论文检索

一般度量图上的对数高斯 Cox 过程AI 解读

Abstract The modelling of spatial point processes has advanced considerably, yet extending these models to non-Euclidean domains, such as road networks, remains a challenging problem. We propose a novel framework for log-Gaussian Cox processes on general compact metric graphs by leveraging Gaussian Whittle–Matérn fields, which are solutions to fractional-order stochastic differential equations on metric graphs. To achieve computationally efficient likelihood-based inference,…

度量图上高斯 Whittle–Matérn 随机场的统计推断AI 解读

Abstract Whittle–Matérn fields are a recently introduced class of Gaussian processes on metric graphs, specified as solutions to a fractional-order stochastic differential equation. Unlike previous covariance-based methods, these fields are well-defined for any compact metric graph and can provide Gaussian processes with differentiable sample paths. We derive the main statistical properties, including the consistency and asymptotic normality of maximum likelihood estimators…

有效尾部假说：市场效率的极值视角AI 解读

In finance, the Efficient Market Hypothesis posits that asset prices reflect all available information in the market. Several empirical investigations show that market efficiency drops when it undergoes extreme events. Many models for multivariate extremes focus on positive dependence, making them unsuitable for studying extremal dependence in financial markets where data often exhibit both positive and negative extremal dependence. To this end, we construct regular…

空间自混杂：空间回归中与平滑度有关的估计偏差AI 解读

Abstract The estimation of regression parameters in spatially referenced data plays a crucial role across various scientific domains. A common approach involves employing an additive regression model to capture the relationship between observations and covariates, accounting for spatial variability not explained by the covariates through a Gaussian random field. We study the effect of misspecified covariates, in particular when the misspecification changes the smoothness. We…

稳健性、模型检验与层级模型AI 解读

Abstract Model checking is essential to evaluate the adequacy of statistical models and the validity of inferences drawn from them. Particularly, hierarchical models such as latent Gaussian models (LGMs) pose unique challenges as it is difficult to check assumptions on the latent parameters. Diagnostic statistics are often used to quantify the degree to which a model fit deviates from the observed data. We construct diagnostic statistics by (a) defining an alternative model…

利用变分贝叶斯与拉普拉斯近似拟合潜在非高斯模型AI 解读

Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that contain inherently non-Gaussian features, such as sudden jumps or spikes, that adversely affect the inferences and predictions made using an LGM. These datasets require more general latent non-Gaussian models (LnGMs) that can handle…

紧致度量空间随机场渐近最优线性预测的充要条件AI 解读

Optimal linear prediction (aka. kriging) of a random field {Z(x)}x∈X indexed by a compact metric space (X,dX) can be obtained if the mean value function m:X→R and the covariance function ϱ:X×X→R of Z are known. We consider the problem of predicting the value of Z(x∗) at some location x∗∈X based on observations at locations {xj}j=1n, which accumulate at x∗ as n→∞ (or, more generally, predicting φ(Z) based on {φj(Z)}j=1n for linear functionals φ,φ1,…,φn). Our main result…

皮层表面 fMRI 数据分析的贝叶斯一般线性模型方法AI 解读

Cortical surface fMRI (cs-fMRI) has recently grown in popularity versus traditional volumetric fMRI. In addition to offering better whole-brain visualization, dimension reduction, removal of extraneous tissue types, and improved alignment of cortical areas across subjects, it is also more compatible with common assumptions of Bayesian spatial models. However, as no spatial Bayesian model has been proposed for cs-fMRI data, most analyses continue to employ the classical…

基于随机偏微分方程的多元 G 型 Matérn 随机场AI 解读

Summary For many applications with multivariate data, random-field models capturing departures from Gaussianity within realizations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of stochastic partial differential equations with additive type G noise whose marginal covariance functions are of Matérn type. We consider four increasingly flexible constructions of the noise, where the first two are similar to…