Comparing spatially varying coefficient models: a case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests

In this paper, we compare and contrast a Bayesian spatially varying coefficient process (SVCP) model with a geographically weighted regression (GWR) model for the estimation of the potentially spatially varying regression effects of alcohol outlets and illegal drug activity on violent crime in Houston, Texas. In addition, we focus on the inherent coefficient shrinkage properties of the Bayesian SVCP model as a way to address increased coefficient variance that follows from collinearity in GWR models. We outline the advantages of the Bayesian model in terms of reducing inflated coefficient variance, enhanced model flexibility, and more formal measuring of model uncertainty for prediction. We find spatially varying effects for alcohol outlets and drug violations, but the amount of variation depends on the type of model used. For the Bayesian model, this variation is controllable through the amount of prior influence placed on the variance of the coefficients. For example, the spatial pattern of coefficients is similar for the GWR and Bayesian models when a relatively large prior variance is used in the Bayesian model.      

An Aggregate Constraint Method for Inequality-constrained Least Squares Problems

The inequality-constrained least squares (ICLS) problem can be solved by the simplex algorithm of quadratic programming. The ICLS problem may also be reformulated as a Bayesian problem and solved by using the Bayesian principle. This paper proposes using the aggregate constraint method of non-linear programming to solve the ICLS problem by converting many inequality constraints into one equality constraint, which is a basic augmented Lagrangean algorithm for deriving the solution to equality-constrained non-linear programming problems. Since the new approach finds the active constraints, we can derive the approximate algorithm-dependent statistical properties of the solution. As a result, some conclusions about the superiority of the estimator can be approximately made. Two simulated examples are given to show how to compute the approximate statistical properties and to show that the reasonable inequality constraints can improve the results of geodetic network with an ill-conditioned normal matrix.     

Indoor localization for pedestrians with real-time capability using multi-sensor smartphones

ABSTRACT

The localization of persons or objects usually refers to a position determined in a spatial reference system. Outdoors, this is usually accomplished with Global Navigation Satellite Systems (GNSS). However, the automatic positioning of people in GNSS-free environments, especially inside of buildings (indoors) poses a huge challenge. Indoors, satellite signals are attenuated, shielded or reflected by building components (e.g. walls or ceilings). For selected applications, the automatic indoor positioning is possible based on different technologies (e.g. WiFi, RFID, or UWB). However, a standard solution is still not available. Many indoor positioning systems are only suitable for specific applications or are deployed under certain conditions, e.g. additional infrastructures or sensor technologies. Smartphones, as popular cost-effective multi-sensor systems, is a promising indoor localization platform for the mass-market and is increasingly coming into focus. Today’s devices are equipped with a variety of sensors that can be used for indoor positioning. In this contribution, an approach to smartphone-based pedestrian indoor localization is presented. The novelty of this approach refers to a holistic, real-time pedestrian localization inside of buildings based on multi-sensor smartphones and easy-to-install local positioning systems. For this purpose, the barometric altitude is estimated in order to derive the floor on which the user is located. The 2D position is determined subsequently using the principle of pedestrian dead reckoning based on user's movements extracted from the smartphone sensors. In order to minimize the strong error accumulation in the localization caused by various sensor errors, additional information is integrated into the position estimation. The building model is used to identify permissible (e.g. rooms, passageways) and impermissible (e.g. walls) building areas for the pedestrian. Several technologies contributing to higher precision and robustness are also included. For the fusion of different linear and non-linear data, an advanced algorithm based on the Sequential Monte Carlo method is presented.     

Bayesian methods for estimating multi-segment discharge rating curves

This study explores Bayesian methods for handling compound stage–discharge relationships, a problem which arises in many natural rivers. It is assumed: (1) the stage–discharge relationship in each rating curve segment is a power-law with a location parameter, or zero-plane displacement; (2) the segment transitions are abrupt and continuous; and (3) multiplicative measurement errors are of equal variance. The rating curve fitting procedure is then formulated as a piecewise regression problem where the number of segments and the associated changepoints are assumed unknown. Procedures are developed for describing both global and site-specific prior distributions for all rating curve parameters, including the changepoints. Estimation and uncertainty analysis is evaluated using Markov chain Monte Carlo simulation (MCMC) techniques. The first model explored accounts for parameter and model uncertainties in the interpolated area, i.e. within the range of available stage–discharge measurements. A second model is constructed in an attempt to include the uncertainty in extrapolation, which is necessary when the rating curve is used to estimate discharges beyond the highest or lowest measurement. This is done by assuming that the rate of changepoints both inside and outside the measured area follows a Poisson process. The theory is applied to actual data from Norwegian gauging stations. The MCMC solutions give results that appear sensible and useful for inferential purposes, though the latter model needs further efforts in order to obtain a more efficient simulation scheme.     

Bayesian power-law regression with a location parameter,with applications for construction of discharge rating curves

This paper presents a Bayesian approach for fitting the standard power-law rating curve model to a set of stage-discharge measurements. Methods for eliciting both regional and at-site prior information, and issues concerning the determination of prior forms, are discussed. An efficient MCMC algorithm for the specific problem is derived. The appropriateness of the proposed method is demonstrated by applying the model to both simulated and real-life data. However, some problems came to light in the applications, and these are discussed.     

Model and parameter uncertainty in IDF relationships under climate change

Quantifying distributional behavior of extreme events is crucial in hydrologic designs. Intensity Duration Frequency (IDF) relationships are used extensively in engineering especially in urban hydrology, to obtain return level of extreme rainfall event for a specified return period and duration. Major sources of uncertainty in the IDF relationships are due to insufficient quantity and quality of data leading to parameter uncertainty due to the distribution fitted to the data and uncertainty as a result of using multiple GCMs. It is important to study these uncertainties and propagate them to future for accurate assessment of return levels for future. The objective of this study is to quantify the uncertainties arising from parameters of the distribution fitted to data and the multiple GCM models using Bayesian approach. Posterior distribution of parameters is obtained from Bayes rule and the parameters are transformed to obtain return levels for a specified return period. Markov Chain Monte Carlo (MCMC) method using Metropolis Hastings algorithm is used to obtain the posterior distribution of parameters. Twenty six CMIP5 GCMs along with four RCP scenarios are considered for studying the effects of climate change and to obtain projected IDF relationships for the case study of Bangalore city in India. GCM uncertainty due to the use of multiple GCMs is treated using Reliability Ensemble Averaging (REA) technique along with the parameter uncertainty. Scale invariance theory is employed for obtaining short duration return levels from daily data. It is observed that the uncertainty in short duration rainfall return levels is high when compared to the longer durations. Further it is observed that parameter uncertainty is large compared to the model uncertainty.     

基于贝叶斯网络分类的遥感影像变化检测

遥感成像过程中,地面、大气等诸多要素的不确定性和波段之间的相关性等原因影响了分类精度,导致变化检测的不准确性。为了提高分类精度往往需要引入先验知识。贝叶斯网络是一种新的数据表达和推理模型,对数据没有严格的正态分布前提要求,通过动态地调整先验概率密度,能有效提高分类精度。以北京通州地区1996-05-29和2001-05-19两个时相的陆地卫星Landsat TM遥感影像为例,介绍了基于贝叶斯网络的分类算法,并在此基础上实现了两个时相遥感影像的变化检测。实验结果表明:基于贝叶斯网络分类算法的后分类比较变化检测方法是遥感影像变化检测的一种新的有效方法。     

Data structures for three-dimensional spatial information systems in geology

Abstract

The accumulation of geological information in digital form, due to modern exploration methods, has introduced the possibility of applying geographical information system technology to the field of geology. To achieve the benefits in information management and in data analysis and interpretation, however, it will be necessary to develop spatial models and associated data structures which are specifically designed for working in three dimensions. Some progress in this direction has already been demonstrated, with the application of octree spatial subdivision techniques to the storage of uniform volume elements representing mineral properties. By imposing octree tessellations on more precisely-defined geometric data, such as triangulated surfaces and polygon line segments, it may now be possible to combine efficient spatial addressing with topologically-coded boundary representations of geological strata. The development of storage schemes capable of representing such geological boundary models at different scales poses a particular problem, a possible solution to which may be by means of hierarchical classification of the vertices of triangulated surfaces according to shape contribution.     

基于贝叶斯框架的各向异性页岩储层岩石物理反演技术

页岩岩石物理建模旨在建立页岩矿物组分、微观结构、流体填充与岩石弹性参数的关系.对四川盆地龙马溪组页岩进行岩石物理建模研究,针对页岩黏土含量高、层间微裂缝发育等特点,利用Backus平均理论描述页岩黏土矿物弹性参数,利用Chapman理论计算与水平微裂缝有关的VTI各向异性,并利用Bond变换考虑地层倾角的影响.提出以黏土矿物纵、横波速度和孔隙纵横比为拟合参数进行岩石物理反演的方法,并引入贝叶斯框架减小反演的多解性.由已知的黏土矿物纵、横波速度和孔隙纵横比作为先验信息,并以测井纵、横波速度作为约束条件建立反演的目标函数,同时利用粒子群算法进行最优化搜索.计算结果表明,基于先验约束和粒子群算法的反演方法能够较准确地反演黏土矿物的弹性参数、孔隙形态参数以及裂缝密度等参数.计算得到的黏土纵、横波速度较高,并且在一定范围内变化,这可能与龙马溪组页岩的黏土矿物组分中具有较高弹性模量的伊利石含量较高有关,同时也与黏土定向排列等微观物性特征有关.反演得到的裂缝密度与纵波各向异性参数ε呈明显的正相关,而与横波各向异性参数γ相关性较小.另外,页岩各向异性参数与黏土垂向的纵横波速度有较强的相关性.

     

海洋环境因子对澳洲鲐亲体补充量关系的影响——基于贝叶斯模型平均法的研究

澳洲鲐（Scomber australasicus）是西北太平洋重要的中上层经济鱼类,生命周期相对较短,资源量受补充量影响明显,了解澳洲鲐太平洋群系补充量状况对掌握其资源量及确保其可持续利用具有重要的意义。本文利用产卵场1（30°~32°N,130°~132°E）海表面温度（sea surface temperature,SST1）、产卵场2（34°~35°N,138°~141°E）海表面温度（SST2）、索饵场（35°~45°N,140°~160°E）海表面温度（SST3）、潮位差（tidal range,TR）、太平洋年代际涛动（Pacific decadal oscillation,PDO）和亲体量（spawning stock biomass,SSB）6个影响因子任意组合与补充量构建多个模型,运用贝叶斯模型平均法（Bayesian model averaging,BMA）分析各个环境因子对资源补充量的解释能力,并预测其补充量的变化。结果表明,SSB对补充量具有最长期且稳定的解释能力,其次是SST3,PDO、TR、SST2、SST1也对补充量模型具有一定的解释能力。SST3是环境因子中影响最大的因子,可能是由于补充群体在索饵场内生活时间较长,索饵场温度对仔鱼或鱼卵的生长存活有较大的影响。研究认为,基于BMA的组合预报综合考虑了各个模型的优势,优于单一模型,可用于澳洲鲐资源补充量的预测。