相关论文: An asymptotic Peskun ordering and its application …
Sampling from combinatorial families can be difficult. However, complicated families can often be embedded within larger, simpler ones, for which easy sampling algorithms are known. We take advantage of such a relationship to describe a…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
Representations of branching Markov processes and their measure-valued limits in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a "level,"…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…
We consider exchangeable Markov multi-state survival processes -- temporal processes taking values over a state-space$\mathcal{S}$ with at least one absorbing failure state $\flat \in \mathcal{S}$ that satisfy natural invariance properties…
Strassen's classical martingale coupling theorem states that two real-valued random variables are ordered in the convex (resp.\ increasing convex) stochastic order if and only if they admit a martingale (resp.\ submartingale) coupling. By…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…
This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as…
Galton's rank order statistic is one of the oldest statistical tools for two-sample comparisons. It is also a very natural index to measure departures from stochastic dominance. Yet, its asymptotic behaviour has been investigated only…
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…
We introduce a class of stochastic processes with reinforcement consisting of a sequence of random partitions $\{\mathcal{P}_t\}_{t \ge 1}$, where $\mathcal{P}_t$ is a partition of $\{1,2,\dots, Rt\}$. At each time~$t$,~$R$ numbers are…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…
An easy-to-implement form of the Metropolis Algorithm is described which, unlike most standard techniques, is well suited to sampling from multi-modal distributions on spaces with moderate numbers of dimensions (order ten) in environments…
For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…
It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…
We present an intuitive, conceptual, but semi-rigorous introduction to the celebrated Markov Chain Monte Carlo method using a simple model of population dynamics as our motivation and focusing on a few elementary distributions.…
Stochastic dominance has not been too employed in practice due to its important limitations. To increase its versatility, the concept has recently been adapted by introducing various indices that measure the degree to which one probability…
Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g. uninsurable labor…