贝叶斯网络结构学习及其应用研究

阐述了贝叶斯网络结构学习的内容与方法 ,提出一种基于条件独立性 (CI)测试的启发式算法。从完全潜在图出发 ,融入专家知识和先验常识 ,有效地减少网络结构的搜索空间 ,通过变量之间的CI测试 ,将全连接无向图修剪成最优的潜在图 ,近似于有向无环图的无向版。通过汽车故障诊断实例 ,验证了该算法的可行性与有效性。     

一种解算病态问题的方法--两步解法

提出了一种解算病态问题的方法———两步解法。在两步计算中,均采用L曲线法来确定正则化参数α。通过算例,比较了该方法和LS估计、岭估计及截断奇异值方法的效果。结果表明,该方法要明显优于LS估计、岭估计及截断奇异值法。     

A Bayesian method for linear, inequality-constrained adjustment and its application to GPS positioning

One of the typical approaches to linear, inequality-constrained adjustment (LICA) is to solve a least-squares (LS) problem subject to the linear inequality constraints. The main disadvantage of this approach is that the statistical properties of the estimate are not easily determined and thus no general conclusions about the superiority of the estimate can be made. A new approach to solving the LICA problem is proposed. The linear inequality constraints are converted into prior information on the parameters with a uniform distribution, and consequently the LICA problem is reformulated into a Bayesian estimation problem. It is shown that the LS estimate of the LICA problem is identical to the Bayesian estimate based on the mode of the posterior distribution. Finally, the Bayesian method is applied to GPS positioning. Results for four field tests show that, when height information is used, the GPS phase ambiguity resolution can be improved significantly and the new approach is feasible.     

Empirical Maximum Likelihood Kriging: The General Case

Although linear kriging is a distribution-free spatial interpolator, its efficiency is maximal only when the experimental data follow a Gaussian distribution. Transformation of the data to normality has thus always been appealing. The idea is to transform the experimental data to normal scores, krige values in the “Gaussian domain” and then back-transform the estimates and uncertainty measures to the “original domain.” An additional advantage of the Gaussian transform is that spatial variability is easier to model from the normal scores because the transformation reduces effects of extreme values. There are, however, difficulties with this methodology, particularly, choosing the transformation to be used and back-transforming the estimates in such a way as to ensure that the estimation is conditionally unbiased. The problem has been solved for cases in which the experimental data follow some particular type of distribution. In general, however, it is not possible to verify distributional assumptions on the basis of experimental histograms calculated from relatively few data and where the uncertainty is such that several distributional models could fit equally well. For the general case, we propose an empirical maximum likelihood method in which transformation to normality is via the empirical probability distribution function. Although the Gaussian domain simple kriging estimate is identical to the maximum likelihood estimate, we propose use of the latter, in the form of a likelihood profile, to solve the problem of conditional unbiasedness in the back-transformed estimates. Conditional unbiasedness is achieved by adopting a Bayesian procedure in which the likelihood profile is the posterior distribution of the unknown value to be estimated and the mean of the posterior distribution is the conditionally unbiased estimate. The likelihood profile also provides several ways of assessing the uncertainty of the estimation. Point estimates, interval estimates, and uncertainty measures can be calculated from the posterior distribution.     

Reservoir Characterization of McMurray Formation by 2D Geostatistical Modeling

There is a need to estimate reserve uncertainty for large lease areas. Detailed 3D models of heterogeneity are not necessarily required, but there is a need to integrate all available data into an in-situ reserve estimate with uncertainty. A 2D mapping approach is presented to appraise reserves accounting for multiple variables, multiple data sources, and uncertainty. The approach can be considered in three primary steps: (1) Bayesian updating is used to determine local distributions of uncertainty for each primary variable while integrating multiple secondary information, (2) matrix simulation is employed to jointly and simultaneously simulate multiple collocated variables to determine a derived variable such as OOIP, and (3) probability field simulation then is applied to permit joint simulation of multiple locations. This methodology permits local and global uncertainty assessment while integrating multiple sources of information. An application to the McMurray Formation in Alberta, Canada is demonstrated.     

Bayesian approach to daily rainfall modelling to estimate monthly net infiltration using the Thornthwaite water budget and Curve Number methods

The Thornthwaite and Mather water budget is a simple and frequently applicable tool to estimate surpluses of water, which are not stored in the soil profile. Combining it with the empiric CN-method of the US Soil Conservation Service (US-SCS), which is applied to daily rainfall records, it is possible to estimate the runoff, and this way, from the difference between surpluses and runoff, to estimate the net infiltration that would recharge a phreatic aquifer. In order to apply both methods during a sequence of years, it is necessary to predict the number of rain events per month, and the rainfall depth for each event. In this work, the author proposes a methodology based on the theorem of Bayes to estimate the number of occurrences of rainy events in a considered month conditioning the forecast to the monthly rainfall. In addition, an exponential distribution to generate rainfall depth knowing the monthly rainfall was done. Both algorithms were applied in four stations of the southern region of Santa Fe province (Argentina). More than 7,600 forecasts of rain occurrences and rainfall depths were compared with the observed records. Moreover, the runoff values estimated by means of the US-SCS method, using the observed rainfall and using rainfalls predicted with the algorithms were also compared. In both cases, the obtained results were also very satisfactory. The proposed methodologies allow the correct application of the balance of Thornthwaite and Mather together with the US-SCS method and a good forecast of monthly runoff and net infiltration.     

Uncertainties in Facies Proportion Estimation I. Theoretical Framework: The Dirichlet Distribution

To simulate geological models comprising several litho-types—or facies—we need first to estimate their proportions, which are often poorly known. The corresponding uncertainties can be modelled using a Bayesian approach for inverting the multinomial distribution. The result obtained is known as the Dirichlet distribution. It can be simulated by decomposition into independent conditional distributions. Application of the model is extended to the case of nonstationary proportions and, with some approximation, to the case of correlated spatial data. The mathematical developments presented in the appendices provide a more precise and general definition of the distribution, several decomposition formulae into independent variables, the determination of remarkable stability properties, and the resulting consequences for the conditional and marginal distributions.