Modelling dependence structures of extreme wind speed using bivariate distribution: a Bayesian approach

When investigating extremes of weather variables, it is seldom that a single weather station determines the damage, and extremes may be caused from the combined behaviour of several weather stations. To investigate joint dependence of extreme wind speed, a bivariate generalised extreme value distribution (BGEVD) was considered from frequentist and Bayesian approaches to analyse the extremes of component-wise monthly maximum wind speed at selected weather stations in South Africa. In the frequentist approach, the parameters of extreme value distributions (EVDs) were estimated with maximum likelihood, whereas in the Bayesian approach the Markov Chain Monte Carlo (MCMC) technique was used with the Metropolis–Hastings algorithm. The results showed that when fitted to component-wise maxima of extreme weather variables, the BGEVD provided apparent benefits over the univariate method, which allowed information to be pooled across stations and resulted in improved precision of the estimates for the parameters and return levels of the distributions. The paper also discusses a method to construct informative priors empirically using historical data of the underlying process from weather characteristics of four pairs of surrounding weather stations at various distances. The results from the Bayesian analysis showed that posterior inference might be affected by the choice of priors that were used to formulate the informative priors. From the results, it could be inferred that the Bayesian approach provides a satisfactory estimation strategy in terms of precision, compared with the frequentist approach, because it accounts for uncertainty in parameters and return level estimations.     

北京城市热岛的定量监测及规划模拟研究

为定量地评估北京城市热岛现状并预测未来北京城市热岛发展趋势,分别采用气温资料、遥感资料和城市规划资料进行了研究分析。对北京20个气象台站按照台站距离城市中心的距离划分为远郊、近郊和城市三类,分别计算三种类型站点经过海拔订正后的年平均气温,利用1971-2012年城市站和远郊站的年平均气温差值估算北京气温热岛的时间变化;利用1987-2012年的NOAA/AVHRR和Landsat-TM两种不同分辨率的卫星资料,采用定量化的指标--地表热岛强度和热岛比例指数分别估算了不同时期北京地区和城六区热岛强度和范围,并对北京平原地区的城市热岛状况进行了评估;利用2020年的北京城市规划土地利用资料,结合2008年的城市热岛现状监测结果对2020年的北京热岛状况进行了模拟分析。研究结果表明,北京城市的气温热岛与遥感监测地表热岛在时间变化趋势上具有一致性,不同分辨率卫星资料监测地表热岛在时空分布上也具有一致性。其中1971-2012年,以年平均气温计算的北京城市热岛强度增温率为0.33℃·（10 a）-1,近5年（2008-2012）平均热岛为1.12℃。遥感监测结果显示1987-2001年北京地区的热岛持续增强,2001年之后由于北京申奥的成功进行了大面积的旧城改造和绿化,使得城市热岛强度和范围在2004年和2008年有所降低,2008年之后城市热岛继续向东、南和北方向扩展,并出现了中心城区热岛与通州、顺义、大兴、昌平热岛连成片的趋势,到2012年城六区热岛面积百分比已从1990年的31%增加到77%。由热岛比例指数确定的北京各区县热岛强度排名前三分别是城区、海淀和丰台,延庆县最低。对2020年城市规划图热岛模拟结果显示北京热岛已由“摊大饼”演变为“中心＋周边分散”模式,中心城区热岛强度和范围明显减弱,周边广大远郊区将出现分散?     

Bayesian spatial prediction

This paper presents a complete Bayesian methodology for analyzing spatial data, one which employs proper priors and features diagnostic methods in the Bayesian spatial setting. The spatial covariance structure is modeled using a rich class of covariance functions for Gaussian random fields. A general class of priors for trend, scale, and structural covariance parameters is considered. In particular, we obtain analytic results that allow easy computation of the predictive distribution for an arbitrary prior on the parameters of the covariance function using importance sampling. The computations, as well as model diagnostics and sensitivity analysis, are illustrated with a set of precipitation data.     

Spatiotemporal hierarchical modelling of extreme precipitation in Western Australia using anisotropic Gaussian random fields

We discuss an approach for the statistical modelling of extreme precipitation events in South-West Australia over space and time, using a latent spatiotemporal process where precipitation maxima follow a generalised extreme value distribution. Temporal features are captured by modelling trends on the location and scale parameters. Spatial features are captured using anisotropic Gaussian random fields. Site specific explanatory variables are also incorporated. We fit several models using Bayesian inferential methods to precipitation extremes recorded at 36 weather stations around the Western Australian state capital city of Perth over the period 1907–2009. Model choice is performed using the DIC criterion. The best fitting model shows significant non-stationarity over time, with extreme precipitation events becoming less frequent. Extreme precipitation events are stronger at coastal locations, with the intensity decreasing as we head to the higher and drier areas to the North-East.     

Field-scale roles of density, temperature, nitrogen, and predation on aphid population dynamics

Robust analyses of noisy, stage-structured, irregularly spaced, field-scale data incorporating multiple sources of variability and nonlinear dynamics remain very limited, hindering understanding of how small-scale studies relate to large-scale population dynamics. We used a novel, complementary Bayesian and frequentist state-space model analysis to ask how density, temperature, plant nitrogen, and predators affect cotton aphid (Aphis gossypii) population dynamics in weekly data from 18 field-years and whether estimated effects are consistent with small-scale studies. We found clear roles of density and temperature but not of plant nitrogen or predators, for which Bayesian and frequentist evidence differed. However, overall predictability of field-scale dynamics remained low. This study demonstrates stage-structured state-space model analysis incorporating bottom-up, top-down, and density-dependent effects for within-season (nearly continuous time), nonlinear population dynamics. The analysis combines Bayesian posterior evidence with maximum-likelihood estimation and frequentist hypothesis testing using average one-step-ahead residuals.     

Generalized extreme value regression for ordinal response data

This paper introduces a flexible skewed link function for modeling ordinal response data with covariates based on the generalized extreme value (GEV) distribution. Commonly used probit, logit and complementary log-log links are prone to link misspecification because of their fixed skewness. The GEV link is flexible in fitting the skewness in the response curve with a free shape parameter. Using Bayesian methodology, it automatically detects the skewness in the response curve along with the model fitting. The flexibility of the proposed model is illustrated by its application to an ecological survey data about the coverage of Berberis thunbergii in New England. We employ the latent variable approach by Albert and Chib (J Am Stat Assoc 88:669–679, (1993) to develop computational schemes. For model selection, we employ the Deviance Information Criterion (DIC).     

近60年新疆库尔勒市的气候变化特点分析

根据库尔勒市气象局和研究区安装的自动气象站的气象资料,采用滑动平均、距平分析、线性回归等方法,分析库尔勒市近60年的气候变化的基本特征,结果表明：（1）库尔勒市平均温度有4暖3冷的冷暖变化阶段,该地区平均气温呈上升趋势,特别是20世纪90年代以后气温明显增加;近10年的气温变化较大,比前50年的平均值上升了1℃;平均气温存在着明显的线性升温趋势。（2）库尔勒市年降水量变化趋势不是很明显,有2多4少的干湿变化阶段。近10年的降水量与前50年的降水量相比较偏少了2．4mm;年降水量不存在明显的线性变化趋势。（3）库尔勒市平均极端最高最低气温呈上升趋势,60年来该地区最高气温上升率与南疆最高气温上升率一致。近10年的极端最高最低气温与前50年的分别上升0．36℃和1．2℃,最低气温的上升对年平均气温的升高贡献最大。（4）通过比较库尔勒市气象站提供的气象数据和自动气象站提供的数据可以看出,该区域一定程度上受到城市热岛效应和人为干扰,因此需要在城市周边的某些地区安装气象仪器,以提高气象数据的精确性。     

A stratified model for the assessment of meteorologically adjusted trends of surface ozone

We consider the problem of assessing long-term trends of ozone concentrations measured on a single site located in an urban area. Among the many methods proposed in the literature to eliminate the confounding effect of changing weather conditions, we employ a stratification of daily maxima based on regression trees. Within each stratum conditional independence and Weilbull distribution are assumed for maxima. Long-term trend is defined non-parametrically by the sequence of yearly medians. Models are estimated following the Bayesian approach. The alternative assumptions of common and stratum specific trends are compared and a model with common trend for all strata is selected for the analyzed real dataset. The conditional independence assumption is checked by the comparison with a model including an autoregressive component.     

A Bayesian strategy for combining predictions from empirical and process-based models

We present a strategy for using an empirical forest growth model to reduce uncertainty in predictions made with a physiological process-based forest ecosystem model. The uncertainty reduction is carried out via Bayesian melding, in which information from prior knowledge and a deterministic computer model is conditioned on a likelihood function. We used predictions from an empirical forest growth model G-HAT in place of field observations of aboveground net primary productivity (ANPP) in a deciduous temperate forest ecosystem. Using Bayesian melding, priors for the inputs of the process-based forest ecosystem PnET-II were propagated through the model, and likelihoods for the PnET-II output ANPP were calculated using the G-HAT predictions. Posterior distributions for ANPP and many PnET-II inputs obtained using the G-HAT predictions largely matched posteriors obtained using field data. Since empirical growth models are often more readily available than extensive field data sets, the method represents a potential gain in efficiency for reducing the uncertainty of process-based model predictions when reliable empirical models are available but high-quality data are not.     

云贵高原1961-2006年大气能见度和消光因素变化趋势及原因

根据云贵高原203个气象台站1961—2006年大气能见度、降水、相对湿度、风速和天气现象等观测资料,采用倾向率方法对能见度和大气消光系数的变化趋势进行了分析。还应用Mann-Kendall方法对19km能见度、霾日数和消光系数的多年变化进行了气候突变检验。结果表明,有84.2%台站出现了能见度减少趋势。减少最多为-11km·10a-1,最少为-1km·10a-1。减少的平均气候倾向率在1961—1979年为0.96km·10a-1,1980—2006年为1.6km·10a-1,高原平均能见度从60年代的约34km下降到目前的约27km。另一方面,有15.8%台站能见度有增加趋势,且多集中在人类活动较为稀少的高海拔山区。有71%的台站19km能见度频率出现减少的趋势,平均倾向率为-2%·10a-1,主要出现在高原东部和中部人口和工业稠密区。该地区同时也出现霾日增加的现象。Mann-Kendall检测结果表明,19km能见度频率减少和霾日数增加现象出现突变的时间相同。年平均消光系数发生突变的时间稍推后。认为能见度下降、消光因素增加的原因与人为排放污染物浓度增加有密切关系。     

An application of Bayesian variable selection to spatial concurrent linear models

Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the spatial processes, but in applications the data may display strong nonstationary patterns. In this article, we propose a Bayesian variable selection approach based on wavelet tools to address this problem. The proposed approach does not involve any stationarity assumptions on the priors, and instead we impose a mixture prior directly on each wavelet coefficient. We introduce an option to control the priors such that high resolution coefficients are more likely to be zero. Computationally efficient MCMC procedures are provided to address posterior sampling, and uncertainty in the estimation is assessed through posterior means and standard deviations. Examples based on simulated data demonstrate the estimation accuracy and advantages of the proposed method. We also illustrate the performance of the proposed method for real data obtained through remote sensing.     

A Bayesian framework for stable isotope mixing models

Stable isotope sourcing is used to estimate proportional contributions of sources to a mixture, such as in the analysis of animal diets and plant nutrient use. Statistical methods for inference on the diet proportions using stable isotopes have focused on the linear mixing model. Existing frequentist methods provide inferences when the diet proportion vector can be uniquely solved for in terms of the isotope ratios. Bayesian methods apply for arbitrary numbers of isotopes and diet sources but existing models are somewhat limited as they assume that trophic fractionation or discrimination is estimated without error or that isotope ratios are uncorrelated. We present a Bayesian model for the estimation of mean diet that accounts for uncertainty in source means and discrimination and allows correlated isotope ratios. This model is easily extended to allow the diet proportion vector to depend on covariates, such as time. Two data sets are used to illustrate the methodology. Code is available for selected analyses.     

Hierarchical modeling of count data with application to nuclear fall-out

We propose a method for a Bayesian hierarchical analysis of count data that are observed at irregular locations in a bounded domain of R². We model the data as having been observed on a fine regular lattice, where we do not have observations at all the sites. The counts are assumed to be independent Poisson random variables whose means are given by a log Gaussian process. In this article, the Gaussian process is assumed to be either a Markov random field (MRF) or a geostatistical model, and we compare the two models on an environmental data set. To make the comparison, we calibrate priors for the parameters in the geostatistical model to priors for the parameters in the MRF. The calibration is obtained empirically. The main goal is to predict the hidden Poisson-mean process at all sites on the lattice, given the spatially irregular count data; to do this we use an efficient MCMC. The spatial Bayesian methods are illustrated on radioactivity counts analyzed by Diggle et al. (1998).     

河西地区近50年参考作物蒸散量的演变趋势及其影响因素

根据河西地区17站点近50年的逐日气象资料,利用Penman-Monteith方程计算了逐日ET0,以Mann-Kendall法对各站不同季节、年ET0平均总量进行趋势检验。结果表明：武威、古浪、天祝3站年ET0呈增加趋势,其余14站均呈下降趋势,其中有9站通过显著性水平检验。春、夏、秋、冬四季酒泉地区和张掖地区各站ET0值均呈下降趋势,武威地区各站变化趋势不一致,且前者ET0值下降趋势总体较后者明显。典型站点ET0与气候要素多元线形回归分析表明：风速是不同季节、不同站点影响ET0变化的首要因子。其次,最高温度、相对湿度、日照时数也是影响年ET0及各站点不同季节ET0变化的主要因子。     

Lifting a veil on diversity: a Bayesian approach to fitting relative-abundance models.

Bayesian methods incorporate prior knowledge into a statistical analysis. This prior knowledge is usually restricted to assumptions regarding the form of probability distributions of the parameters of interest, leaving their values to be determined mainly through the data. Here we show how a Bayesian approach can be applied to the problem of drawing inference regarding species abundance distributions and comparing diversity indices between sites. The classic log series and the lognormal models of relative- abundance distribution are apparently quite different in form. The first is a sampling distribution while the other is a model of abundance of the underlying population. Bayesian methods help unite these two models in a common framework. Markov chain Monte Carlo simulation can be used to fit both distributions as small hierarchical models with shared common assumptions. Sampling error can be assumed to follow a Poisson distribution. Species not found in a sample, but suspected to be present in the region or community of interest, can be given zero abundance. This not only simplifies the process of model fitting, but also provides a convenient way of calculating confidence intervals for diversity indices. The method is especially useful when a comparison of species diversity between sites with different sample sizes is the key motivation behind the research. We illustrate the potential of the approach using data on fruit-feeding butterflies in southern Mexico. We conclude that, once all assumptions have been made transparent, a single data set may provide support for the belief that diversity is negatively affected by anthropogenic forest disturbance. Bayesian methods help to apply theory regarding the distribution of abundance in ecological communities to applied conservation.     

Bayesian analysis under ordered functions of parameters

Ordered parameter problems arise in a wide variety of real world situations and are dealt with extensively in the literature. Traditional frequentist methods for dealing with these problems are rather complicated theoretically, especially when sample sizes are small. Bayesian methods are not widely used because high dimensional numerical integration is often required. However, Markov chain Monte Carlo methods provide alternatives to such numerical integration and also deal with ordered parameter problems in a straightforward manner. Little is known about the situation where functions of parameters are ordered. Such problems may seem to be of little practical concern initially, but one can readily see their importance in situations where ordering is placed on the means and variances of several normal or Gamma populations. For the Gamma distribution we will present real examples where we will analyze monthly precipitation data from San Francisco, California and Oakland Mills, Iowa. For the San Francisco data we will simultaneously order both monthly precipitation means and variances. For the Iowa data we will place ordering on seasonal average while still estimating monthly means. Our results show that we would obtain sharper, more accurate inference when order restrictions are employed.     

贵州省NDVI变化及其与主要气候因子的相关性

运用全球检测与模型研究(GIMMS)组制作的取每隔15 d最大值合成的归一化差异植被指数(NDVI)数据集和贵州省84个气象站点提供的气候资料,分析1987-2003年贵州省植被变化状况以及NDVI与主要气候因子温度、降水的相互关系.结果表明: 17 a间贵州省年均NDVI呈现缓慢下降趋势,但春季NDVI出现了一定幅度的增长,年均NDVI下降主要是冬季NDVI大幅下降造成.植被变化在年际尺度上与温度和降水均无显著相关,但在季节尺度上与春季温度在α=0.05水平上显著相关.整体上看,春季NDVI与温度和降水的相关系数高于其他季节;温度与NDVI的同季相关高于滞后相关,而降水与NDVI的滞后相关却高于同季相关;与温度的相关性高于降水.     

Regression models for exceedance data via the full likelihood

Many situations in practice require appropriate specification of operating characteristics under extreme conditions. Typical examples include environmental sciences where studies include extreme temperature, rainfall and river flow to name a few. In these cases, the effect of geographic and climatological inputs are likely to play a relevant role. This paper is concerned with the study of extreme data in the presence of relevant auxiliary information. The underlying model involves a mixture distribution: a generalized Pareto distribution is assumed for the exceedances beyond a high threshold and a non-parametric approach is assumed for the data below the threshold. Thus, the full likelihood including data below and above the threshold is considered in the estimation. The main novelty is the introduction of a regression structure to explain the variation of the exceedances through all tail parameters. Estimation is performed under the Bayesian paradigm and includes model choice. This allows for determination of higher quantiles under each covariate configuration and upper bounds for the data, where appropriate. Simulation results show that the models are appropriate and identifiable. The models are applied to the study of two temperature datasets: maxima in the U.S.A. and minima in Brazil, and compared to other related models.     

Impact of time series data on calibration and prediction uncertainty for a deterministic hydrogeochemical model

Model calibration is fundamental in applications of deterministic process-based models. Uncertainty in model predictions depends much on the input data and observations available for model calibration. Here we explored how model predictions (forecasts) and their uncertainties vary with the length of time series data used in calibration. As an example we used the hydrogeochemical model MAGIC and data from Birkenes, a small catchment in southern Norway, to simulate future water chemistry under a scenario of reduced acid deposition. A Bayesian approach with a Markov Chain Monte Carlo (MCMC) technique was used to calibrate the model to different lengths of observed data (4–29 years) and to estimate the prediction uncertainty each calibration. The results show that the difference between modelled and observed water chemistry (calibration goodness of fit) in general decreases with increasing length of the time series used in calibration. However, there are considerable differences for different time series of the same length. The results also show that the uncertainties in predicted future acid neutralizing capacity were lowest (i.e. the distribution peak narrowest) when using the longest time series for calibration. As for calibration success, there were considerable differences between the future distributions (prediction uncertainty) for the different calibrations.     

Bayesian estimation of kinetic rate constants in a food-web model of polycyclic aromatic hydrocarbon bioaccumulation

Water, sediments, fish and other biota were sampled from fixed stations along bayous in the LaBranche Wetlands of Louisiana as part of an environmental contamination study in 1996 and 1997. In order to understand the biological fate of some of these contaminants, a spotted gar (Lepisosteus oculatus) food-web model was developed from site-specific data and established bioaccumulation modeling assumptions. Based on gut contents analysis, the gar were found to feed on terrestrial arthropods, a variety of small fish, aquatic insects, crayfish and grass shrimp. A Bayesian approach (a hierarchical model and Markov Chain Monte Carlo simulation) was used to estimate the kinetic rate constants of uptake from water, dietary uptake and total elimination for the food-web model using site-specific measurements of naphthalene, phenanthrene, and benzanthracene concentrations, reference literature inputs, and a hierarchical statistical model. This iterative simulation method resulted in a distribution of the parameters for each chemical comprised of the last 3000 values from four separate Markov Chains of length 15,000–25,000 iterations. The posterior parameter values were found to be consistent with rate constants published in the literature for various fish species, and were used to determine distributions of predicted gar PAH concentrations.