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In this second part of our two-part paper, we provide a detailed, frequentist framework for propagating uncertainties within our multivariate linear least squares model. This permits us to quantify the impact of uncertainties in…
This work is motivated by an application for the homogeneization of GNSS-derived IWV (Integrated Water Vapour) series. Indeed, these GPS series are affected by abrupt changes due to equipment changes or environemental effects. The detection…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…
Many models of physics beyond the Standard Model include towers of particles whose masses follow an approximately periodic pattern with little spacing between them. These resonances might be too weak to detect individually, but could be…
Capturing the dependence structure of multivariate extreme events is a major concern in many fields involving the management of risks stemming from multiple sources, e.g. portfolio monitoring, insurance, environmental risk management and…
The analysis of record-breaking events is of interest in fields such as climatology, hydrology or anthropology. In connection with the record occurrence, we propose three distribution-free statistics for the changepoint detection problem.…
Standard diffusion models for graph generation typically rely on uniform time-stepping, an approach that overlooks the non-homogeneous dynamics of distributional evolution on complex manifolds. In this paper, we present an…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
We introduce directional regularity, a new definition of anisotropy for multivariate functional data. Instead of taking the conventional view, which determines anisotropy as a notion of smoothness along a dimension, directional regularity…
We propose a novel family of test statistics to detect the presence of changepoints in a sequence of dependent, possibly multivariate, functional-valued observations. Our approach allows to test for a very general class of changepoints,…
The aim of sequential change-point detection is to issue an alarm when it is thought that certain probabilistic properties of the monitored observations have changed. This work is concerned with nonparametric, closed-end testing procedures…
This paper considers the problem of comparing two processes with panel data. A nonparametric test is proposed for detecting a monotone change in the link between the two process distributions. The test statistic is of CUSUM type, based on…
In environmental science applications, extreme events frequently exhibit a complex spatio-temporal structure, which is difficult to describe flexibly and estimate in a computationally efficient way using state-of-art parametric…
A general inversion technique for the recovery of the underlying distribution function for observed galactic disks is presented and illustrated. Under the assumption that these disks are axi-symmetric and thin, the proposed method yields…
We consider a network of sensors deployed to sense a spatio-temporal field and estimate a parameter of interest. We are interested in the case where the temporal process sensed by each sensor can be modeled as a state-space process that is…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
Assume that there are multiple data streams (channels, sensors) and in each stream the process of interest produces generally dependent and non-identically distributed observations. When the process is in a normal mode (in-control), the…
Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known (or estimable from replicate data). A generalized method of moments approach can be used to estimate model…
Numerous approaches are proposed in the literature for non-stationarity marginal extreme value inference, including different model parameterisations with respect to covariate, and different inference schemes. The objective of this article…