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Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…

Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…

Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…

When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…

Sampling from circular distributions is a fundamental task in directional statistics. A key challenge in acceptance-rejection methods lies in selecting an efficient envelope density, as poor choices can lead to low acceptance rates and…

A two-stage normal hierarchical model called the Fay--Herriot model and the empirical Bayes estimator are widely used to provide indirect and model-based estimates of means in small areas. However, the performance of the empirical Bayes…

The paper proposes a Riemannian Manifold Hamiltonian Monte Carlo sampler to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The…

Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…

Most existing methods for testing equality of means of functional data from multiple populations rely on assumptions of equal covariance and/or Gaussianity. In this work we provide a new testing method based on a statistic that is…

The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow…

We consider sampling from a Gibbs distribution by evolving finitely many particles. We propose a preconditioned version of a recently proposed noise-free sampling method, governed by approximating the score function with the numerically…

The focus of this paper is on the quantification of sampling variation in frequentist probabilistic forecasts. We propose a method of constructing confidence sets that respects the functional nature of the forecast distribution, and use…

Efficient sampling from high-dimensional distributions is a challenging issue which is encountered in many large data recovery problems involving Markov chain Monte Carlo schemes. In this context, sampling using Hamiltonian dynamics is one…

We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…

In this paper, we analyse a method for approximating the distribution function and density of a random variable that depends in a non-trivial way on a possibly high number of independent random variables, each with support on the whole real…

Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators.…

We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…

The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to conduct such sampling, but such a method can converge…

We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the…

In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…