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Fastest Mixing Markov Chain on a Graph
Markov chains second largest eigenvalue modulus fast mixing
2015/7/10
We consider a symmetric random walk on a connected graph, where each edge is labeled with the probability of transition between the two adjacent vertices. The associated Markov chain has a uniform equ...
Fastest Mixing Markov Chain on Graphs with Symmetries
Markov chains fast mixing eigenvalue optimization semidefi nite programming
2015/7/9
We show how to exploit symmetries of a graph to efficiently compute the fastest mixing Markov chain on the graph (i.e., find the transition probabilities on the edges to minimize the second-largest ei...
Accelerated Regeneration for Markov Chain Simulations
Accelerated Regeneration Markov Chain Simulations
2015/7/8
This paper describes a generalization of the classical regenerative method of simulation output analysis. Instead of blocking a generated sample path on returns to a fixed return state, a more general...
A Markov Chain Perspective on Adaptive Monte Carlo Algorithms
Markov Chain Perspective Adaptive Monte Carlo Algorithms
2015/7/8
This paper discusses some connections between adaptive Monte Carlo algorithms and general state space Markov chains. Adaptive algorithms are iterative methods in which previously generated samples are...
Exact Estimation for Markov Chain Equilibrium Expectations
Exact Estimation Markov Chain Equilibrium Expectations
2015/7/6
We introduce a new class of Monte Carlo methods, which we call exact estimation algorithms. Such algorithms provide unbiased estimators for equilibrium expectations associated with real-valued functio...
Coupled coarse graining and Markov Chain Monte Carlo for lattice systems
Markov chain monte carlo random lattice model the short-range particles energy
2014/12/24
We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. ...
Inference in Kingman's Coalescent with Particle Markov Chain Monte Carlo Method
Inference Kingman's Coalescent with Particle Markov Chain Monte Carlo Method
2013/6/13
We propose a new algorithm to do posterior sampling of Kingman's coalescent, based upon the Particle Markov Chain Monte Carlo methodology. Specifically, the algorithm is an instantiation of the Partic...
Convergence rate of Markov chain methods for genomic motif discovery
Gibbs sampler DNA slow mixing spectral gap multimodal
2013/4/27
We analyze the convergence rate of a simplified version of a popular Gibbs sampling method used for statistical discovery of gene regulatory binding motifs in DNA sequences. This sampler satisfies a v...
Discrepancy bounds for uniformly ergodic Markov chain quasi-Monte Carlo
Information visualization Formal Concept Analysis Galois sub-hierarchy
2013/4/27
In [Chen, D., Owen, Ann. Stat., 39, 673--701, 2011] Markov chain Monte Carlo (MCMC) was studied under the assumption that the driver sequence is a deterministic sequence rather than independent U(0,1)...
Improving the Asymptotic Performance of Markov Chain Monte-Carlo by Inserting Vortices
Inserting Vortices Markov Chain Monte-Carlo Asymptotic Performance
2012/11/23
We present a new way of converting a reversible finite Markov chain into a non-reversible one, with a theoretical guarantee that the asymptotic variance of the MCMC estimator based on the non-reversib...
Adaptive Markov Chain Monte Carlo confidence intervals
Adaptive Markov Chain Monte Carlo confidence intervals
2012/11/22
In Adaptive Markov Chain Monte Carlo (AMCMC) simulation, classical estimators of asymptotic variances are inconsistent in general. In this work we establish that despite this inconsistency, confidence...
The three-state toric homogeneous Markov chain model has Markov degree two
three-state toric homogeneous Markov chain model Markov degree two
2012/9/18
We prove that the three-state toric homogenous Markov chain model has Markov degree two. In algebraic terminology this means, that a certain class of toric
ideals are generated by quadratic binomials...
Adaptive Markov Chain Monte Carlo for Auxiliary Variable Method and Its Application to Parallel Tempering
Adaptive Markov Chain Monte Carlo Auxiliary Variable Method Parallel Tempering Conver-gence
2012/9/19
Auxiliary variable methods such as the Parallel Tempering and the cluster Monte Carlo methods generate samples that follow a target distri-bution by using proposal and auxiliary distributions.In sampl...
On nonlinear Markov chain Monte Carlo
Foster–Lyapunov condition interacting Markov chains nonlinear Markov kernels
2011/7/19
Let $\mathscr{P}(E)$ be the space of probability measures on a measurable space $(E,\mathcal{E})$. In this paper we introduce a class of nonlinear Markov chain Monte Carlo (MCMC) methods for simulatin...
A simple variance inequality for U-statistics of a Markov chain with applications
U-statistics Markov chains Inequalities Limit theorems
2011/7/19
We establish a simple variance inequality for U-statistics whose underlying sequence of random variables is an ergodic Markov Chain.