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We introduce a performance-driven framework for constructing strictly causal forward-oriented observables in strongly non-stationary time series. The method combines a robustly normalized composite of heterogeneous indicators with a…
We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates…
Forecasting multivariate time series is a computationally intensive task challenged by extreme or redundant samples. Recent resampling methods aim to increase training efficiency by reweighting samples based on their running losses.…
Estimation of spatially-varying parameters for computationally expensive forward models governed by partial differential equations is addressed. A novel multiscale Bayesian inference approach is introduced based on deep probabilistic…
A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear…
Various nonparametric approaches for Bayesian spectral density estimation of stationary time series have been suggested in the literature, mostly based on the Whittle likelihood approximation. A generalization of this approximation has been…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving…
This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…
Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…
Causal inference in multivariate time series is challenging due to the fact that the sampling rate may not be as fast as the timescale of the causal interactions. In this context, we can view our observed series as a subsampled version of…
We introduce state-space models where the functionals of the observational and the evolutionary equations are unknown, and treated as random functions evolving with time. Thus, our model is nonparametric and generalizes the traditional…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general…
Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned…
Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…
Multivariate peaks over thresholds modeling based on generalized Pareto distributions has up to now only been used in few and mostly 2-dimensional situations. This paper contributes theoretical understanding, physically based models,…
Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the…
We present a method for the joint analysis of a panel of possibly nonstationary time series. The approach is Bayesian and uses a covariate-dependent infinite mixture model to incorporate multiple time series, with mixture components…
Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…