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A non-Bayesian, regression-based or generalized least squares (GLS)-based approach is formally proposed to estimate a class of time-varying AR parameter models. This approach has partly been used by Ito et al. (2014, 2016a,b), and is proven…

Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…

To study the impact of climate variables on morbidity of some diseases in Mexico, we propose a spatio-temporal varying coefficients regression model. For that we introduce a new spatio-temporal dependent process prior, in a Bayesian…

The availability of data on economic uncertainty sparked a lot of interest in models that can timely quantify episodes of international spillovers of uncertainty. This challenging task involves trading off estimation accuracy for more…

Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by…

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…

In this paper we are interested in the problem of adaptive state observation of linear time-varying (LTV) systems where the system and the input matrices depend on unknown time-varying parameters. It is assumed that these parameters satisfy…

For high contrast imaging systems, the time delay is one of the major limiting factors for the performance of the extreme adaptive optics (AO) sub-system and, in turn, the final contrast. The time delay is due to the finite time needed to…

Autocovariance of the error term in a time series model plays a key role in the estimation and inference for the model that it belongs to. Typically, some arbitrary parametric structure is assumed upon the error to simplify the estimation,…

This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…

Traditional partial differential equations with constant coefficients often struggle to capture abrupt changes in real-world phenomena, leading to the development of variable coefficient PDEs and Markovian switching models. Recently,…

We develop a new Bayesian approach to estimating panel spatial autoregressive models with a known number of latent common factors, where N, the number of cross-sectional units, is much larger than T, the number of time periods. Without…

In the present work, we consider variable selection and shrinkage for the Gaussian dynamic linear regression within a Bayesian framework. In particular, we propose a novel method that allows for time-varying sparsity, based on an extension…

Many important problems can be modeled as a system of interconnected entities, where each entity is recording time-dependent observations or measurements. In order to spot trends, detect anomalies, and interpret the temporal dynamics of…

A variational inference-based framework for training a multi-output Gaussian process latent variable model, specifically tailored to the tails-up spatio-temporal stream network, is developed. Training, given a censored observational data…

Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

Graph models provide efficient tools to capture the underlying structure of data defined over networks. Many real-world network topologies are subject to change over time. Learning to model the dynamic interactions between entities in such…