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空间出生—死亡—移动过程：基本性质与强度函数估计AI 解读

Abstract Many spatiotemporal data record the time of birth and death of individuals, along with their spatial trajectories during their lifetime, whether through continuous-time observations or discrete-time observations. Natural applications include epidemiology, individual-based modelling in ecology, spatiotemporal dynamics observed in bioimaging and computer vision. The aim of this article is to estimate in this context the birth and death intensity functions that depend…

Gibbs 点过程似然估计的一致性AI 解读

Strong consistency of the maximum likelihood estimator (MLE) for parametric Gibbs point process models is established. The setting is very general. It includes pairwise pair potentials, finite and infinite multibody interactions and geometrical interactions, where the range can be finite or infinite. The Gibbs interaction may depend linearly or nonlinearly on the parameters, a particular case being hardcore parameters and interaction range parameters. As important examples,…

行列式点过程模型与统计推断AI 解读

Summary Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern data sets where nearby points repel each other. Such data are usually modelled by Gibbs point processes, where the likelihood and moment expressions are intractable and simulations are time consuming. We exploit the appealing probabilistic properties of DPPs to develop parametric…

非恒定长记忆参数的检测AI 解读

This article deals with detection of a nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with a constant long memory parameter, typically an I ( d ) series with d > −.5 . The alternative corresponds to an increase in persistence and includes in particular an abrupt or gradual change from I ( d 1 ) to I ( d 2 ), −.5 < d 1 < d 2 . We discuss several test statistics based on the ratio of forward and backward…

平稳带标记 Gibbs 点过程的残差与拟合优度检验AI 解读

Summary The inspection of residuals is a fundamental step for investigating the quality of adjustment of a parametric model to data. For spatial point processes, the concept of residuals has been recently proposed as an empirical counterpart of the Campbell equilibrium equation for marked Gibbs point processes. The paper focuses on stationary marked Gibbs point processes and deals with asymptotic properties of residuals for such processes. In particular, the consistency and…