论文检索

时空点过程的部分线性单指标模型与函数主成分分析AI 解读

We model spatially and temporally indexed point process data as a multi-level log-Gaussian Cox process where the log intensity function depends on a partially linear single-index structure of spatio-temporal covariates and three latent functional random effects representing the spatial and temporal random effects as well as their interactions. We assume that the latent functional effects are Gaussian processes with Karhunen-Loève representations, and model the unknown link…

多元函数型时间序列的图主成分分析AI 解读

In this paper, we consider multivariate functional time series with a two-way dependence structure: a serial dependence across time points and a graphical interaction among the multiple functions within each time point. We develop the notion of dynamic weak separability, a more general condition than those assumed in literature, and use it to characterize the two-way structure in multivariate functional time series. Based on the proposed weak separability, we develop a…

群组网络Hawkes过程AI 解读

In this work, we study the event occurrences of individuals interacting in a network. To characterize the dynamic interactions among the individuals, we propose a group network Hawkes process (GNHP) model whose network structure is observed and fixed. In particular, we introduce a latent group structure among individuals to account for the heterogeneous user-specific characteristics. A maximum likelihood approach is proposed to simultaneously cluster individuals in the…

重复标记点过程中的标记与点依赖：偏差校正及检验AI 解读

Mark-point dependence plays a critical role in research problems that can be fitted into the general framework of marked point processes. In this work, we focus on adjusting for mark-point dependence when estimating the mean and covariance functions of the mark process, given independent replicates of the marked point process. We assume that the mark process is a Gaussian process and the point process is a log-Gaussian Cox process, where the mark-point dependence is…

高维多元点过程的潜在网络结构学习AI 解读

Learning the latent network structure from large scale multivariate point process data is an important task in a wide range of scientific and business applications. For instance, we might wish to estimate the neuronal functional connectivity network based on spiking times recorded from a collection of neurons. To characterize the complex processes underlying the observed data, we propose a new and flexible class of nonstationary Hawkes processes that allow both excitatory…

具有形状约束成对相关函数的聚集点过程半参数拟合优度检验AI 解读

Specification of a parametric model for the intensity function is a fundamental task in statistics for spatial point processes. It is, therefore, crucial to be able to assess the appropriateness of a suggested model for a given point pattern dataset. For this purpose, we develop a new class of semiparametric goodness-of-fit tests for the specified parametric first-order intensity, without assuming a full data generating mechanism that is needed for the existing popular Monte…

空间平稳函数场的弱可分性检验AI 解读

For spatially dependent functional data, a generalized Karhunen-Loève expansion is commonly used to decompose data into an additive form of temporal components and spatially correlated coefficients. This structure provides a convenient model to investigate the space-time interactions, but may not hold for complex spatio-temporal processes. In this work, we introduce the concept of weak separability, and propose a formal test to examine its validity for non-replicated…

利用具有活跃与非活跃状态的聚集点过程学习人类活动模式AI 解读

Modeling event patterns is a central task in a wide range of disciplines. In applications such as studying human activity patterns, events often arrive clustered with sporadic and long periods of inactivity. Such heterogeneity in event patterns poses challenges for existing point process models. In this article, we propose a new class of clustered point processes that alternate between active and inactive states. The proposed model is flexible, highly interpretable, and can…

多元点模式数据的半参数多项 logistic 回归AI 解读

We propose a new method for analysis of multivariate point pattern data observed in a heterogeneous environment and with complex intensity functions. We suggest semiparametric models for the intensity functions that depend on an unspecified factor common to all types of points. This is for example well suited for analyzing spatial covariate effects on events such as street crime activities that occur in a complex urban environment. A multinomial conditional composite…

病例—对照点模式数据的随机拟似然AI 解读

We propose a novel stochastic quasi-likelihood estimation procedure for case-control point processes. Quasi-likelihood for point processes depends on a certain optimal weight function and for the new method the weight function is stochastic since it depends on the control point pattern. The new procedure also provides a computationally efficient implementation of quasi-likelihood for univariate point processes in which case a synthetic control point process is simulated by…

线性回归中贝叶斯因子的零假设分布AI 解读

We show that under the null, the 2 log(Bayes factor) is asymptotically distributed as a weighted sum of chi-squared random variables with a shifted mean. This claim holds for Bayesian multi-linear regression with a family of conjugate priors, namely, the normal-inverse-gamma prior, the g-prior, and the normal prior. Our results have three immediate impacts. First, we can compute analytically a p-value associated with a Bayes factor without the need of permutation. We provide…

纵向数据半参数协方差分析模型的广义准似然比检验AI 解读

We model generalized longitudinal data from multiple treatment groups by a class of semiparametric analysis of covariance models, which take into account the parametric effects of time dependent covariates and the nonparametric time effects. In these models, the treatment effects are represented by nonparametric functions of time and we propose a generalized quasi-likelihood ratio test procedure to test if these functions are identical. Our estimation procedure is based on…

空间点过程的拟似然AI 解读

Summary Fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates. When Cox or cluster process models are used to accommodate clustering that is not accounted for by the available covariates, likelihoodbased inference becomes computationally cumbersome owing to the complicated nature of the…

时空点过程的函数主成分分析及疾病监测应用AI 解读

In disease surveillance applications, the disease events are modeled by spatio-temporal point processes. We propose a new class of semiparametric generalized linear mixed model for such data, where the event rate is related to some known risk factors and some unknown latent random effects. We model the latent spatio-temporal process as spatially correlated functional data, and propose Poisson maximum likelihood and composite likelihood methods based on spline approximations…

平稳随机过程衍生预测变量的测量误差校正：可卡因治疗数据应用AI 解读

In a cocaine dependence treatment study, we use linear and nonlinear regression models to model posttreatment cocaine craving scores and first cocaine relapse time. A subset of the covariates are summary statistics derived from baseline daily cocaine use trajectories, such as baseline cocaine use frequency and average daily use amount. These summary statistics are subject to estimation error and can therefore cause biased estimators for the regression coefficients. Unlike…

利用风险人口的空间汇总信息估计个体风险AI 解读

We propose a novel alternative to case-control sampling for the estimation of individual-level risk in spatial epidemiology. Our approach uses weighted estimating equations to estimate regression parameters in the intensity function of an inhomogeneous spatial point process, when information on risk-factors is available at the individual level for cases, but only at a spatially aggregated level for the population at risk. We develop data-driven methods to select the weights…

高斯随机场驱动空间点过程的充分降维AI 解读

Summary We develop a sufficient dimension reduction paradigm for inhomogeneous spatial point processes driven by Gaussian random fields. Specifically, we introduce the notion of the kth-order central intensity subspace. We show that a central subspace can be defined as the combination of all central intensity subspaces. For many commonly used spatial point process models, we find that the central subspace is equivalent to the first-order central intensity subspace. To…

已知参数强度形式下非齐次空间点过程二阶统计量的非参数方差估计AI 解读

We introduce new variance estimation procedures for second-order statistics that are computed from a single realization of intensity reweighted stationary spatial point processes. The statistics are defined either on a subset B of the observation window or on the whole window. For the former, we use subblocks that have the same size and shape as B as "replicates" of B in order to estimate the target variance. For the latter, we develop a subsampling estimator for a key…

非齐次空间点过程的两步估计AI 解读

Summary The paper is concerned with parameter estimation for inhomogeneous spatial point processes with a regression model for the intensity function and tractable second-order properties (K-function). Regression parameters are estimated by using a Poisson likelihood score estimating function and in the second step minimum contrast estimation is applied for the residual clustering parameters. Asymptotic normality of parameter estimates is established under certain mixing…

非齐次空间点过程的一致非参数强度估计AI 解读

A common nonparametric approach to estimate the intensity function of an inhomogeneous spatial point process is through kernel smoothing. When conducting the smoothing, one typically uses events only in a local set around the point of interest. But the resulting estimator often is inconsistent, because the number of events in a fixed set is of order 1 for spatial point processes. In this article we propose a new covariate-based kernel smoothing method to estimate the…

强度函数成比例的非齐次空间点过程二阶分析AI 解读

We consider pairs of spatial point processes with intensity functions sharing a common multiplicative term. We introduce two novel approaches to estimating the pair correlation function for one of the point processes by treating the other as a baseline so as to account for the unspecified part of the intensity functions. The first approach is based on nonparametric kernel-smoothing, whereas the second approach uses a conditional likelihood estimation approach to fit a…

非齐次空间点过程统计量的方差估计AI 解读

Summary The paper introduces a new approach to estimate the variance of statistics that are computed from an inhomogeneous spatial point process. The approach proposed is based on the assumption that the observed point process can be thinned to be a second-order stationary point process, where the thinning probability depends only on the first-order intensity function of the (unthinned) original process. The resulting variance estimator is proved to be asymptotically…

非齐次空间点模式的稀疏化分块自助方差估计AI 解读

When modeling inhomogeneous spatial point patterns, it is of interest to fit a parametric model for the first-order intensity function (FOIF) of the process in terms of some measured covariates. Estimates for the regression coefficients, say , can be obtained by maximizing a Poisson maximum likelihood criterion. Little work has been done on the asymptotic distribution of except in some special cases. In this article we show that is asymptotically normal for a general class…

平稳空间点过程的最小二乘拟合AI 解读

Summary The K-function is a popular tool for fitting spatial point process models owing to its simplicity and wide applicability. In this work we study the properties of least squares estimators of model parameters and propose a new method of model fitting via the K-function by using subsampling. We demonstrate consistency and asymptotic normality of our estimators of model parameters and compare the efficiency of our procedure with existing procedures. This is done through…