Related papers: The projected dynamic linear model for time series…

The last decades have seen an unprecedented increase in the availability of data sets that are inherently global and temporally evolving, from remotely sensed networks to climate model ensembles. This paper provides a view of statistical…

With extreme weather events becoming more common, the risk posed by surface water flooding is ever increasing. In this work we propose a model, and associated Bayesian inference scheme, for generating probabilistic (high-resolution…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

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 manuscript the fixed-lag smoothing problem for conditionally linear Gaussian state-space models is investigated from a factor graph perspective. More specifically, after formulating Bayesian smoothing for an arbitrary state-space…

Learning accurate predictive models of real-world dynamic phenomena (e.g., climate, biological) remains a challenging task. One key issue is that the data generated by both natural and artificial processes often comprise time series that…

In many real-world scenarios, we often deal with streaming data that is sequentially collected over time. Due to the non-stationary nature of the environment, the streaming data distribution may change in unpredictable ways, which is known…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

In real-world scenarios like traffic and energy, massive time-series data with missing values and noises are widely observed, even sampled irregularly. While many imputation methods have been proposed, most of them work with a local…

Sequential probabilistic inference from streaming observations requires modeling distributions over future trajectories as new observations arrive. Although diffusion and flow-matching models are effective at capturing high-dimensional,…

We consider online prediction of a latent dynamic spatiotemporal process and estimation of the associated model parameters based on noisy data. The problem is motivated by the analysis of spatial data arriving in real-time and the current…

We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…

Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…

Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

A Bayesian approach is developed to analyze change points in multivariate time series and space-time data. The methodology is used to assess the impact of extended inundation on the ecosystem of the Gulf Plains bioregion in northern…

The characterization of particle diffusion is a classical problem in physics and probability theory. The field of microrheology is based on experiments in which microscopic tracer beads are placed into a non-Newtonian fluid and tracked…

We present a scalable and robust Bayesian inference method for linear state space models. The method is applied to demand forecasting in the context of a large e-commerce platform, paying special attention to intermittent and bursty target…

This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…

This survey delves into the application of diffusion models in time-series forecasting. Diffusion models are demonstrating state-of-the-art results in various fields of generative AI. The paper includes comprehensive background information…