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Statistical inference in evolutionary models with site-dependence is a long-standing challenge in phylogenetics and computational biology. We consider the problem of approximating marginal sequence likelihoods under dependent-site models of…
Poisson's equation has a lot of applications in various areas. Usually it is hard to derive the explicit expression of the solution of Poisson's equation for a Markov chain on an infinitely many state space. We will present a computational…
The time to converge to the steady state of a finite Markov chain can be greatly reduced by a lifting operation, which creates a new Markov chain on an expanded state space. For a class of quadratic objectives, we show an analogous behavior…
This paper studies the subgeometric convergence of the stationary distribution in taking the infinite-level limit of a finite-level M/G/1-type Markov chain, that is, in letting the upper boundary level go to infinity. This study is…
We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. Classical simulation-based approaches assume access to the underlying process so that trajectories of…
Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…
We propose a Markov Chain Monte Carlo (MCMC) algorithm based on Gibbs sampling with parallel tempering to solve nonlinear optimal control problems. The algorithm is applicable to nonlinear systems with dynamics that can be approximately…
In this paper, we consider the multiple probabilistic covering location problem (MPCLP), which attempts to open a fixed number of facilities to maximize the total covered customer demand under a joint probabilistic coverage setting. We…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
Markov chain Monte Carlo (MCMC) is the predominant tool used in Bayesian parameter estimation for hierarchical models. When the model expands due to an increasing number of hierarchical levels, number of groups at a particular level, or…
We propose an approach for optimizing nonbinary (NB) quasi-cyclic (QC) LDPC codes. This approach combines constructing of base parity-check matrices by simulated annealing and labeling the obtained base matrices aimed at maximizing the…
To ensure the system stability of the $\bf{\mathcal{H}_{2}}$-guaranteed cost optimal decentralized control problem (ODC), an approximate semidefinite programming (SDP) problem is formulated based on the sparsity of the gain matrix of the…
Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even with gradient information provided.…
Long-term load forecast (LTLF) for area distribution feeders is one of the most critical tasks frequently performed in electric distribution utility companies. For a specific planning area, cost-effective system upgrades can only be planned…
The maximum likelihood estimation of the left-truncated log-logistic distribution with a given truncation point is analyzed in detail from both mathematical and numerical perspectives. These maximum likelihood equations often do not possess…
We propose a stochastic gradient Markov chain Monte Carlo (SG-MCMC) algorithm for scalable inference in mixed-membership stochastic blockmodels (MMSB). Our algorithm is based on the stochastic gradient Riemannian Langevin sampler and…
Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a…
We introduce a class of Adapted Increasingly Rarely Markov Chain Monte Carlo (AirMCMC) algorithms where the underlying Markov kernel is allowed to be changed based on the whole available chain output but only at specific time points…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
In this paper, we develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent…