相关论文: Exactly computing the tail of the Poisson-Binomial…
Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion,…
Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been used for this task which enjoy fewer assumptions on the distributions than the…
We explore the use of higher-order tail area approximations for Bayesian simulation. These approximations give rise to an alternative simulation scheme to MCMC for Bayesian computation of marginal posterior distributions for a scalar…
Accurate reconstruction of probability density functions (PDFs) from data is essential in engineering applications. Classical global moment-based polynomial approximations often suffer from oscillations, instability in the tails, and…
We consider some nonuniformly hyperbolic invertible dynamical systems which are modeled by a Gibbs-Markov-Young tower. We assume a polynomial tail for the inducing time and a polynomial control of hyperbolicity, as introduced by Alves,…
Our focus is on the design and analysis of efficient Monte Carlo methods for computing tail probabilities for the suprema of Gaussian random fields, along with conditional expectations of functionals of the fields given the existence of…
Variational Bayes methods approximate the posterior density by a family of tractable distributions whose parameters are estimated by optimisation. Variational approximation is useful when exact inference is intractable or very costly. Our…
We consider a basic problem in unsupervised learning: learning an unknown \emph{Poisson Binomial Distribution}. A Poisson Binomial Distribution (PBD) over $\{0,1,\dots,n\}$ is the distribution of a sum of $n$ independent Bernoulli random…
The detection of change-points in heterogeneous sequences is a statistical challenge with applications across a wide variety of fields. In bioinformatics, a vast amount of methodology exists to identify an ideal set of change-points for…
We consider a two dimensional skip-free reflecting random walk on a nonnegative integer quadrant. We are interested in the tail asymptotics of its stationary distribution, provided its existence is assumed. We derive exact tail asymptotics…
We develop a new bidirectional algorithm for estimating Markov chain multi-step transition probabilities: given a Markov chain, we want to estimate the probability of hitting a given target state in $\ell$ steps after starting from a given…
In this short note, we derive a precise tail expansion for Gaussian multiplicative chaos (GMC) associated to the 2d GFF on the unit disk with zero average on the unit circle (and variants). More specifically, we show that to first order the…
Count regression models are necessary for examining discrete dependent variables alongside covariates. Nonetheless, when data display outliers, overdispersion, and an abundance of zeros, traditional methods like the zero-inflated negative…
Bayesian composite likelihood estimation of the tail index of a heavy-tailed distribution is addressed when data are randomly right-censored. Maximum a posteriori and mean posterior estimators are constructed under Jeffrey's prior…
A perturbative approach is used to derive approximations of arbitrary order to estimate high percentiles of sums of positive independent random variables that exhibit heavy tails. Closed-form expressions for the successive approximations…
The probabilistic bisection algorithm (PBA) solves a class of stochastic root-finding problems in one dimension by successively updating a prior belief on the location of the root based on noisy responses to queries at chosen points. The…
We propose a novel approach for detecting change points in high-dimensional linear regression models. Unlike previous research that relied on strict Gaussian/sub-Gaussian error assumptions and had prior knowledge of change points, we…
Sampling from a dynamic discrete distribution means drawing an index with probability proportional to a mutable set of weights. Classical constant-time techniques such as the Alias Method are well suited to static distributions, but become…
We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. A simplified version of the bound that parametrizes the ``aggregating distribution'' using a certain pushforward of…
In this paper, we develop a general theory of truncated inverse binomial sampling. In this theory, the fixed-size sampling and inverse binomial sampling are accommodated as special cases. In particular, the classical Chernoff-Hoeffding…