Related papers: Evaluating Approximations of Count Distributions a…

Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…

Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the…

We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with…

This paper is devoted to filtering, smoothing, and prediction of polynomial processes that are partially observed. These problems are known to allow for an explicit solution in the simpler case of linear Gaussian state space models. The key…

This work presents a new methodology to obtain probabilistic interval predictions of a dynamical system. The proposed strategy uses stored past system measurements to estimate the future evolution of the system. The method relies on the use…

We present a scheme by which a probabilistic forecasting system whose predictions have poor probabilistic calibration may be recalibrated by incorporating past performance information to produce a new forecasting system that is demonstrably…

Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector…

The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…

A new integer--valued autoregressive process (INAR) with Generalised Lagrangian Katz (GLK) innovations is defined. This process family provides a flexible modelling framework for count data, allowing for under and over--dispersion,…

We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…

Most time-series models assume that the data come from observations that are equally spaced in time. However, this assumption does not hold in many diverse scientific fields, such as astronomy, finance, and climatology, among others. There…

This paper reviews two main types of prediction interval methods under a parametric framework. First, we describe methods based on an (approximate) pivotal quantity. Examples include the plug-in, pivotal, and calibration methods. Then we…

For discrete-valued time series, predictive inference cannot be implemented through the construction of prediction intervals to some predetermined coverage level, as this is the case for real-valued time series. To address this problem, we…

We propose a new model for nonstationary integer-valued time series which is particularly suitable for data with a strong trend. In contrast to popular Poisson-INGARCH models, but in line with classical GARCH models, we propose to pick the…

We propose a flexible Bayesian approach for sparse Gaussian graphical modeling of multivariate time series. We account for temporal correlation in the data by assuming that observations are characterized by an underlying and unobserved…

A set of probabilities along with corresponding quantiles are often used to define predictive distributions or probabilistic forecasts. These quantile predictions offer easily interpreted uncertainty of an event, and quantiles are generally…

Dynamic Linear Models (DLMs) are commonly employed for time series analysis due to their versatile structure, simple recursive updating, ability to handle missing data, and probabilistic forecasting. However, the options for count time…

Learning vector autoregressive models from multivariate time series is conventionally approached through least squares or maximum likelihood estimation. These methods typically assume a fully connected model which provides no direct insight…

We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…

We develop an automated variational method for inference in models with Gaussian process (GP) priors and general likelihoods. The method supports multiple outputs and multiple latent functions and does not require detailed knowledge of the…