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Skew-t copula models are attractive for the modeling of financial data because they allow for asymmetric and extreme tail dependence. We show that the copula implicit in the skew-t distribution of Azzalini and Capitanio (2003) allows for a…
To obtain a probabilistic model for a dependent variable based on some set of explanatory variables, a distributional approach is often adopted where the parameters of the distribution are linked to regressors. In many classical models this…
In recent work, robust mixture modelling approaches using skewed distributions have been explored to accommodate asymmetric data. We introduce parsimony by developing skew-t and skew-normal analogues of the popular GPCM family that employ…
This study aims to improve the spatial representation of uncertainties when regressing surface wind speeds from large-scale atmospheric predictors for sub-seasonal forecasting. Sub-seasonal forecasting often relies on large-scale…
Earth System Models (ESM) are our main tool for projecting the impacts of climate change. However, running these models at sufficient resolution for local-scale risk-assessments is not computationally feasible. Deep learning-based…
General Circulation Models (GCMs) are widely used for future climate projections, but their coarse spatial resolution and systematic biases limit their direct use for impact studies. This limitation is particularly critical for wind-related…
Diffusion models have recently gained recognition for generating diverse and high-quality content, especially in image synthesis. These models excel not only in creating fixed-size images but also in producing panoramic images. However,…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…
Large-scale structures, observed today, are generally believed to have grown from random, small-amplitude inhomogeneities, present in the early Universe. We investigate how gravitational instability drives the distribution of these…
In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates…
Growth mixture models (GMMs) incorporate both conventional random effects growth modeling and latent trajectory classes as in finite mixture modeling; therefore, they offer a way to handle the unobserved heterogeneity between subjects in…
Nonstationarity is a major challenge in analyzing spatial data. For example, daily precipitation measurements may have increased variability and decreased spatial smoothness in areas with high mean rainfall. Common nonstationary covariance…
Sliced inverse regression is one of the most popular sufficient dimension reduction methods. Originally, it was designed for independent and identically distributed data and recently extend to the case of serially and spatially dependent…
Compositional data find broad application across diverse fields due to their efficacy in representing proportions or percentages of various components within a whole. Spatial dependencies often exist in compositional data, particularly when…
We present a detailed review of large-scale structure (LSS) study using the discrete wavelet transform (DWT). After describing how one constructs a wavelet decomposition we show how this bases can be used as a complete statistical…
We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…
Bayesian spatial modeling of heavy-tailed distributions has become increasingly popular in various areas of science in recent decades. We propose a Weibull regression model with spatial random effects for analyzing extreme economic loss.…
There has been considerable recent interest in Bayesian modeling of high-dimensional networks via latent space approaches. When the number of nodes increases, estimation based on Markov Chain Monte Carlo can be extremely slow and show poor…
The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…