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We study limiting properties of ratios of ordered points of point processes whose intensity measures have regularly varying tails, giving a systematic treatment which points the way to "large-trimming" properties of extremal processes and a…

We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields to a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish…

Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with…

Concentration bounds for non-product, non-Haar measures are fairly recent: the first such result was obtained for contracting Markov chains by Marton in 1996 via the coupling method. The work that followed, with few exceptions, also used…

We introduce a generalization of the Adaptive Multilevel Splitting algorithm in the discrete time dynamic setting, namely when it is applied to sample rare events associated with paths of Markov chains. By interpreting the algorithm as a…

Tuning of measurement models is challenging in real-world applications of sequential Monte Carlo methods. Recent advances in differentiable particle filters have led to various efforts to learn measurement models through neural networks.…

We study dual volume sampling, a method for selecting k columns from an n x m short and wide matrix (n <= k <= m) such that the probability of selection is proportional to the volume spanned by the rows of the induced submatrix. This method…

Many applications in the field of statistics require Markov chain Monte Carlo methods. Determining appropriate starting values and run lengths can be both analytically and empirically challenging. A desire to overcome these problems has led…

A sampling procedure for the transition matrix Monte Carlo method is introduced that generates the density of states function over a wide parameter range with minimal coding effort.

We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…

Markov Chain Monte Carlo (MCMC) techniques are now widely used for cosmological parameter estimation. Chains are generated to sample the posterior probability distribution obtained following the Bayesian approach. An important issue is how…

Computing the volume of a polytope in high dimensions is computationally challenging but has wide applications. Current state-of-the-art algorithms to compute such volumes rely on efficient sampling of a Gaussian distribution restricted to…

This work delves into presenting a probabilistic method for analyzing linear process data with weakly dependent innovations, focusing on detecting change-points in the mean and estimating its spectral density. We develop a test for…

We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our…

We investigate applications of deep neural networks to a point process having an intensity with mixing covariates processes as input. Our generic model includes Cox-type models and marked point processes as well as multivariate point…

For many probability distributions of interest, it is quite difficult to obtain samples efficiently. Often, Markov chains are employed to obtain approximately random samples from these distributions. The primary drawback to traditional…

The estimation of absorption time distributions of Markov jump processes is an important task in various branches of statistics and applied probability. While the time-homogeneous case is classic, the time-inhomogeneous case has recently…

This paper proposes nonparametric two-sample tests for the direct comparison of the probabilities of a particular transition between states of a continuous time nonhomogeneous Markov process with a finite state space. The proposed tests are…

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…

Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…