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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…
Determinantal point processes (DPP) serve as a practicable modeling for many applications of repulsive point processes. A known approach for simulation was proposed in \cite{Hough(2006)}, which generate the desired distribution point wise…
Graphs are commonly used to model various complex systems, including social networks, power grids, transportation networks, and biological systems. In many applications, the connectivity of these networks can be expressed through the Mean…
We introduce the idea that resampling from past observations in a Markov Chain Monte Carlo sampler can fasten convergence. We prove that proper resampling from the past does not disturb the limit distribution of the algorithm. We illustrate…
More than ever, today we are left with the abundance of molecular data outpaced by the advancements of the phylogenomic methods. Especially in the case of presence of many genes over a set of species under the phylogeny question, more…
We explore two notions of stationary processes. The first is called a random-step Markov process in which the stationary process of states, $(X_i)_{i \in \mathbb{Z}}$ has a stationary coupling with an independent process on the positive…
In this paper we propose a perfect simulation algorithm for the Exponential Random Graph Model, based on the Coupling From The Past method of Propp & Wilson (1996). We use a Glauber dynamics to construct the Markov Chain and we prove the…
We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss networks. We use a variation of Dominated Coupling From The Past for which we simulate a…
A number of perfect simulation algorithms for multi-server First Come First Served queues have recently been developed. Those of Connor and Kendall (2015) and Blanchet, Pei, and Sigman (2015) use dominated Coupling from the Past (domCFTP)…
Inference for belief networks using Gibbs sampling produces a distribution for unobserved variables that differs from the correct distribution by a (usually) unknown error, since convergence to the right distribution occurs only…
Fork-join network is a class of queueing networks with applications in manufactory, healthcare and computation systems. In this paper, we develop a simulation algorithm that (1) generates i.i.d. samples of the job sojourn time, jointly with…
What can one say on convergence to stationarity of a finite state Markov chain that behaves "locally" like a nearest neighbor random walk on ${\mathbb Z}$ ? The model we consider is a version of nearest neighbor lazy random walk on the…
The first-passage time (FPT) is the time it takes a system variable to cross a given boundary for the first time. In the context of Markov networks, the FPT is the time a random walker takes to reach a particular node (target) by hopping…
We show that efficient approximate sampling algorithms, combined with a slow exponential time oracle for computing its output distribution, can be combined into constructing efficient perfect samplers, which sample exactly from a target…
Rare event sampling algorithms are essential for understanding processes that occur infrequently on the molecular scale, yet they are important for the long-time dynamics of complex molecular systems. One of these algorithms, transition…
This paper proposes simple perfect samplers using monotone birth-and-death processes (BD-processes), which draw samples from an arbitrary finite discrete target distribution. We first construct a monotone BD-process whose stationary…
In this paper, we present a novel iterative Monte Carlo method for approximating the stationary probability of a single state of a positive recurrent Markov chain. We utilize the characterization that the stationary probability of a state…
We study the representation of stationary Gaussian Markov random fields as factors of i.i.d. processes, with a focus on their approximation by finitely dependent distributions. Our model is a Gaussian field on $\mathbf{Z}^d$ such that the…
We present a simple way to learn a transformation that maps samples of one distribution to the samples of another distribution. Our algorithm comprises an iteration of 1) drawing samples from some simple distribution and transforming them…
We (claim to) prove the extremely surprising fact that NP=RP. It is achieved by creating a Fully Polynomial-Time Randomized Approximation Scheme (FPRAS) for approximately counting the number of independent sets in bounded degree graphs,…