Theory for Reconstruction of an Unknown Number of Contaminant Sources using Probabilistic Inference

We address the inverse problem of source reconstruction for the difficult case of multiple sources when the number of sources is unknown a priori. The problem is solved using a Bayesian probabilistic inferential framework in which Bayesian probability theory is used to derive the posterior probability density function for the number of sources and for the parameters (e.g., location, emission rate, release time and duration) that characterize each source. A mapping (source–receptor relationship) that relates a multiple source distribution to the concentration measurements made by an array of detectors is formulated based on a forward-time Lagrangian stochastic model. A computationally efficient methodology for determination of the likelihood function for the problem, based on an adjoint representation of the source–receptor relationship and realized in terms of a backward-time Lagrangian stochastic model, is described. An efficient computational algorithm based on a parallel tempered Metropolis-coupled reversible-jump Markov chain Monte Carlo (MCMC) method is formulated and implemented to draw samples from the posterior probability density function of the source parameters. This methodology allows the MCMC method to initiate jumps between the hypothesis spaces corresponding to different numbers of sources in the source distribution and, thereby, allows a sample from the full joint posterior distribution of the number of sources and the parameters for each source to be obtained. The proposed methodology for source reconstruction is tested using synthetic concentration data generated for cases involving two and three unknown sources.     

Application of fuzzy clustering and fuzzy classification to evaluate the provenance of glacial till

To evaluate the provenance of glacial till, the trace element content of magnetite was used. Magnetite was present in all known rock types and all till samples in the area investigated. By using fuzzy-set theory it was possible to group samples of magnetite taken from bedrock into relatively homogeneous and geologically meaningful groups and also, by fuzzy classification, to relate the till samples to the rocks in such a way that the relative contribution of each rock type to the till is estimated. Each rock and till sample is assigned a membership value between 0 and 1 for each rock type. The membership values, for a certain rock type in the till, are then interpolated by kriging onto maps. Magnetites from skarns associated with sulfide ores especially are rather distinct, and so a map of such membership values for till unveils all known ore deposits some 1–5 km downstreamin the general direction of the ice flow. Other anomalies show up which cannot be related to hitherto known ores or mineralizations.     

序贯平差的稳健化处理

本文从最小二乘贝叶斯原理出发,指出了序贯平差的一般原则,据此平差原理,每组观测可以分别处理,从而很客易应用稳健估计方法获得稳健的序贯解。本文算例说明了可行性。     

Stochastic prediction in geomorphology using Bayesian inference models

Bayesian inference modeling may be applied to empirical stochastic prediction in geomorphology where outcomes of geomorphic processes can be expressed by probability density functions. Natural variations in process outputs are accommodated by the probability model. Uncertainty in the values of model parameters is reduced by considering statistically independent prior information on long-term, parameter behavior. Formal combination of model and parameter information yields a Bayesian probability distribution that accounts for parameter uncertainty, but not for model uncertainty or systematic error which is ignored herein. Prior information is determined by ordinary objective or subjective methods of geomorphic investigation. Examples involving simple stochastic models are given, as applied to the prediction of shifts in river courses, alpine rock avalanches, and fluctuating river bed levels. Bayesian inference models may be applied spatially and temporally as well as to functions of a random variable. They provide technically superior forecasts, for a given shortterm data set, to those of extrapolation or stochastic simulation models. In applications the contribution of the field geomorphologist is of fundamental quantitative importance.     

Error Estimates for a Time Discretization Method for the Richards' Equation

We present a numerical analysis of a time discretization method applied to Richards' equation. Written in its saturation-based form, this nonlinear parabolic equation models water flow into unsaturated porous media. Depending on the soil parameters, the diffusion coefficient may vanish or explode, leading to degeneracy in the original parabolic equation. The numerical approach is based on an implicit Euler time discretization scheme and includes a regularization step, combined with the Kirchhoff transform. Convergence is shown by obtaining error estimates in terms of the time step and of the regularization parameter.     

动态系统的抗差Kaliman滤波

离散历元的动态观测量及其相应的动态模型可能存在异常，若数据处理模型不考虑对这些异常的特别处理，则动态模型参数估值及其所提供的动态信息将极不可靠。基于贝叶斯统计和抗差估计原理，我们构造了一种抗差滤波算法。该算法考虑观测分布和参数验前分布均为污染分布。并利用一个实测网验算该算法和模型的可靠性。     

Analysis of Wave Directional Spreading by Bayesian Parameter Estimation

A spatial array of wave gauges installed on an observatoion platform has been designed and arranged to measure the lo-cal features of winter monsoon directional waves off Taishi coast of Taiwan. A new method, named the Bayesian Parameter Estimation Method(BPEM) , is developed and adopted to determine the main direction and the directional spreading parame-ter of directional spectra. The BPEM could be considered as a regression analysis to find the maximum joint probability of parameters, which best approximates the observed data from the Bayesian viewpoint. The result of the analysis of field wave data demonstrates the highly dependency of the characteristics of normalized directional spreading on the wave age. The Mit-suyasu type empirical formula of directional spectrum is therefore modified to be representative of monsoon wave field. More-over, it is suggested that Smax could be expressed as a function of wave steepness. The values of Smax decrease with increas-ing steepness. Finally, a local directi     

山东和邻区前兆震群综合判定指标的研究及其预报效能的评估

本文利用1970－1992年山东及邻区11次震群资料,对其单项及综合指标作了计算和研究,据《地震学分析预报方法程式指南》判断其前兆性。同时对前兆震与未来强震距离、间隔时间作了统计、并对其预报的成功率、虚报率、漏报率进行了贝叶斯估计。