What is the effective sample size of a spatial point process?

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Ian W. Renner, David I. Warton, Francis K.C. Hui
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引用次数: 4

Abstract

Point process models are a natural approach for modelling data that arise as point events. In the case of Poisson counts, these may be fitted easily as a weighted Poisson regression. Point processes lack the notion of sample size. This is problematic for model selection, because various classical criteria such as the Bayesian information criterion (BIC) are a function of the sample size, n, and are derived in an asymptotic framework where n tends to infinity. In this paper, we develop an asymptotic result for Poisson point process models in which the observed number of point events, m, plays the role that sample size does in the classical regression context. Following from this result, we derive a version of BIC for point process models, and when fitted via penalised likelihood, conditions for the LASSO penalty that ensure consistency in estimation and the oracle property. We discuss challenges extending these results to the wider class of Gibbs models, of which the Poisson point process model is a special case.

空间点过程的有效样本量是多少?
点过程模型是对作为点事件产生的数据进行建模的自然方法。在泊松计数的情况下,这些可以很容易地拟合为加权泊松回归。点过程缺乏样本大小的概念。这对于模型选择是有问题的,因为各种经典准则,如贝叶斯信息准则(BIC)是样本量n的函数,并且是在n趋于无穷大的渐近框架中导出的。在本文中,我们开发了泊松点过程模型的渐近结果,其中观察到的点事件数m在经典回归环境中起着样本大小的作用。根据这一结果,我们为点过程模型导出了一个版本的BIC,当通过惩罚似然进行拟合时,LASSO惩罚的条件确保了估计和oracle属性的一致性。我们讨论了将这些结果扩展到更广泛的吉布斯模型的挑战,其中泊松点过程模型是一个特例。
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来源期刊
Australian & New Zealand Journal of Statistics
Australian & New Zealand Journal of Statistics 数学-统计学与概率论
CiteScore
1.30
自引率
9.10%
发文量
31
审稿时长
>12 weeks
期刊介绍: The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association. The main body of the journal is divided into three sections. The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data. The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context. The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems.
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