Probability distributions and statistical inference for axial data

Observations on axes which lack information on the direction of propagation are referred to as axial data. Such data are often encountered in enviromental sciences, e.g. observations on propagations of cracks or on faults in mining walls. Even though such observations are recorded as angles, circular probability models are inappropriate for such data since the constraint that observations lie only in [0, π) needs to be enforced. Probability models for such axial data are argued here to have a general structure stemming from that of wrapping a circular distribution on a semi-circle. In particular, we consider the most popular circular model, the von Mises or circular normal distribution, and derive the corresponding axial normal distribution. Certain properties of this distribution are established. Maximum likelihood estimation of its parameters are shown to be surprisingly, in contrast to trigonometric moment estimation, numerically quite appealing. Finally we illustrate our results by several real life axial data sets. Received: September 2004/ Revised: December 2004     

杭州城市热岛空间分布及时域-频域多尺度变化特征

利用杭州20个自动气象站逐时数据计算2006年四季各站平均热岛强度,用薄盘样条函数法研究杭州城市热岛的空间变化,发现:夏秋季时较强,而春冬季强度较弱;总体趋势是杭州市丰体城区最大,向外辐散,逐渐减弱.利用2006年2月～2007年2月逐时气象数据,结合Morlet小波变换方法分析了杭州热岛周期变化特征,发现:其在频域上具有多尺度的周期振荡,尺度主要是24 h(日)、168 h(周)和1 490 h(2月).以日为周期的热岛强度与局地气候系统、地面长波辐射、近地层热量交换、人为热的日周期变化有关;而以周为周期的热岛强度变化成因主要与人类活动及城市大气污染物排放的"周末效应"有显著的关系;以2个月为周期的变化特征与一些较大尺度的自然变化相关.结果表明,杭州城市热岛时空变化是天气系统、地面长波辐射、下垫面、大气污染、人为热、人类活动、近地层热量交换等共同作用的结果.     

Intertype mark correlation function: A new tool for the analysis of species interactions

The spatial pattern of the different species in complex ecosystems reflects the underlying ecological processes. In this paper a second order moment function is proposed and tested to analyse the spatial distribution of a mark, which could be a tree characteristic such as diameter or height, between two different types of points, which could be two different tree species. The proposed function was a conditional density function based on the intertype K_rs(d) function, incorporating as test function the correlation of the marks between pairs composed of points of different types. The results obtained in simulated and real plots prove that the function is capable of revealing the scale at which spatial correlation of the mark between two types of points exists. The proposed function allows the spatial association between individuals of different species at different life stages to be identified. This analysis may reveal information on species ecology and interspecific interactions in forest ecosystems.     

Spatial distribution of soil heavy metal pollution estimated by different interpolation methods: accuracy and uncertainty analysis

Mapping the spatial distribution of contaminants in soils is the basis of pollution evaluation and risk control. Interpolation methods are extensively applied in the mapping processes to estimate the heavy metal concentrations at unsampled sites. The performances of interpolation methods (inverse distance weighting, local polynomial, ordinary kriging and radial basis functions) were assessed and compared using the root mean square error for cross validation. The results indicated that all interpolation methods provided a high prediction accuracy of the mean concentration of soil heavy metals. However, the classic method based on percentages of polluted samples, gave a pollution area 23.54-41.92% larger than that estimated by interpolation methods. The difference in contaminated area estimation among the four methods reached 6.14%. According to the interpolation results, the spatial uncertainty of polluted areas was mainly located in three types of region: (a) the local maxima concentration region surrounded by low concentration (clean) sites, (b) the local minima concentration region surrounded with highly polluted samples; and (c) the boundaries of the contaminated areas.     

Comparative performance of generalized additive models and multivariate adaptive regression splines for statistical modelling of species distributions

Two statistical modelling techniques, generalized additive models (GAM) and multivariate adaptive regression splines (MARS), were used to analyse relationships between the distributions of 15 freshwater fish species and their environment. GAM and MARS models were fitted individually for each species, and a MARS multiresponse model was fitted in which the distributions of all species were analysed simultaneously. Model performance was evaluated using changes in deviance in the fitted models and the area under the receiver operating characteristic curve (ROC), calculated using a bootstrap assessment procedure that simulates predictive performance for independent data. Results indicate little difference between the performance of GAM and MARS models, even when MARS models included interaction terms between predictor variables. Results from MARS models are much more easily incorporated into other analyses than those from GAM models. The strong performance of a MARS multiresponse model, particularly for species of low prevalence, suggests that it may have distinct advantages for the analysis of large datasets. Its identification of a parsimonious set of environmental correlates of community composition, coupled with its ability to robustly model species distributions in relation to those variables, can be seen as converging strongly with the purposes of traditional ordination techniques.     

Development of pedestrian- and vehicle-related safety performance functions using Bayesian bivariate hierarchical models with mode-specific covariates

Introduction: Pedestrian safety is a major concern as traffic crashes are the leading cause of fatalities and injuries for commuters. Traffic safety research in the past has developed various strategies to counteract traffic crashes, including the safety performance function (SPF). However, there is still a need for research dedicated to enhancing the SPF for pedestrians from perspectives of methodological framework and data input. To fill this gap, this study aims to add to the current SPF development practice literature by focusing on pedestrian-involved collisions, while considering the typical vehicle ones as well. Methods: First, bivariate models are used to account for the common unobserved heterogeneity shared by the pedestrian- and vehicle-related crashes at the same intersections. Second, variable importance ranking technique is used, along with correlation analysis, to determine mode-specific feature input. Third, the exposure information for both modes, annual pedestrian count, and annual daily vehicles traveled are used for model development. Fourth, a recent Bayesian inference approach (integrated nested Laplace approximation (INLA)) was adopted for bivariate setting. Finally, different evaluation criteria are used to facilitate comprehensive model assessment. Results: The results reveal different statistically significant factors contributing to each of the modes. The offset intersection provides better safety performance for both pedestrians and drivers as compared to other intersection designs. The model findings also corroborate the sensibility of using the bivariate models, rather than the separate univariate ones. Practical Applications: The study shows that pedestrians are more vulnerable to various intersection features such as left-turn channelization, intersection control, urban and rural population group, presence of signal mastarm on the cross-street, and mainline average daily traffic. Greater focus should be directed toward such intersection features to improve pedestrian safety.     

Spatial smoothing techniques for the assessment of habitat suitability

Precise knowledge about factors influencing the habitat suitability of a certain species forms the basis for the implementation of effective programs to conserve biological diversity. Such knowledge is frequently gathered from studies relating abundance data to a set of influential variables in a regression setup. In particular, generalised linear models are used to analyse binary presence/absence data or counts of a certain species at locations within an observation area. However, one of the key assumptions of generalised linear models, the independence of observations is often violated in practice since the points at which the observations are collected are spatially aligned. In this paper, we describe a general framework for semiparametric spatial generalised linear models that allows for the routine analysis of non-normal spatially aligned regression data. The approach is utilised for the analysis of a data set of synthetic bird species in beech forests, revealing that ignorance of spatial dependence actually may lead to false conclusions in a number of situations.

A capture-recapture model with heterogeneity and behavioural response

We develop the non-parametric maximum likelihood estimator (MLE) of the full M_bh capture-recapture model which utilizes both initial capture and recapture data and permits both heterogeneity (h) between animals and behavioural (b) response to capture. Our MLE procedure utilizes non-parametric maximum likelihood estimation of mixture distributions (Lindsay, 1983; Lindsay and Roeder, 1992) and the EM algorithm (Dempsteret al., 1977). Our MLE estimate provides the first non-parametric estimate of the bivariate capture-recapture distribution.Since non-parametric maximum likelihood estimation exists for submodels M_h (allowing heterogeneity only), Mb (allowing behavioural response only) and M₀ (allowing no changes), we develop maximum likelihood-based model selection, specifically the Akaike information criterion (AIC) (Akaike, 1973). The AIC procedure does well in detecting behavioural response but has difficulty in detecting heterogeneity.