Related papers: Normal approximation for functions of hidden Marko…

We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a…

Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on…

Point and interval estimation of future disability inception and recovery rates are predominantly carried out by combining generalized linear models (GLM) with time series forecasting techniques into a two-step method involving parameter…

Generalised Bayesian inference updates prior beliefs using a loss function, rather than a likelihood, and can therefore be used to confer robustness against possible mis-specification of the likelihood. Here we consider generalised Bayesian…

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…

The aim of this paper is to propose diffusion strategies for distributed estimation over adaptive networks, assuming the presence of spatially correlated measurements distributed according to a Gaussian Markov random field (GMRF) model. The…

The original Donsker theorem says that a standard random walk converges in distribution to a Brownian motion in the space of continuous functions. It has recently been extended to enriched random walks and enriched Brownian motion. We use…

A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…

Numerical stochastic perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice field theory. The standard algorithms based on the Langevin equation, however, suffer from several limitations which in…

A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…

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…

In this paper we extend Stein's method to the distribution of the product of $n$ independent mean zero normal random variables. A Stein equation is obtained for this class of distributions, which reduces to the classical normal Stein…

We study the generalization properties of stochastic gradient methods for learning with convex loss functions and linearly parameterized functions. We show that, in the absence of penalizations or constraints, the stability and…

Although stochastic models driven by latent Markov processes are widely used, the classical importance sampling methods based on the exponential tilting for these models suffers from the difficulties in computing the eigenvalues and…

Computational procedures for the stationary probability distribution, the group inverse of the Markovian kernel and the mean first passage times of an irreducible Markov chain, are developed using perturbations. The derivation of these…

To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…

We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to…

In this paper we introduce a family of stochastic gradient estimation techniques based of the perturbative expansion around the mean of the sampling distribution. We characterize the bias and variance of the resulting Taylor-corrected…

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…

Generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non-Gaussian responses including binary and count data. In this paper, a new likelihood approach for fitting…