发表机构
DTIS, ONERA, Université Paris-Saclay（DTIS，ONERA，巴黎萨克雷大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
SLGP包通过空间逻辑高斯过程实现条件密度场的非参数估计，采用随机傅里叶特征和凸优化，提供MAP、拉普拉斯和MCMC三种模式，并在斐济-汤加地震数据上验证。
AI 中文摘要
SLGP包提供了对由协变量索引的概率密度场的非参数估计，适用于样本量不均匀且很少或没有重复观测的数据。空间逻辑高斯过程（Spatial Logistic Gaussian Process）将逻辑密度变换应用于联合指标-响应域上的有限秩高斯过程，从而生成一个在位置、形状和模态上自适应的条件密度先验。本文的贡献在于实现：采用有限秩随机傅里叶特征（Random-Fourier-Feature）表示，使变换后的过程在数值上保持稳定；采用对数凹似然，使拟合成为一个凸问题；以及一系列用于归一化积分的求积捷径，将每次观测的计算成本转变为每个网格的计算成本。提供了三种估计模式：最大后验（MAP）、拉普拉斯近似和全马尔可夫链蒙特卡洛（MCMC）。我们通过经典的斐济-汤加地震目录展示了该包，估计了震源深度分布在该区域内的变形情况，并应用于一个离散响应变体。
英文摘要
The SLGP package provides nonparametric estimation of fields of probability densities indexed by covariates, from unevenly sized samples with few or no replicates. A Spatial Logistic Gaussian Process applies a logistic density transformation to a finite-rank Gaussian process over a joint index-response domain, yielding a prior over conditional densities that adapts in location, shape, and modality. The contribution of this paper is the implementation: a finite-rank Random-Fourier-Feature representation that keeps the transformed process numerically tame, a log-concave likelihood that makes the fit a convex problem, and a family of quadrature shortcuts for the normalising integrals that turn a per-observation cost into a per-grid cost. Three estimation modes are available: MAP, Laplace, and full MCMC. We demonstrate the package throughout on the classical Fiji-Tonga earthquake catalogue, estimating how the distribution of hypocentre depths deforms across the region, and on a discrete-response variant.
