Conditionally heteroscedastic intensity‐dependent marking of log Gaussian Cox processes

Spatial marked point processes are models for systems of points which are randomly distributed in space and provided with measured quantities called marks. This study deals with marking, that is methods of constructing marked point processes from unmarked ones. The focus is density‐dependent marking where the local point intensity affects the mark distribution. This study develops new markings for log Gaussian Cox processes. In these markings, both the mean and variance of the mark distribution depend on the local intensity. The mean, variance and mark correlation properties are presented for the new markings, and a Bayesian estimation procedure is suggested for statistical inference. The performance of the new approach is studied by means of simulation experiments. As an example, a tropical rainforest data is modelled.     

Improving the process of process modelling by the use of domain process patterns

The use of business process models has become prevalent in a wide area of enterprise applications. But while their popularity is expanding, concerns are growing with respect to their proper creation and maintenance. An obvious way to boost the efficiency of creating high-quality business process models would be to reuse relevant parts of existing models. At this point, however, limited support exists to guide process modellers towards the usage of appropriate model content. In this paper, a set of content-oriented patterns is presented, which is extracted from a large set of process models from the order management and manufacturing production domains. The patterns are derived using a newly proposed set of algorithms, which are being discussed in this paper. The authors demonstrate how such Domain Process Patterns, in combination with information on their historic usage, can support process modellers in generating new models. To support the wider dissemination and development of Domain Process Patterns within and beyond the studied domains, an accompanying website has been set up.     

What Happened to Discrete Chaos,the Quenouille Process,and the Sharp Markov Property? Some History of Stochastic Point Processes

The use of properties of a Poisson process to study the randomness of stars is traced back to a 1767 paper. The process was used and rediscovered many times, and we mention some of the early scientific areas. The name Poisson process was first used in print in 1940, and we believe the term was coined in the corridors of Stockholm University some time between 1936 and 1939. We follow the early developments of doubly stochastic processes and cluster processes, and describe different efforts to apply the Markov property to point processes.     

Analysis of failure time using threshold regression with semi‐parametric varying coefficients

Many new statistical models may enjoy better interpretability and numerical stability than traditional models in survival data analysis. Specifically, the threshold regression (TR) technique based on the inverse Gaussian distribution is a useful alternative to the Cox proportional hazards model to analyse lifetime data. In this article we consider a semi‐parametric modelling approach for TR and contribute implementational and theoretical details for model fitting and statistical inferences. Extensive simulations are carried out to examine the finite sample performance of the parametric and non‐parametric estimates. A real example is analysed to illustrate our methods, along with a careful diagnosis of model assumptions.     

国际化过程模型与国际新创企业模型的比较——以知识为分析视角

作为中小企业国际化研究的代表性理论模型,国际化过程模型和国际新创企业模型之间既有显著的差异也存在着密切的联系。二者之间的比较分析,有望成为构建更具一般性的中小企业国际化理论框架的出发点。本文以知识为主要分析视角,讨论了知识在不同理论模型中的作用,并从理论根源、知识角色、知识来源与获取机制等维度对两种理论模型进行了比较分析。     

A Statistical analysis of spatial point patterns A case study

In the project "statistical image analysis" of CWI we have studied some spatial point patterns that originated from biological observations. These observations were the positions of so called EGF-receptors on the surface of human carcinoma cells.
We propose a stochastic model for these point patterns. Since the EGF-receptors appear in clusters on the cell surface, we have opted for the Poisson-cluster-process as the model. We estimated the three parameters in this process by means of a method described by Diggle. We also did some work in assessing the statistical reliability of our estimates.     

A new marked point process model for the federal funds rate target: Methodology and forecast evaluation

Forecasts of key interest rates set by central banks are of paramount concern for investors and policy makers. Recently it has been shown that forecasts of the federal funds rate target, the most anticipated indicator of the Federal Reserve Bank's monetary policy stance, can be improved considerably when its evolution is modeled as a marked point process (MPP). This is due to the fact that target changes occur in discrete time with discrete increments, have an autoregressive nature and are usually in the same direction. We propose a model which is able to account for these dynamic features of the data. In particular, we combine Hamilton and Jordà's [2002. A model for the federal funds rate target. Journal of Political Economy 110(5), 1135–1167] autoregressive conditional hazard (ACH) and Russell and Engle's [2005. A discrete-state continuous-time model of financial transactions prices and times: the autoregressive conditional multinomial-autoregressive conditional duration model. Journal of Business and Economic Statistics 23(2), 166 – 180] autoregressive conditional multinomial (ACM) model. The paper also puts forth a methodology to evaluate probability function forecasts of MPP models. By improving goodness of fit and point forecasts of the target, the ACH–ACM qualifies as a sensible modeling framework. Furthermore, our results show that MPP models deliver useful probability function forecasts at short and medium term horizons.     

基于买卖强度的交易策略及其实证分析

文章引入了点过程中的Hawkes过程来进行股票买卖强度的拟合与预测,并提供了基于该有效预测的交易策略。文中首先对所使用的Hawkes过程进行了介绍,并从理论上说明其在高频金融数据拟合中的优势;之后叙述了极大似然方法在Hawkes模型参数估计中的具体应用;最后,结合由wind数据库中选取的内地股票市场中的股票实例,使用Hawkes过程进行强度预测、策略构建与盈利情况分析,证实了该模型在实际拟合中的优势与策略的有效性。     

Minimax optimality of CUSUM for an autoregressive model

Different change point models for AR(1) processes are reviewed. For some models, the change is in the distribution conditional on earlier observations. For others, the change is in the unconditional distribution. Some models include an observation before the first possible change time – others not. Earlier and new CUSUM type methods are given, and minimax optimality is examined. For the conditional model with an observation before the possible change, there are sharp results of optimality in the literature. The unconditional model with possible change at (or before) the first observation is of interest for applications. We examined this case and derived new variants of four earlier suggestions. By numerical methods and Monte Carlo simulations, it was demonstrated that the new variants dominate the original ones. However, none of the methods is uniformly minimax optimal.     

A nonparametric measure of spatial interaction in point patterns

The strength and range of interpoint interactions in a spatial point process can be quantified by the function J = (1 - G)/(1 - F), where G is the nearest-neighbour distance distribution function and F the empty space function of the process. J(r) is identically equal to 1 for a Poisson process; values of J(r) smaller or larger than 1 indicate clustering or regularity, respectively. We show that, for a large class of point processes, J(r) is constant for distances r greater than the range of spatial interaction. Hence both the range and type of interaction can be inferred from J without parametric model assumptions. It is also possible to evaluate J(r) explicitly for many point process models, so that J is also useful for parameter estimation. Various properties are derived, including the fact that the J function of the superposition of independent point processes is a weighted mean of the J functions of the individual processes. Estimators of J can be constructed from standard estimators of F and G. We compute estimates of J for several standard point pattern datasets and implement a Monte Carlo test for complete spatial randomness.     

On the inclusion of bivariate marked point processes in graphical models

Graphical models use graphs to represent conditional independence relationships among random variables of a multivariate probability distribution. This paper introduces a new kind of chain graph models in which nodes also represent marked point processes. This is relevant to the analysis of event history data, i.e. data consisting of random sequences of events or time durations of states. Survival analysis and duration models are particular cases. This article considers the case of two marked point processes. The idea consists of representing a whole process by a single node and a conditional independence statement by a lack of connection. We refer to the resulting models as graphical duration models.     

Marked point process hotspot maps for homicide and gun crime prediction in Chicago

Crime hotspot maps are a widely used and successful method of displaying spatial crime patterns and allocating police resources. However, hotspot maps are often created over a single timescale using only one crime type. In the case of short-term hotspot maps that utilize several weeks of crime data, risk estimates suffer from a high variance, especially for low frequency crimes such as homicide. Long-term hotspot maps that utilize several years of data fail to take into account near-repeat effects and emerging hotspot trends. In this paper we show how point process models of crime can be extended to include leading indicator crime types, while capturing both short-term and long-term patterns of risk, through a marked point process approach. Several years of data and many different crime types are systematically combined to yield accurate hotspot maps that can be used for the purpose of predictive policing of gun-related crime. We apply the methodology to a large, open source data set which has been made available to the general public online by the Chicago Police Department.     

Estimators of distance distributions for spatial patterns

Baddeley and Gill (1994, 1996) have introduced an edge-corrected Kaplan–Meier type estimator of the empty space function, which is very important in point process statistics. The present paper suggests a further estimator of this function, which is based on a method used by Hanisch (1984) for unbiased edge-corrected estimation of the nearest neighbour distance distribution function. Moreover, it turns out that the Kaplan–Meier and the new estimator are closely related, since their densities are border method or minus-sampling type estimators.     

Aspects of second‐order analysis of structured inhomogeneous spatio‐temporal point processes

Statistical methodology for spatio‐temporal point processes is in its infancy. We consider second‐order analysis based on pair correlation functions and K‐functions for general inhomogeneous spatio‐temporal point processes and for inhomogeneous spatio‐temporal Cox processes. Assuming spatio‐temporal separability of the intensity function, we clarify different meanings of second‐order spatio‐temporal separability. One is second‐order spatio‐temporal independence and relates to log‐Gaussian Cox processes with an additive covariance structure of the underlying spatio‐temporal Gaussian process. Another concerns shot‐noise Cox processes with a separable spatio‐temporal covariance density. We propose diagnostic procedures for checking hypotheses of second‐order spatio‐temporal separability, which we apply on simulated and real data.     

The Candy model: properties and inference

In this paper we study the Candy model, a marked point process introduced by S toica et al. (2000) . We prove Ruelle and local stability, investigate its Markov properties, and discuss how the model may be sampled. Finally, we consider estimation of the model parameters and present a simulation study.     

Performance of methods to conduct mediation analysis with time-to-event outcomes

Previous studies have discouraged the use of the Cox proportional hazards (PH) model for traditional mediation analysis as it might provide biased results. Accelerated failure time (AFT) models have been proposed as an alternative for Cox PH models. In addition, the use of the potential outcomes framework has been proposed for mediation models with time-to-event outcomes. The aim of this paper is to investigate the performance of traditional mediation analysis and potential outcomes mediation analysis based on both the Cox PH and the AFT model. This is done by means of a Monte Carlo simulation study and the illustration of the methods using an empirical data set. Both the product-of-coefficients method of the traditional mediation analysis and the potential outcomes framework yield unbiased estimates with respect to their own underlying indirect effect value for simple mediation models with a time-to-event outcome and estimated based on Cox PH or AFT.     

改进AHP主观性的DEA/AHP新模型

本文提出了一种DEA(数据包络分析)与AHP(层次分析法)结合的新模型。该模型有别于目前国内很多将AHP作为约束锥的DEA混合模型。通过对模型的阐述和算例的验证,得到了DEA/AHP方法相对于DEA的优势。并指出了以AHP作为约束锥的DEA混合模型的不足,以及本文提出的DEA/AHP方法对于AHP主观性的改进,并实现了DEA方法中决策单元的完全排序。     

Analysing Multivariate Spatial Point Processes with Continuous Marks: A Graphical Modelling Approach

This paper discusses the application of graphical modelling in the statistical analysis of marked point patterns. We consider a multivariate planar point process with quantitative marks. After a survey of statistical methods for marked point processes, a new graphical model is presented. The sub‐processes of marked points with identical discrete marks are identified with nodes of a graph, which is used to describe aspects of the spatial relationship: If two sub‐patterns are similar, then an arc is made between the corresponding nodes. Similarity is defined based on spectral densities, which makes the computations efficient. The resulting graph presents all these pairwise similarities simultaneously. We demonstrate the application of our method in the analysis of a multi‐species forest, where the points are tree locations, the discrete marks tree species and the quantitative marks are the diameters at breast height.     

Non- and semi-parametric estimation of interaction in inhomogeneous point patterns

We develop methods for analysing the 'interaction' or dependence between points in a spatial point pattern, when the pattern is spatially inhomogeneous. Completely non-parametric study of interactions is possible using an analogue of the K -function. Alternatively one may assume a semi-parametric model in which a (parametrically specified) homogeneous Markov point process is subjected to (non-parametric) inhomogeneous independent thinning. The effectiveness of these approaches is tested on datasets representing the positions of trees in forests.