Scalable modeling of nonstationary covariance functions with non-folding B-spline deformation

Optimally adaptive Bayesian spectral density estimation for stationary and nonstationary processes

This article improves on existing methods to estimate the spectral density of stationary and nonstationary time series assuming a Gaussian process prior. By optimising an appropriate eigendecomposition using a smoothing spline covariance structure, our method more appropriately models data with both simple and complex periodic structure. We further justify the utility of this optimal eigendecomposition by investigating the performance of alternative covariance functions other than smoothing splines. We show that the optimal eigendecomposition provides a material improvement, while the other co…

AdaptSPEC-X: Covariate Dependent Spectral Modeling of Multiple Nonstationary Time Series

We present a method for the joint analysis of a panel of possibly nonstationary time series. The approach is Bayesian and uses a covariate-dependent infinite mixture model to incorporate multiple time series, with mixture components parameterized by a time varying mean and log spectrum. The mixture components are based on AdaptSPEC, a nonparametric model which adaptively divides the time series into an unknown number of segments and estimates the local log spectra by smoothing splines. We extend AdaptSPEC to handle missing values, a common feature of time series which can cause difficulties fo…

Flexible models for nonstationary dependence: Methodology and examples

There are many situations when modelling environmental phenomena for which it is not appropriate to assume a stationary dependence structure. \cite{sampson1992} proposed an approach to allowing nonstationarity in dependence based on a deformed space: coordinates from original geographic "$G$" space are mapped to a new dispersion "$D$" space in which stationary dependence is a reasonable assumption. \cite{sampson1992} achieve this with two deformation functions, which are chosen as thin plate splines, each representing how one of the two coordinates in $D$-space relates to the original $G$-spac…

deform：一个通过变形与维度扩展实现非平稳空间高斯过程模型的R包

deform: An R Package for Nonstationary Spatial Gaussian Process Models by Deformations and Dimension Expansion

针对平稳高斯过程难以捕捉大域连续空间依赖的问题，R包deform提供易用函数，支持空间变形、维度扩展两种非平稳GP拟合与可视化，还可实现预测与模拟。

Deep Compositional Spatial Models

Spatial processes with nonstationary and anisotropic covariance structure are often used when modelling, analysing and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and isotropic covariance structure on a warped spatial domain. However, the warping function is generally difficult to fit and not constrained to be injective, often resulting in `space-folding.' Here, we propose modelling an injective warping function through a composition of multiple elemental injective functions in a deep-learning framework. We consider two cases; …

聚集函数数据的层次模型

A Hierarchical Model for Aggregated Functional Data

在许多科学领域，人们的目标是仅根据对聚集总体曲线的观察来估计潜在子总体平均曲线。所谓聚合曲线，我们指的是无法单独观察到的函数数据的线性组合。我们假设有几条具有线性独立系数的聚合曲线。更具体地说，我们假设每个聚合曲线是一个独立的部分实现的高斯过程与平均建模通过加权线性组合的分解曲线。我们建模的高斯过程的平均值作为一个光滑的函数近似的函数属于一个有限维空间${\cal H}_K$，它是由$K$ B-样条基函数跨越。我们探讨两种不同规格的协方差函数的高斯过程：一个是假设一个恒定的方差在整个域的过程中，和一个更一般的方差结构，这本身是建模为一个平滑的功能，提供一个非平稳的协方差函数。推理过程是按照贝叶斯范式进行的，允许在估计分解曲线时考虑专家的意见。此外，它自然地提供了与参数估计和拟合值相关的不确定性。我们的模型适用于广泛的应用。我们集中在两个不同的实际例子：近红外光谱数据的校准问题和不同类型的消费者之间的能量分布的分析。