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The adapted Wasserstein ($AW$) distance refines the classical Wasserstein ($W$) distance by incorporating the temporal structure of stochastic processes. This makes the $AW$-distance well-suited as a robust distance for many dynamic…
Sensitivity methods for the analysis of the outputs of discrete Bayesian networks have been extensively studied and implemented in different software packages. These methods usually focus on the study of sensitivity functions and on the…
In cluster analysis, a common first step is to scale the data aiming to better partition them into clusters. Even though many different techniques have throughout many years been introduced to this end, it is probably fair to say that the…
Recently, a Wasserstein-type distance for Gaussian mixture models has been proposed. However, that framework can only be generalized to identifiable mixtures of general elliptically contoured distributions whose components come from the…
Random matrix theory is used to assess the significance of weak correlations and is well established for Gaussian statistics. However, many complex systems, with stock markets as a prominent example, exhibit statistics with power-law tails,…
Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…
It is shown that a noncentral Wishart mixture of noncentral Wishart distributions with the same degrees of freedom yields a noncentral Wishart distribution, thereby extending the main result of Jones and Marchand [Stat 10 (2021), Paper No.…
We provide statistical analysis methods for samples of curves when the image but not the parametrisation of the curves is of interest. A parametrisation invariant analysis can be based on the elastic distance of the curves modulo warping,…
Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology and economy. In this work we develop a theory for the eigenvalue fluctuations of diluted…
Bayesian networks are one of the most widely used classes of probabilistic models for risk management and decision support because of their interpretability and flexibility in including heterogeneous pieces of information. In any applied…
We analyze the complexity of sampling from a class of heavy-tailed distributions by discretizing a natural class of It\^o diffusions associated with weighted Poincar\'e inequalities. Based on a mean-square analysis, we establish the…
We compute spectra of large stochastic matrices $W$, defined on sparse random graphs, where edges $(i,j)$ of the graph are given positive random weights $W_{ij}>0$ in such a fashion that column sums are normalized to one. We compute spectra…
We prove a large deviations principle for the class of multidimensional affine stochastic volatility models considered in (Gourieroux, C. and Sufana, R., J. Bus. Econ. Stat., 28(3), 2010), where the volatility matrix is modelled by a…
Randomized algorithms depend on accurate sampling from probability distributions, as their correctness and performance hinge on the quality of the generated samples. However, even for common distributions like Binomial, exact sampling is…
Recent technological advances in many domains including both genomics and brain imaging have led to an abundance of high-dimensional and correlated data being routinely collected. Classical multivariate approaches like Multivariate Analysis…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
The normalized stress metric measures how closely distances between vertices in a graph drawing match the graph-theoretic distances between those vertices. It is one of the most widely employed quality metrics for graph drawing, and is even…
Sensitivity analysis is an important tool used in many domains of computational science to either gain insight into the mathematical model and interaction of its parameters or study the uncertainty propagation through the input-output…
Pearson's chi-squared test is widely used to assess the uniformity of discrete histograms, typically relying on a continuous chi-squared distribution to approximate the test statistic, since computing the exact distribution is…
This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where $\pm \x$ are equivalent), for…