Related papers: Supplement to "Markov Chain Monte Carlo Based on D…
Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics. A full exposition of Markov chains and their use…
Due to its constrained support, the Dirichlet distribution is uniquely suited to many applications. The constraints that make it powerful, however, can also hinder practical implementations, particularly those utilizing Markov Chain Monte…
The tail chain of a Markov chain can be used to model the dependence between extreme observations. For a positive recurrent Markov chain, the tail chain aids in describing the limit of a sequence of point processes $\{N_n,n\geq1\}$,…
Markov chain Monte Carlo is an inherently serial algorithm. Although likelihood calculations for individual steps can sometimes be parallelized, the serial evolution of the process is widely viewed as incompatible with parallelization,…
Markov decision processes are typically used for sequential decision making under uncertainty. For many aspects however, ranging from constrained or safe specifications to various kinds of temporal (non-Markovian) dependencies in task and…
Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and non-defective processes and all possible scenarios we identify the corresponding…
This chapter surveys progress on three related topics in perturbations of Markov chains: the motivating question of when and how "perturbed" MCMC chains are developed, the theoretical problem of how perturbation theory can be used to…
We investigate the concatenation of Markov processes. Our primary concern is to utilize processes constructed in this manner for Monte Carlo integration. To enable this using conventional methods, it is essential to demonstrate the Markov…
The decreasing Markov chain on \{1,2,3, \ldots\} with transition probabilities $p(j,j-i) \propto 1/i$ arises as a key component of the analysis of the beta-splitting random tree model. We give a direct and almost self-contained…
This article proposes a new generalization of the Multivariate Markov Chains (MMC) model. The future values of a Markov chain commonly depend on only the past values of the chain in an autoregressive fashion. The generalization proposed in…
The purpose of this article is threefold. First, it provides the reader with a few useful and efficient tools which should enable her/him to evaluate nontrivial determinants for the case such a determinant should appear in her/his research.…
A discussion on the possibility of reducing the variance of quasi-Monte Carlo estimators in applications. Further details are provided in the accompanying paper "Variance Reduction for Quasi-Monte Carlo".
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This is a supplement to the paper "Liquidity based modeling of asset price bubbles via random matching". The supplement is organized as follows. First, we prove Theorem 3.13 in [1] which provides the existence of the dynamical system D…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…
This article contains lecture notes on the constrained path Monte Carlo method and its applications to study the Hubbard model. The lectures were given at the NATO Advanced Summer Institute held in Ithaca NY (1998). The article is published…
This paper presents a numerical method to calculate the value function for a general discounted impulse control problem for piecewise deterministic Markov processes. Our approach is based on a quantization technique for the underlying…
This review treats the mathematical and algorithmic foundations of non-reversible Markov chains in the context of event-chain Monte Carlo (ECMC), a continuous-time lifted Markov chain that employs the factorized Metropolis algorithm. It…
This is a supplement to the paper "Goncharov's Relations in Bloch's higher Chow Group CH^3(F,5)" submitted as math.AG/0105084. We check the admissiblility of all the cycles appearing in the main article.
We propose a new Markov chain Monte Carlo method in which trial configurations are generated by evolving a state, sampled from a prior distribution, using a Markov transition matrix. We present two prototypical algorithms and derive their…