Browsing by Subject "math.PR"
Now showing items 1-20 of 40
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A Large Deviation Approach to Posterior Consistency in Dynamical Systems
In this paper, we provide asymptotic results concerning (generalized) Bayesian inference for certain dynamical systems based on a large deviation approach. Given a sequence of observations $y$, a class of model ... -
A Merge-Split Proposal for Reversible Monte Carlo Markov Chain Sampling of Redistricting Plans
We describe a Markov chain on redistricting plans that makes relatively global moves. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Sampling the space of plans amounts ... -
A stochastic version of Stein Variational Gradient Descent for efficient sampling
We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful for Bayesian inference. The method is to apply ... -
A Variation on the Donsker-Varadhan Inequality for the Principial Eigenvalue
(2017-04-23)The purpose of this short note is to give a variation on the classical Donsker-Varadhan inequality, which bounds the first eigenvalue of a second-order elliptic operator on a bounded domain $\Omega$ by the largest mean first ... -
Asymptotic behavior of branching diffusion processes in periodic media
We study the asymptotic behavior of branching diffusion processes in periodic media. For a super-critical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, ... -
Asymptotic behavior of the Brownian frog model
We introduce an extension of the frog model to Euclidean space and prove properties for the spread of active particles. The new geometry introduces a phase transition that does not occur for the frog model on the lattice. ... -
Complexity of randomized algorithms for underdamped Langevin dynamics
We establish an information complexity lower bound of randomized algorithms for simulating underdamped Langevin dynamics. More specifically, we prove that the worst $L^2$ strong error is of order $\Omega(\sqrt{d}\, N^{-3/2})$, ... -
Convergence of Stratified MCMC Sampling of Non-Reversible Dynamics
We present a form of stratified MCMC algorithm built with non-reversible stochastic dynamics in mind. It can also be viewed as a generalization of the exact milestoning method, or form of NEUS. We prove convergence of the ... -
Coupling and Decoupling to bound an approximating Markov Chain
(2017-07-27)This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple ... -
Ergodicity and Lyapunov functions for Langevin dynamics with singular potentials
(2017-11-30)We study Langevin dynamics of $N$ particles on $R^d$ interacting through a singular repulsive potential, e.g.~the well-known Lennard-Jones type, and show that the system converges to the unique invariant Gibbs measure ... -
Error bounds for Approximations of Markov chains
(2017-11-30)The first part of this article gives error bounds for approximations of Markov kernels under Foster-Lyapunov conditions. The basic idea is that when both the approximating kernel and the original kernel satisfy a Foster-Lyapunov ... -
Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
(2017-04-23)We consider in this work stochastic differential equation (SDE) model for particles in contact with a heat bath when the memory effects are non-negligible. As a result of the fluctuation-dissipation theorem, the differential ... -
Geometric ergodicity of Langevin dynamics with Coulomb interactions
This paper is concerned with the long time behavior of Langevin dynamics of {\em Coulomb gases} in $\mathbf{R}^d$ with $d\geq 2$, that is a second order system of Brownian particles driven by an external force and ... -
Gibbsian dynamics and the generalized Langevin equation
We study the statistically invariant structures of the nonlinear generalized Langevin equation (GLE) with a power-law memory kernel. For a broad class of memory kernels, including those in the subdiffusive regime, ... -
Higher order asymptotics for large deviations -- Part I
For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit ... -
Higher order asymptotics for large deviations -- Part II
We obtain asymptotic expansions for the large deviation principle (LDP) for continuous time stochastic processes with weakly dependent increments. As a key example, we show that additive functionals of solutions ... -
Learning interacting particle systems: diffusion parameter estimation for aggregation equations
(2018-02-14)In this article, we study the parameter estimation of interacting particle systems subject to the Newtonian aggregation. Specifically, we construct an estimator $\widehat{\nu}$ with partial observed data to approximate the ... -
Limiting Behaviors of High Dimensional Stochastic Spin Ensemble
Lattice spin models in statistical physics are used to understand magnetism. Their Hamiltonians are a discrete form of a version of a Dirichlet energy, signifying a relationship to the Harmonic map heat flow equation. The ... -
Moderate Deviation for Random Elliptic PDEs with Small Noise
(2017-04-23)Partial differential equations with random inputs have become popular models to characterize physical systems with uncertainty coming from, e.g., imprecise measurement and intrinsic randomness. In this paper, we perform ... -
Multi-Scale Merge-Split Markov Chain Monte Carlo for Redistricting
We develop a Multi-Scale Merge-Split Markov chain on redistricting plans. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Sampling the space of plans amounts to dividing ...
