相关论文: Geographical Hidden Markov Tree for Flood Extent M…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…
The impact of statistical methodologies on studying groundwater has been significant in the last several decades, due to cheaper computational abilities and presence of technologies that enable us to extract and measure more and more data.…
Atmospheric inverse modelling is a method for reconstructing historical fluxes of green-house gas between land and atmosphere, using observed atmospheric concentrations and an atmospheric tracer transport model. The small number of observed…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
Fluid approximations have seen great success in approximating the macro-scale behaviour of Markov systems with a large number of discrete states. However, these methods rely on the continuous-time Markov chain (CTMC) having a particular…
Natural data observed in $\mathbb{R}^n$ is often constrained to an $m$-dimensional manifold $\mathcal{M}$, where $m < n$. This work focuses on the task of building theoretically principled generative models for such data. Current generative…
Chaotic dynamical systems exhibit strong sensitivity to initial conditions and often contain unresolved multiscale processes, making deterministic forecasting fundamentally limited. Generative models offer an appealing alternative by…
In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…
We consider the task of learning mappings from sequential data to real-valued responses. We present and evaluate an approach to learning a type of hidden Markov model (HMM) for regression. The learning process involves inferring the…
Tackling the difficult problem of estimating spatially distributed hydrological parameters, especially for floods on ungauged watercourses, this contribution presents a novel seamless regionalization technique for learning complex regional…
Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
Flooding remains a major global challenge, worsened by climate change and urbanization, demanding advanced solutions for effective disaster management. While traditional 2D flood mapping techniques provide limited insights, 3D flood…
We consider monotonic, multiple regression for a set of contiguous regions (lattice data). The regression functions permissibly vary between regions and exhibit geographical structure. We develop new Bayesian non-parametric methodology…
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…
Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this…
In the frame of designing a knowledge discovery system, we have developed stochastic models based on high-order hidden Markov models. These models are capable to map sequences of data into a Markov chain in which the transitions between the…
The stochastics two-layer quasi-geostrophic flow model is an intermediate system between the single-layer two dimensional barotropic flow model and the continuously stratified three dimensional baroclinic flow model. This model is widely…
A Markov tree is a probabilistic graphical model for a random vector indexed by the nodes of an undirected tree encoding conditional independence relations between variables. One possible limit distribution of partial maxima of samples from…
Plant phenotyping (Guo et al. 2021; Pieruschka et al. 2019) focuses on studying the diverse traits of plants related to the plants' growth. To be more specific, by accurately measuring the plant's anatomical, ontogenetical, physiological…