Stochastic seismic inversion is the combination of geostatistics and seismic inversion technology which integrates information from seismic records, well logs, and geostatistics into a posterior probability density fu...Stochastic seismic inversion is the combination of geostatistics and seismic inversion technology which integrates information from seismic records, well logs, and geostatistics into a posterior probability density function （PDF） of subsurface models. The Markov chain Monte Carlo （MCMC） method is used to sample the posterior PDF and the subsurface model characteristics can be inferred by analyzing a set of the posterior PDF samples. In this paper, we first introduce the stochastic seismic inversion theory, discuss and analyze the four key parameters： seismic data signal-to-noise ratio （S/N）, variogram, the posterior PDF sample number, and well density, and propose the optimum selection of these parameters. The analysis results show that seismic data S/N adjusts the compromise between the influence of the seismic data and geostatistics on the inversion results, the variogram controls the smoothness of the inversion results, the posterior PDF sample number determines the reliability of the statistical characteristics derived from the samples, and well density influences the inversion uncertainty. Finally, the comparison between the stochastic seismic inversion and the deterministic model based seismic inversion indicates that the stochastic seismic inversion can provide more reliable information of the subsurface character.展开更多
An existing Bayesian flood frequency analysis method is applied to quantile estimation for Pearson type three (P-III) probability distribution. The method couples prior and sample information under the framework of Ba...An existing Bayesian flood frequency analysis method is applied to quantile estimation for Pearson type three (P-III) probability distribution. The method couples prior and sample information under the framework of Bayesian formula, and the Markov Chain Monte Carlo (MCMC) sampling approach is used to estimate posterior distributions of parameters. Different from the original sampling algorithm (i.e. the important sampling) used in the existing approach, we use the adaptive metropolis (AM) sampling technique to generate a large number of parameter sets from Bayesian parameter posterior distributions in this paper. Consequently, the sampling distributions for quantiles or the hydrological design values are constructed. The sampling distributions of quantiles are estimated as the Bayesian method can provide not only various kinds of point estimators for quantiles, e.g. the expectation estimator, but also quantitative evaluation on uncertainties of these point estimators. Therefore, the Bayesian method brings more useful information to hydrological frequency analysis. As an example, the flood extreme sample series at a gauge are used to demonstrate the procedure of application.展开更多
The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the unc...The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.展开更多
基金supported by the National Major Science and Technology Project of China on Development of Big Oil-Gas Fields and Coalbed Methane (No. 2008ZX05010-002)
文摘Stochastic seismic inversion is the combination of geostatistics and seismic inversion technology which integrates information from seismic records, well logs, and geostatistics into a posterior probability density function （PDF） of subsurface models. The Markov chain Monte Carlo （MCMC） method is used to sample the posterior PDF and the subsurface model characteristics can be inferred by analyzing a set of the posterior PDF samples. In this paper, we first introduce the stochastic seismic inversion theory, discuss and analyze the four key parameters： seismic data signal-to-noise ratio （S/N）, variogram, the posterior PDF sample number, and well density, and propose the optimum selection of these parameters. The analysis results show that seismic data S/N adjusts the compromise between the influence of the seismic data and geostatistics on the inversion results, the variogram controls the smoothness of the inversion results, the posterior PDF sample number determines the reliability of the statistical characteristics derived from the samples, and well density influences the inversion uncertainty. Finally, the comparison between the stochastic seismic inversion and the deterministic model based seismic inversion indicates that the stochastic seismic inversion can provide more reliable information of the subsurface character.
基金supported by the National Basic Research Pro-gram of China ("973" Program) (Grant No. 2007CB714104)the National Natural Science Foundation of China (Grant No. 50779013)
文摘An existing Bayesian flood frequency analysis method is applied to quantile estimation for Pearson type three (P-III) probability distribution. The method couples prior and sample information under the framework of Bayesian formula, and the Markov Chain Monte Carlo (MCMC) sampling approach is used to estimate posterior distributions of parameters. Different from the original sampling algorithm (i.e. the important sampling) used in the existing approach, we use the adaptive metropolis (AM) sampling technique to generate a large number of parameter sets from Bayesian parameter posterior distributions in this paper. Consequently, the sampling distributions for quantiles or the hydrological design values are constructed. The sampling distributions of quantiles are estimated as the Bayesian method can provide not only various kinds of point estimators for quantiles, e.g. the expectation estimator, but also quantitative evaluation on uncertainties of these point estimators. Therefore, the Bayesian method brings more useful information to hydrological frequency analysis. As an example, the flood extreme sample series at a gauge are used to demonstrate the procedure of application.
文摘The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.
