8 Experimental Gaussian pdf generated using a LHS and b MC. 3.1 Description of Sampling Techniques 3.2 Properties of Sampling Techniques 3.3 Historical Development. An application of the LHS technique in the field of rock slope stability assessment will then be discussed. method by the LHS in order to improve the efficiency of the sequential Gaussian simulation. Random, Stratified and Latin Hypercube Sampling.
The development of the LHS technique will first be described and then compared with the Monte Carlo sampling technique. This has been successfully applied to rock slope stability analyses concerning plane and wedge failure and has been found to represent the original data more closely than could Monte Carlo sample sets of the same size. 1) with the uniform probability density function (p.d.f.) is listed below. Latin hypercube sample of a 5 x 5 matrix (after Cheng and Druzdzel, 2000).For each sample, i,j, the sample values of X,Y are determined by:, where n is the sample size, x and y are random. The stratification is accomplished by dividing the vertical axis on the graph of the distribution function of a random variable Xj into n nonoverlapping intervals of equal length, where n is the number of computer runs to be made. LHS, in essence, is a constrained randomisation sampling scheme which is sensitive to the extreme values of the data range. The Latin Hypercube Sampling (LHS) is a type of stratified Monte Carlo (MC). LHS uses a stratified sampling scheme to improve on the coverage of the input space. However computation time can be substantial if significant sampling errors are to be avoided.Īn alternative approach has been developed which uses the Latin Hypercube Sampling (LHS) approach to the same algorithms. Such analyses have been succesfully solved using a Monte Carlo Sampling approach based on well-established deterministic algorithms. Papers also reflect shifts in attitudes about data analysis (e.g., less formal hypothesis testing, more fitted models via graphical analysis), and in how important application areas are managed (e.g., quality assurance through robust design rather than detailed inspection).A probabilistic approach to slope stability analysis allows the observed natural variability of many parameters to be taken into consideration.
The model outputs studied are the mean and the 5- and 95-percentile of the areal fraction.
In a case study the efficiency of Latin hypercube sampling is compared experimentally to that of simple random sampling. This includes an emphasis on new statistical approaches to screening, modeling, pattern characterization, and change detection that take advantage of massive computing capabilities. Following the method of Stein, this article shows how a Latin hypercube sample can be drawn from a Gaussian random field. Papers in the journal reflect modern practice. Latin hypercube sampling (LHS) is a statistical method for generating a near-random sample of parameter values from a multidimensional distribution. Application of proposed methodology is justified, usually by means of an actual problem in the physical, chemical, or engineering sciences.
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Its content features papers that describe new statistical techniques, illustrate innovative application of known statistical methods, or review methods, issues, or philosophy in a particular area of statistics or science, when such papers are consistent with the journal's mission. Download PDF Abstract: Three sampling methods are compared for efficiency on a number of test problems of various complexity for which analytic quadratures are available. The mission of Technometrics is to contribute to the development and use of statistical methods in the physical, chemical, and engineering sciences. The LHS method operates in the following manner to generate a sample size N from the n variables.
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