Lévy-based growth models

A spatio-temporal model and inference tools for longitudinal count data on multicolor cell growth

Multicolor cell spatio-temporal image data have become important to investigate organ development and regeneration, malignant growth or immune responses by tracking different cell types both in vivo and in vitro. Statistical modeling of image data from common longitudinal cell experiments poses significant challenges due to the presence of complex spatio-temporal interactions between different cell types and difficulties related to measurement of single cell trajectories. Current analysis methods focus mainly on univariate cases, often not considering the spatio-temporal effects affecting cell…

On building and fitting a spatio-temporal change-point model for settlement and growth at Bourewa, Fiji Islands

The Bourewa beach site on the Rove Peninsula of Viti Levu is the earliest known human settlement in the Fiji Islands. How did the settlement at Bourewa develop in space and time? We have radiocarbon dates on sixty specimens, found in association with evidence for human presence, taken from pits across the site. Owing to the lack of diagnostic stratigraphy, there is no direct archaeological evidence for distinct phases of occupation through the period of interest. We give a spatio-temporal analysis of settlement at Bourewa in which the deposition rate for dated specimens plays an important role…

Identification of Causalities in Spatio-temporal Data

This paper contributes to the understanding of strongly coupled spatio-temporal processes by describing a generic method based on Granger causality. The method is validated by the robust identification of causality regimes and of their phase diagram for an urban morphogenesis model that couples network growth with density. The application to the real case study of Greater Paris transportation projects shows a link between territorial dynamics, more particularly of real estate and socio-economic, and the anticipated network growth. We finally discuss potential extensions to other temporal and s…

时空点过程下经验非平衡最优传输的精确收敛速率

Sharp Convergence Rates of Empirical Unbalanced Optimal Transport for Spatio-Temporal Point Processes

该研究针对时空点过程观测下的非平衡最优传输经验估计量，在弱平稳与次二次方差增长假设下，推导了精确收敛速率及匹配下界，验证了多种点过程下的近似极小极大最优性。

Large Deviation Principle for the Whittaker 2d Growth Model

The Whittaker 2d growth model is a triangular continuous Markov diffusion process that appears in many scientific contexts. It has been theoretically intriguing to establish a large deviation principle for this 2d process with a scaling factor. The main challenge is the spatiotemporal interactions and dynamics that may depend on potential sample-path intersections. We develop such a principle with a novel rate function. Our approach is mainly based on Schider's Theorem, contraction principle, and special treatment for intersecting sample paths.

DIR-ST$^2$: Delineation of Imprecise Regions Using Spatio--Temporal--Textual Information

An imprecise region is referred to as a geographical area without a clearly-defined boundary in the literature. Previous clustering-based approaches exploit spatial information to find such regions. However, the prior studies suffer from the following two problems: the subjectivity in selecting clustering parameters and the inclusion of a large portion of the undesirable region (i.e., a large number of noise points). To overcome these problems, we present DIR-ST$^2$, a novel framework for delineating an imprecise region by iteratively performing density-based clustering, namely DBSCAN, along w…