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We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modeling approach of a wrapped normal distribution that describes angular variables and angular…
Normal variance mixtures are a class of multivariate distributions that generalize the multivariate normal by randomizing (or mixing) the covariance matrix via multiplication by a non-negative random variable W. The multivariate t…
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate…
A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the…
We propose estimating the scale parameter (mean of the eigenvalues) of the scatter matrix of an unspecified elliptically symmetric distribution using weights obtained by solving Tyler's M-estimator of the scatter matrix. The proposed…
We characterise the learning of a mixture of two clouds of data points with generic centroids via empirical risk minimisation in the high dimensional regime, under the assumptions of generic convex loss and convex regularisation. Each cloud…
Heavy-tailed probability distributions are extremely useful and play a crucial role in modeling different types of financial data sets. This study presents a two-pronged methodology. First, a mixture probability distribution is created by…
The paper focuses on a class of light-tailed multivariate probability distributions. These are obtained via a transformation of the margins from a heavy-tailed original distribution. This class was introduced in Balkema et al. (J.…
Multivariate data occurs in a wide range of fields, with ever more flexible model specifications being proposed, often within a multivariate generalised linear mixed effects (MGLME) framework. In this article, we describe an extended…
Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the…
Fully describing the entire data set is essential in multivariate risk assessment, since moderate levels of one variable can influence another, potentially leading it to be extreme. Additionally, modelling both non-extreme and extreme…
In this paper, the multivariate tail covariance (MTCov) for generalized skew-elliptical distributions is considered. Some special cases for this distribution, such as generalized skew-normal, generalized skew student-t, generalized…
We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint…
The mixed effects model for repeated measures (MMRM) has been widely used for the analysis of longitudinal clinical data collected at a number of fixed time points. We propose a robust extension of the MMRM for skewed and heavy-tailed data…
We consider a family of multivariate distributions with heavy-tailed margins and the type I elliptical dependence structure. This class of risks is common in finance, insurance, environmental and biostatistic applications. We obtain the…
The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…
We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with $t$ marginals obtained through scale…
Robots rely on motion planning to navigate safely and efficiently while performing various tasks. In this paper, we investigate motion planning through Bayesian inference, where motion plans are inferred based on planning objectives and…
Heavy tailed distributions present a tough setting for inference. They are also common in industrial applications, particularly with Internet transaction datasets, and machine learners often analyze such data without considering the biases…
This article introduces a non-parametric information-theoretic approach to inference about the tail of a continuous or a discrete distribution. Leveraging a new concept named tail profile -- a set of information-theoretic quantities…