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As deep neural networks continue to revolutionize various application domains, there is increasing interest in making these powerful models more understandable and interpretable, and narrowing down the causes of good and bad predictions. We…

Bayesian inference for nonlinear diffusions, observed at discrete times, is a challenging task that has prompted the development of a number of algorithms, mainly within the computational statistics community. We propose a new direction,…

Data augmentation improves the convergence of iterative algorithms, such as the EM algorithm and Gibbs sampler by introducing carefully designed latent variables. In this article, we first propose a data augmentation scheme for the…

Linear mixed models (LMMs) are used as an important tool in the data analysis of repeated measures and longitudinal studies. The most common form of LMMs utilize a normal distribution to model the random effects. Such assumptions can often…

The purpose of this paper is to provide a discussion, with illustrating examples, on Bayesian forecasting for dynamic generalized linear models (DGLMs). Adopting approximate Bayesian analysis, based on conjugate forms and on Bayes linear…

We develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We…

We consider Markov models of stochastic processes where the next-step conditional distribution is defined by a kernel density estimator (KDE), similar to Markov forecast densities and certain time-series bootstrap schemes. The KDE Markov…

Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted to a discrete and uniform time grid. They are thus not well suited to explain often irregularly spaced discrete event data from continuous-time phenomena. We show…

As deep neural networks continue to revolutionize various application domains, there is increasing interest in making these powerful models more understandable and interpretable, and narrowing down the causes of good and bad predictions. We…

Contextual optimization enhances decision quality by leveraging side information to improve predictions of uncertain parameters. However, existing approaches face significant challenges when dealing with multimodal or mixtures of…

Physics parameterizations are often needed for numerical weather prediction (NWP) of precipitation forecast. This is mainly because the resolutions of most computational atmospheric models are not fine enough to explicitly resolve sub-grid…

This work presents a novel data augmentation solution for non-stationary multivariate time series and its application to failure prognostics. The method extends previous work from the authors which is based on time-varying autoregressive…

Gait analysis is critical in the early detection and intervention of motor neurological disorders in infants. Despite its importance, traditional methods often struggle to model the high variability and rapid developmental changes inherent…

Stationary time series models built from parametric distributions are, in general, limited in scope due to the assumptions imposed on the residual distribution and autoregression relationship. We present a modeling approach for univariate…

Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…

Generalized linear models (GLMs) using a regression procedure to fit relationships between predictor and target variables are widely used in automobile insurance data. Here, in the process of ratemaking and in order to compute the premiums…

Bayesian Generalized Nonlinear Models (BGNLM) offer a flexible nonlinear alternative to GLM while still providing better interpretability than machine learning techniques such as neural networks. In BGNLM, the methods of Bayesian Variable…

This work focuses on channel estimation in extremely large aperture array (ELAA) systems, where near-field propagation and spatial non-stationarity introduce complexities that hinder the effectiveness of traditional estimation techniques. A…

We propose a sparse vector autoregressive (VAR) hidden semi-Markov model (HSMM) for modeling temporal and contemporaneous (e.g. spatial) dependencies in multivariate nonstationary time series. The HSMM's generic state distribution is…

Standard simultaneous autoregressive (SAR) models typically assume normally distributed errors, an assumption often violated in real-world datasets that frequently exhibit non-normal, skewed, or heavy-tailed characteristics. New SAR models…