Bayesian probabilities of earthquake occurrences in Greece and surrounding areas

The Bayesian extreme-value distribution of earthquake occurrences has been adopted to estimate the seismic hazard in some seismogenic zones in Greece and surrounding regions. Seismic moment, slip rate, earthquake recurrence rate and magnitude were considered as basic parameters for computing the prior estimates of the seismicity. These estimates are then updated in terms of Bayes' theorem and historical estimates of seismicity associated with each zone.High probabilities for earthquakes withM6.0 have been obtained for the northwestern part of Greece as well as for the southwestern part of the Hellenic arc.     

Manual hierarchical clustering of regional geochemical data using a Bayesian finite mixture model

Interpretation of regional scale, multivariate geochemical data is aided by a statistical technique called “clustering.” We investigate a particular clustering procedure by applying it to geochemical data collected in the State of Colorado, United States of America. The clustering procedure partitions the field samples for the entire survey area into two clusters. The field samples in each cluster are partitioned again to create two subclusters, and so on. This manual procedure generates a hierarchy of clusters, and the different levels of the hierarchy show geochemical and geological processes occurring at different spatial scales. Although there are many different clustering methods, we use Bayesian finite mixture modeling with two probability distributions, which yields two clusters. The model parameters are estimated with Hamiltonian Monte Carlo sampling of the posterior probability density function, which usually has multiple modes. Each mode has its own set of model parameters; each set is checked to ensure that it is consistent both with the data and with independent geologic knowledge. The set of model parameters that is most consistent with the independent geologic knowledge is selected for detailed interpretation and partitioning of the field samples.     

Bayesian Equivalent Sample Toolkit (BEST): an Excel VBA program for probabilistic characterisation of geotechnical properties from limited observation data

In site investigation, the amount of observation data obtained for geotechnical property characterisation is often too sparse to obtain meaningful statistics and probability distributions of geotechnical properties. To address this problem, a Bayesian equivalent sample method was recently developed. This paper aims to generalize the Bayesian equivalent sample method to various geotechnical properties, when measured by different direct or indirect test procedures, and to implement the generalized method in Excel by developing an Excel VBA program called Bayesian Equivalent Sample Toolkit (BEST). The BEST program makes it possible for practitioners to apply the Bayesian equivalent sample method without being compromised by sophisticated algorithms in probability, statistics and simulation. The program is demonstrated and validated through examples of soil and rock property characterisations.     

Prediction of categorical spatial data via Bayesian updating

This study introduces a transition probability-based Bayesian updating (BU) approach for spatial classification through expert system. Transition probabilities are interpreted as expert opinions for updating the prior marginal probabilities of categorical response variables. The main objective of this paper is to provide a spatial categorical variable prediction method which has a solid theoretical foundation and yields relatively higher classification accuracy compared with conventional ones. The basic idea is to first build a linear Bayesian updating (LBU) model that corresponds to an application of Bayes’ theorem. Since the linear opinion pool is intrinsically suboptimal and underconfident, the beta-transformed Bayesian updating (BBU) model is proposed to overcome this limitation. Another type of BU approach, conditional independent Bayesian updating (CIBU), is derived based on conditional independent experts. It is shown that traditional Markovian-type categorical prediction (MCP) is equivalent to a particular CIBU model with specific parameters. As three variants of the BU method, these techniques are illustrated in synthetic and real-world case studies, comparison results with both the LBU and MCP favor the BBU model.     

改进的果蝇优化与Tikhonov正则化相结合的病态问题稳健解法

在对基本果蝇优化算法的优化流程进行深入分析的基础上,通过改变其随机搜索方向与增加搜索半径调整系数,给出了一种改进的果蝇优化算法(IFOA)。并在IFOA算法的目标函数中引入正则化项,提出了将IFOA算法与Tikhonov正则化方法进行结合以进行病态问题解算的方法。通过实例分析表明:该方法的解算精度要优于遗传算法和单一的Tikhonov正则化方法;在观测值含有粗差时,使用最小二乘法进行求解,其结果与真值的偏差会迅速增大,而此时本文方法的解算结果具有一定的稳健性。与以遗传算法为代表的智能搜索方法相比,本文方法具有参数设置少、计算速度快、寻优过程简单等特点,在病态问题解算中更具有实用性。     

A Bayesian Network Approach for Offshore Risk Analysis Through Linguistic Variables

This paper presents a new approach for offshore risk analysis that is capable of dealing with linguistic probabilities in Bayesian networks(BNs).In this paper,linguistic probabilities are used to describe occurrence likelihood of hazardous events that may cause possible accidents in offshore operations.In order to use fuzzy information,an f-weighted valuation function is proposed to transform linguistic judgements into crisp probability distributions which can be easily put into a BN to model causal relationships among risk factors.The use of linguistic variables makes it easier for human experts to express their knowledge,and the transformation of linguistic judgements into crisp probabilities can significantly save the cost of computation,modifying and maintaining a BN model.The flexibility of the method allows for multiple forms of information to be used to quantify model relationships,including formally assessed expert opinion when quantitative data are lacking,or when only qualitative or vague statements can be made.The model is a modular representation of uncertain knowledge caused due to randomness,vagueness and ignorance.This makes the risk analysis of offshore engineering systems more functional and easier in many assessment contexts.Specifically,the proposed f-weighted valuation function takes into account not only the dominating values,but also the α-level values that are ignored by conventional valuation methods.A case study of the collision risk between a Floating Production,Storage and Off-loading(FPSO) unit and the authorised vessels due to human elements during operation is used to illustrate the application of the proposed model.     

Seismic hazard maps for Jordan and vicinity

Probabilistic methods are used to quantify the seismic hazard in Jordan and neighbouring regions. The hazard model incorporates the uncertainties associated with the seismicity parameters and the attenuation equation. Seven seismic sources are identified in the region and the seismicity parameters of these sources are estimated by making use of all the available information. Seismic hazard computations and the selection of peak ground acceleration and modified Mercalli intensity values at the nodes of a 25 × 25 km mesh covering the region under study are carried out by two different computer programs.The results of the study are presented through a set of seismic hazard maps displaying iso-acceleration and iso-intensity contours corresponding to specified return periods. The first set of maps is derived based on the seismicity data assessed in this study and display our best estimate of the seismic hazard for Jordan and the neighbouring areas. The second set of maps which shows the alternative estimate of seismic hazard is based solely on the seismicity parameters reported by other researchers. The third set of maps, called the Bayesian estimate of seismic hazard, reflects the influence of expert opinion involving more conservative assumptions regarding the Red Sea and Araba faults.     

2020年超长梅汛期降水概率预报应用与检验

基于欧洲中期天气预报中心（European Center for Medium-range Weather Forecasts,ECMWF）集合预报资料及浙江全省自动站降水观测资料,采用贝叶斯模型平均（Bayesian Model Average, BMA）方法对2020年浙江超长梅汛期开展降水概率预报订正试验。采用平均绝对误差、连续等级概率评分、布莱尔评分B_S、Talagrand、概率积分变换(Probability Integral Transform, PIT)直方图及属性图检验方法对本次过程BMA订正前后的概率预报进行对比分析,结果表明：①50 d为适用于浙江梅汛期ECMWF集合预报订正的BMA最优训练期,经最优训练期的BMA订正后,预报离散度有所增加,预报误差有所下降;②BMA对0.1 mm、10.0 mm和25.0 mm阈值降水的订正效果显著,经BMA订正后3个阈值的降水预报B_S下降率分别为25.92%、19.29%、4.76%,但对超过50.0 mm的降水订正效果不明显,且随着降水阈值增加,BMA的订正效果减弱;③在强降水个例中,BMA能有效减少各阈值降水预报概率大值落区偏差,使订正后的降水预报概率大值区与观测落区更一致。     

基于贝叶斯逻辑回归模型研究百度街景图像微观建成环境因素对街面犯罪的影响

街面犯罪对公众的生活安全构成一定的威胁。以往对于公共盗窃和寻衅滋事等街面犯罪的研究往往停留在社区甚至更宏观的层面,难以向微观尺度深入,它们忽略了通过环境设计预防犯罪(Crime Prevention Through Environmental Design,CPTED)理论中所主张的地址级的建成环境的精确特征。地址级的微观建成环境被广泛认为对各类犯罪的发生有着直接或间接的影响,然而对微观建成环境的度量一直是一个挑战。先前的大多数研究都是通过调查样本来表征建成环境,会受到两方面的限制:(1)建成环境特征描述不完整的限制;(2)数据在空间覆盖方面具有稀疏性的限制。百度街景图像作为一个新的数据来源,可以被用来提取地址级的微型环境的建成特征,从而使犯罪研究可以聚焦在更微观的尺度中。本研究使用深度学习全卷积图像分割算法从百度街景图像中提取地理位置的环境变量,共选取树木、通车道路、人行道等8种变量来表现研究区微观建成环境的差异。在控制了与街面犯罪有关的其他因素后,采用贝叶斯逻辑回归模型来评估微观建成环境影响因素对公共盗窃和寻衅滋事案件的影响。结果表明加入了微观建成环境物理特征之后的模型表现更好。对...     

Bayesian geological and geophysical data fusion for the construction and uncertainty quantification of 3D geological models

Traditional approaches to develop 3D geological models employ a mix of quantitative and qualitative scientific techniques,which do not fully provide quantification of uncertainty in the constructed models and fail to optimally weight geological field observations against constraints from geophysical data.Here,using the Bayesian Obsidian software package,we develop a methodology to fuse lithostratigraphic field observations with aeromagnetic and gravity data to build a 3D model in a small(13.5 km×13.5 km)region of the Gascoyne Province,Western Australia.Our approach is validated by comparing 3D model results to independently-constrained geological maps and cross-sections produced by the Geological Survey of Western Australia.By fusing geological field data with aeromagnetic and gravity surveys,we show that 89%of the modelled region has>95%certainty for a particular geological unit for the given model and data.The boundaries between geological units are characterized by narrow regions with<95%certainty,which are typically 400-1000 m wide at the Earth's surface and 500-2000 m wide at depth.Beyond~4 km depth,the model requires geophysical survey data with longer wavelengths(e.g.,active seismic)to constrain the deeper subsurface.Although Obsidian was originally built for sedimentary basin problems,there is reasonable applicability to deformed terranes such as the Gascoyne Province.Ultimately,modification of the Bayesian engine to incorporate structural data will aid in developing more robust 3D models.Nevertheless,our results show that surface geological observations fused with geophysical survey data can yield reasonable 3D geological models with narrow uncertainty regions at the surface and shallow subsurface,which will be especially valuable for mineral exploration and the development of 3D geological models under cover.