相关论文: Concentration inequalities with exchangeable pairs…
We explore conditions on the covariance matrices of a consistent chain of mean zero finite mode Gaussian states in order that the chain may be exchangeable or stationary. For an exchangeable chain our conditions are necessary and…
In this work we study systems consisting of a group of moving particles. In such systems, often some important parameters are unknown and have to be estimated from observed data. Such parameter estimation problems can often be solved via a…
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…
Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov…
We study two interacting particle systems, both modeled as a system of $N$ stochastic differential equations driven by Brownian motions with singular kernels and moderate interaction. We show a quantitative result where the convergence rate…
As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables…
We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains which provide constraints on finite time fluctuations of time-additive…
We discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
We are concerned with obtaining novel concentration inequalities for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We not only derive - for the first time - distribution-free Bernstein-like…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
Donsker Theorem is perhaps the most famous invariance principle result for Markov processes. It states that when properly normalized, a random walk behaves asymptotically like a Brownian motion. This approach can be extended to general…
We generalize the well-known zero bias distribution and the $\lambda$-Stein pair to an approximate zero bias distribution and an approximate $\lambda,R$-Stein pair, respectively. Berry Esseen type bounds to the normal, based on approximate…
A method is discussed that allows combining sets of differential or inclusive measurements. It is assumed that at least one measurement was obtained with simultaneously fitting a set of nuisance parameters, representing sources of…
In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the…
The couplings by change of measure are applied to establish log-Harnack inequality(equivalently the entropy-cost estimate) for conditional McKean-Vlasov SDEs and derive the quantitative conditional propagation of chaos in relative entropy…
We provide a nonasymptotic analysis of convergence to stationarity for a collection of Markov chains on multivariate state spaces, from arbitrary starting points, thereby generalizing results in [Khare and Zhou Ann. Appl. Probab. 19 (2009)…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
Although many efficient heuristics have been developed to solve binary optimization problems, these typically produce correlated solutions for degenerate problems. Most notably, transverse-field quantum annealing - the heuristic employed in…
Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or…