A proposal for comparing the reliabilities of alternative seismic hazard models

Differences between statistical unertainty and modeling uncertainty are briefly discussed. It is pointed out that, when different models are proposed for the interpretation of reality, the uncertainty cannot be described in terms of mean value and coefficient of variation. The important question is: which of the proposed models is more reliable than the others? The attention, then, is concentrated on the comparison between different models proposed for the estimate of the required quantity, looking for a criterion leading to the selection of the most reliable one. A criterion for comparison of different models is suggested. In the example of application considered in this paper, it proved to be effective, so that the continuation of numerical experiments, exploring different and more complex situations, seems promising.     

Using regional regression within index flood procedures and an empirical Bayesian estimator

Studies have illustrated the performance of at-site and regional flood quantile estimators. For realistic generalized extreme value (GEV) distributions and short records, a simple index-flood quantile estimator performs better than two-parameter (2P) GEV quantile estimators with probability weighted moment (PWM) estimation using a regional shape parameter and at-site mean and L-coefficient of variation (L-CV), and full three-parameter at-site GEV/PWM quantile estimators. However, as regional heterogeneity or record lengths increase, the 2P-estimator quickly dominates. This paper generalizes the index flood procedure by employing regression with physiographic information to refine a normalized T-year flood estimator. A linear empirical Bayes estimator uses the normalized quantile regression estimator to define a prior distribution which is employed with the normalized 2P-quantile estimator. Monte Carlo simulations indicate that this empirical Bayes estimator does essentially as well as or better than the simpler normalized quantile regression estimator at sites with short records, and performs as well as or better than the 2P-estimator at sites with longer records or smaller L-CV.     

淮河息县站流量概率预报模型研究

应用美国天气局采用的由Roman Krzysztofowicz开发的贝叶斯统计理论建立概率水文预报理论框架，即以分布函数形式定量地描述水文预报不确定度，研究了淮河息县站流量概率预报模型。理论和经验表明，概率预报至少与确定性预报一样有价值，特别当预报不确定度较大时，概率预报比现行确定性预报具有更高的经济价值。     

纵向和横向同时约束AVO反演

为了提高AVO（amplitude versus offset）反演结果的精度和横向连续性,本文提出了一种新的AVO反演约束方法,该方法结合贝叶斯原理和卡尔曼滤波算法实现了对反演参数纵向和横向的同时约束.文章首先结合反演参数的纵向贝叶斯先验概率约束和反演参数的横向连续性假设建立了与卡尔曼滤波算法对应的AVO反演系统的数学模型,然后将该数学模型代入卡尔曼滤波算法框架,利用卡尔曼滤波算法实现了双向约束AVO反演.二维模型测试和实际数据测试结果表明,相对于单纯的纵向贝叶斯先验概率约束,双向约束能更准确地刻画参数的横向变化,得到更准确、横向连续性更好的反演结果.

     

Combining discrete cosine transform and convolutional neural networks to speed up the Hamiltonian Monte Carlo inversion of pre-stack seismic data

Markov chain Monte Carlo algorithms are commonly employed for accurate uncertainty appraisals in non-linear inverse problems. The downside of these algorithms is the considerable number of samples needed to achieve reliable posterior estimations, especially in high-dimensional model spaces. To overcome this issue, the Hamiltonian Monte Carlo algorithm has recently been introduced to solve geophysical inversions. Different from classical Markov chain Monte Carlo algorithms, this approach exploits the derivative information of the target posterior probability density to guide the sampling of the model space. However, its main downside is the computational cost for the derivative computation (i.e. the computation of the Jacobian matrix around each sampled model). Possible strategies to mitigate this issue are the reduction of the dimensionality of the model space and/or the use of efficient methods to compute the gradient of the target density. Here we focus the attention to the estimation of elastic properties (P-, S-wave velocities and density) from pre-stack data through a non-linear amplitude versus angle inversion in which the Hamiltonian Monte Carlo algorithm is used to sample the posterior probability. To decrease the computational cost of the inversion procedure, we employ the discrete cosine transform to reparametrize the model space, and we train a convolutional neural network to predict the Jacobian matrix around each sampled model. The training data set for the network is also parametrized in the discrete cosine transform space, thus allowing for a reduction of the number of parameters to be optimized during the learning phase. Once trained the network can be used to compute the Jacobian matrix associated with each sampled model in real time. The outcomes of the proposed approach are compared and validated with the predictions of Hamiltonian Monte Carlo inversions in which a quite computationally expensive, but accurate finite-difference scheme is used to compute the Jacobian matrix and with those obtained by replacing the Jacobian with a matrix operator derived from a linear approximation of the Zoeppritz equations. Synthetic and field inversion experiments demonstrate that the proposed approach dramatically reduces the cost of the Hamiltonian Monte Carlo inversion while preserving an accurate and efficient sampling of the posterior probability.     

Using a Bayesian estimator to combine information from a cluster analysis and remote sensing data to estimate high-resolution data for agricultural production in Germany

In Germany, a county-resolution data set that consists of 35 land-use and animal-stock categories has been used extensively to assess the impact of agriculture on the environment. However, because such environmental effects as emission or nutrient surplus depend on the location, even a county resolution might produce misleading results. The aim of this article is to propose a Bayesian approach which combines two sorts of information, with one being treated as defining the prior and the other the data to form a posterior, used to estimate a data set at a municipality resolution. We define the joint prior density function based on (i) remote sensing data, thus accounting for differences in county data and missing data at the municipality level, and (ii) the results of a cluster analysis that was previously applied to the micro-census, whereas the data are defined by official statistics at the county level. This approach results in a fairly accurate data set at the municipality level. The results, using the proposed method, are validated by the national research data centre by comparing the estimates to actual observations. The test statistics presented here demonstrate that the proposed approach adequately estimates the production activities.     

基于贝叶斯模型的器测、古气候重建与气候模拟数据的融合试验

气象部门馆藏的西部最早的器测气象资料始于20世纪30年代,不能满足建立20世纪以来中国气候变化序列的需求,而古气候重建或气候模拟资料则可以延伸到器测时代以前。为了探讨长序列多源气候资料序列融合方法,采用贝叶斯方法对中国北疆地区8条树轮气温重建资料、器测资料与国际耦合模式比较计划第5阶段（CMIP5）模式模拟资料进行了融合试验。首先利用器测资料对气温代用资料进行校验与网格重建,并以此作为贝叶斯模型的先验分布,然后,用泰勒图选出了该区域气候模拟效果最佳的几个模式;最后将网格重建和气候模拟序列用贝叶斯模型进行了融合试验。结果表明,贝叶斯融合模型能有效提取各种数据来源的有用信息进行融合,融合结果的长期变化（线性）趋势更接近器测气候序列,并在一定程度上提高了序列的精度,减小了结果的不确定性;并且,融合结果能够纠正先验分布及气候模拟数据的明显偏差,为长年代气候序列重建提供了一个可行的思路。      

基于TIGGE多模式集合的24小时气温BMA 概率预报

利用TIGGE(THORPEX Interactive Grand Global Ensemble)单中心集合预报系统(ECMWF、United Kingdom Meteorological Office、China Meteorological Administration和NCEP)以及由此所构成的多中心模式超级集合预报系统24小时地面日均气温预报,结合淮河流域地面观测率定贝叶斯模型平均(Bayesian model averaging,BMA)参数,从而建立地面日均气温BMA概率预报模型.由此针对淮河流域进行地面日均气温BMA概率预报及其检验与评估,结果表明BMA模型比原始集合预报效果好;单中心的BMA概率预报都有较好的预报效果,其中ECMWF最好.多中心模式超级集合比单中心BMA概率预报效果更好,采用可替换原则比普通的多中心模式超级集合BMA模型计算量小,且在上述BMA集合预报系统中效果最好.它与原始集合预报相比其平均绝对误差减少近7%,其连续等级概率评分提高近10%.基于采用可替换原则的多中心模式超级集合BMA概率预报,针对研究区域提出了极端高温预警方案,这对防范高温天气有着重要意义.     

南水北调中线降水丰枯遭遇风险分析

受降水丰枯变化不确定性和差异性的影响,南水北调中线工程水源区与受水区降水的丰枯遭遇状态各不相同,给南水北调工程水资源调度运行带来风险。联合copula函数和贝叶斯网络理论,建立了南水北调中线工程水源区和受水区降水丰枯遭遇风险分析模型,对南水北调中线工程调水最不利的丰枯遭遇风险概率进行了研究。利用copula函数建立了水源区和受水区年降水量联合分布函数,计算条件概率,结合贝叶斯网络进行丰枯遭遇风险分析。结果表明南水北调中线4个受水区调水风险的概率均在25%以下,并对不同情景的调水风险进行了仿真分析。     

基于Membrane MRF模型的SAR图像贝叶斯去斑

SAR图像可以看作是真实反映地物后向散射特性的无噪图像与相干斑噪声的乘积,通过贝叶斯估计从图像观测值估计出图像真值即可去除相干斑.而贝叶斯去斑的关键在于建立能与SAR图像特性相匹配的先验信息模型.用MembraneMRF模型对先验信息建模,克服了以往所用GMRF模型对参数估计十分敏感的问题,并通过对该模型邻域结构的自适应调整来分类处理处于匀质区域和含结构特征区域的像元,在有效抑制相干斑的同时较好地保持图像的结构特征.仿真和实际SAR图像数据的实验结果,验证了所提方法的有效性.