to ‘learn’ from the results of past iterations so the Markov chain can converge quicker. Unfortunately, adaptive MCMC algorithms are no longer Markovian, so their convergence is difficult to guarantee. In this paper, we develop new diagnostics to determine whether the adaption is still improving the convergence. We present an algorithm...

We consider the problem of estimating continuous-time autoregressive (CAR) processes from discrete-time noisy observations. This can be done within a Bayesian framework using Markov chain Monte Carlo (MCMC) methods. Existing methods include the standard random walk Metropolis algorithm. On the other hand, least-squares (LS) algorithms exist where derivatives are approximated by di erences and p...

As the many examples in this book illustrate, Markov chain Monte Carlo (MCMC) methods have revolutionized Bayesian statistical analyses. Rather than using off-the-shelf models and methods, we can use MCMC to fit application specific models that are designed to account for the particular complexities of a problem at hand. These complex multilevel models are becoming more prevalent throughout the...

We present a novel and powerful strategy for estimating and combining classi ers via ROC curves, decision analysis theory and MCMC simulation. This paradigm also allows us to select samples from an MCMC run in a parsimonious and optimal fashion. Each ROC curve, corresponds to a sample (classi er) obtained with a full Bayesian model, which treats the model dimension, model parameters, regularisa...