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We show how to construct the optimum superstatistical dynamical model for a given experimentally measured time series. For this purpose we generalise the superstatistics concept and study a Langevin equation with a memory kernel whose…

Determinantal point processes are models for regular spatial point patterns, with appealing probabilistic properties. We present their spatio-temporal counterparts and give examples of these models, based on spatio-temporal covariance…

State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series…

This article introduces autocorrelograms for time series of point processes. Such time series usually arise when a longer temporal or spatio-temporal point process is sliced into smaller time units; for example, when an annual process is…

Marked temporal point processes (MTPPs) model sequences of events occurring at irregular time intervals, with wide-ranging applications in fields such as healthcare, finance and social networks. We propose the state-space point process…

Data collected from a bike-sharing system exhibit complex temporal and spatial features. We analyze shared-bike usage data collected in three large cities at the level of individual stations, accounting for station-specific behavior and…

We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a…

Discrete latent space models have recently achieved performance on par with their continuous counterparts in deep variational inference. While they still face various implementation challenges, these models offer the opportunity for a…

Point process data are becoming ubiquitous in modern applications, such as social networks, health care, and finance. Despite the powerful expressiveness of the popular recurrent neural network (RNN) models for point process data, they may…

A new discrete-time shot noise Cox process for spatiotemporal data is proposed. The random intensity is driven by a dependent sequence of latent gamma random measures. Some properties of the latent process are derived, such as an…

This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…

We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary…

Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling…

We propose a novel sparse spatiotemporal dynamic generalized linear model for efficient inference and prediction of bicycle count data. Assuming Poisson distributed counts with spacetime-varying rates, we model the log-rate using…

In this paper, we are interested in linear prediction of a particular kind of stochastic process, namely a marked temporal point process. The observations are event times recorded on the real line, with marks attached to each event. We show…

Gaussian random fields with Mat\'ern covariance functions are popular models in spatial statistics and machine learning. In this work, we develop a spatio-temporal extension of the Gaussian Mat\'ern fields formulated as solutions to a…

A new stochastic model for daily precipitation occurrence processes observed at multiple locations is developed. The modeling concept is to use the indicator function and the elliptical shape of multivariate Gaussian distribution to…

This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…

The statistical modeling of multivariate count data observed on a space-time lattice has generally focused on using a hierarchical modeling approach where space-time correlation structure is placed on a continuous, latent, process. The…

The spectral theory for weakly stationary processes valued in a separable Hilbert space has known renewed interest in the past decade. Here we follow earlier approaches which fully exploit the normal Hilbert module property of the time…