Related papers: Modeling Non-Stationary Processes Through Dimensio…
We introduce computational methods that allow for effective estimation of a flexible, parametric non-stationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field…
Mapping the surrounding environment is essential for the successful operation of autonomous robots. While extensive research has focused on mapping geometric structures and static objects, the environment is also influenced by the movement…
While time series prediction is an important, actively studied problem, the predictive accuracy of time series models is complicated by non-stationarity. We develop a fast and effective approach to allow for non-stationarity in the…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…
We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…
In model-based reinforcement learning, generative and temporal models of environments can be leveraged to boost agent performance, either by tuning the agent's representations during training or via use as part of an explicit planning…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…
Statistical models used to estimate the spatio-temporal pattern in disease risk from areal unit data represent the risk surface for each time period with known covariates and a set of spatially smooth random effects. The latter act as a…
Selected theoretical developments in modeling of deposition of submicrometer size (submicron) particles on solid surfaces, with and without surface diffusion, of interest in colloid, polymer, and certain biological systems, are surveyed. We…
In this research, we propose a novel technique for visualizing nonstationarity in geostatistics, particularly when confronted with a single realization of data at irregularly spaced locations. Our method hinges on formulating a statistic…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
System dynamics (SD) is an effective approach for helping reveal the temporal behavior of complex systems. Although there have been recent developments in expanding SD to include systems' spatial dependencies, most applications have been…
This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…
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…
Motivated by a computer experiment for the design of a rocket booster, this paper explores nonstationary modeling methodologies that couple stationary Gaussian processes with treed partitioning. Partitioning is a simple but effective method…
Astronomical observations suggest that the Universe may be anisotropic on the largest scales. In order to model this situation, we develop a new approach to cosmology that allows for large-scale anisotropy to emerge from the growth of…
This paper investigates the application of Diffusion Policy in non-stationary, vision-based RL settings, specifically targeting environments where task dynamics and objectives evolve over time. Our work is grounded in practical challenges…
A mesoscopic grain-envelope model applying a phase-field front-propagation method is developed to simulate grain growth under additive manufacturing process conditions. The envelope represents the outer surface of dendritic grains through a…