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Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…
The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
This paper concerns the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models with normalized random measure priors. Making use of some recent posterior characterizations for the class of…
The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributions? Many papers on the subject have shown, roughly, that the…
Single-chain Markov chain Monte Carlo simulates realizations from a Markov chain to estimate expectations with the empirical average. The single-chain simulation is generally of considerable length and restricts many advantages of modern…
Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing…
Atomistic simulations provide valuable insights into the physical processes governing material behavior. However, their applicability is fundamentally constrained by the limited time scales accessible to brute-force simulations. This…
To sample from a given target distribution, Markov chain Monte Carlo (MCMC) sampling relies on constructing an ergodic Markov chain with the target distribution as its invariant measure. For any MCMC method, an important question is how to…
This paper shows how one can use Sequential Monte Carlo methods to perform what is typically done using Markov chain Monte Carlo methods. This leads to a general class of principled integration and genetic type optimization methods based on…
We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…
Enriching Brownian motion with regenerations from a fixed regeneration distribution $\mu$ at a particular regeneration rate $\kappa$ results in a Markov process that has a target distribution $\pi$ as its invariant distribution. For the…
Monte Carlo estimation in plays a crucial role in stochastic reaction networks. However, reducing the statistical uncertainty of the corresponding estimators requires sampling a large number of trajectories. We propose control variates…
This article is a tutorial on Markov chain Monte Carlo simulations and their statistical analysis. The theoretical concepts are illustrated through many numerical assignments from the author's book on the subject. Computer code (in Fortran)…
The Markov Chain Monte Carlo (MCMC) algorithm is a widely recognised as an efficient method for sampling a specified posterior distribution. However, when the posterior is multi-modal, conventional MCMC algorithms either tend to become…
We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…
Markov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, whenever either the distribution does not exist in closed form, or, if it does, no efficient method to simulate an independent sample from…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
For many probability distributions of interest, it is quite difficult to obtain samples efficiently. Often, Markov chains are employed to obtain approximately random samples from these distributions. The primary drawback to traditional…