论文标题
用于眼动数据的空间点过程强度的卷积类型模型
A convolution type model for the intensity of spatial point processes applied to eye-movement data
论文作者
论文摘要
在点模式分析中估算一阶强度函数是一个重要的问题，并且已经远离不同的角度接近：参数，半绘图或非参数。我们的方法接近于半参数。由眼动数据激发，我们引入了一个卷积类型模型，其中对数强度被建模为供应$β（\ cdot）$的卷积（供估计），以及单个空间协变量（个人正在寻找眼动数据的图像）。基于傅立叶系列的扩展，我们表明所提出的模型\ rev {可以将其视为具有无限数量系数的}对数线性模型，这对应于$β（\ cdot）$的光谱分解。截断后，我们通过惩罚的泊松可能性来估计这些系数。我们说明了所提出的方法对模拟数据和眼动数据的效率。
Estimating the first-order intensity function in point pattern analysis is an important problem, and it has been approached so far from different perspectives: parametrically, semiparametrically or nonparametrically. Our approach is close to a semiparametric one. Motivated by eye-movement data, we introduce a convolution type model where the log-intensity is modelled as the convolution of a function $β(\cdot)$, to be estimated, and a single spatial covariate (the image an individual is looking at for eye-movement data). Based on a Fourier series expansion, we show that the proposed model \rev{can be viewed as a} log-linear model with an infinite number of coefficients, which correspond to the spectral decomposition of $β(\cdot)$. After truncation, we estimate these coefficients through a penalized Poisson likelihood. We illustrate the efficiency of the proposed methodology on simulated data and on eye-movement data.
