The n-coalescent is a continuous-time Markov chain on a finite set of states, which describes the family relationships among a sample of n members drawn from a large haploid population. Its transition probabilities can be calculated from a factorization of the chain into two independent components, a pure death process and a discrete-time jump chain. For a deeper study, it is useful to construc...

The gating mechanism of a single ion channel is usually modelled by a nite state space continuous time Markov chain. The patch clamp technique enables the experimenter to record the current owing across a single ion channel. In practice, the current is corrupted by noise and low-pass ltering, and is sampled with a typically very short sampling interval. We present a method for performing Bayesi...

We shall be concerned with the problem of determining the quasistationary distributions of an absorbing continuous-time Markov chain directly from the transition-rate matrix Q. We shall present conditions which ensure that any finite μ-invariant probability measure for Q is a quasistationary distribution. Our results will be illustrated with reference to birth and death processes. QUASISTATIONA...

2 Continuous-Time Markov Chains 3 2.1 Time-homogeneous chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Time-inhomogeneous chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Embedded Discrete-Time Markov Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Conditional Expectations . . . . . . . . . . . . . . . . . . ...

In this article we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects on the continuous latent variables are modelled through a flexible semiparametric predictor. We extend existing LVM with simple linear covariate effects by including nonparametric components for nonlinear effects of continuous covariates and interactions with other cova...

Reversible jump methods are the most commonly used Markov chain Monte Carlo tool for exploring variable dimension statistical models. Recently, however, an alternative approach based on birth-and-death processes has been proposed by Stephens for mixtures of distributions.We show that the birth-and-death setting can be generalized to include other types of continuous time jumps like split-and-co...

In this paper the equivalence between various divisible load-scheduling policies and continuous time Markov chains is demonstrated. This provides a basic unification of both data parallel divisible load scheduling and Markov chain models for the first time in 16 years of research. Such equivalence is demonstrated for divisible scheduling on linear daisy chains and single and two level tree netw...

We give a mathematical framework for Exact Milestoning, a recently introduced algorithm for mapping a continuous time stochastic process into a Markov chain or semi-Markov process that can be efficiently simulated and analyzed. We generalize the setting of Exact Milestoning and give explicit error bounds for the error in the Milestoning equation for mean first passage times.

In this article we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects on the continuous latent variables are modelled through a flexible semiparametric predictor. We extend existing LVM with simple linear covariate effects by including nonparametric components for nonlinear effects of continuous covariates and interactions with other cova...

A recent result of Jun Liu's has shown how to compute explicitly the eigen-values and eigenvectors for the Markov chain derived from a special case of the Hastings sampling algorithm, known as the indepdendence Metropolis sampler. In this note, we show how to extend the result to obtain exact n-step transition probabilities for any n. This is done rst for a chain on a nite state space, and then...