Latin hypercube sampling uncertainty analysis

Latin hypercube sampling uncertainty analysis manuals#

Les trois rГ©plicats peuvent tous reproduire prГ©cisГ©ment les cdfs RS-MC correspondantes pour toutes les concentrations de BTEX dans les trois phases. La stabilitГ© du LHS-MC est Г©galement Г©valuГ©e en comparant trois rГ©plicats dвЂ™un LHS-MC. Les cdfs LHS-MC pour les trois diffГ©rentes tailles dвЂ™Г©chantillons peuvent reproduire avec prГ©cision les cdfs RS-MC correspondantes pour les concentrations de benzГЁne, de toluГЁne, dвЂ™Г©thylbenzГЁne et de xylГЁne (BTEX) dans les phases liquides, gazeuses et solides. Pour Г©valuer la capacitГ© du LHS-MC Г produire des fonctions de distribution cumulative (cdfs) qui reproduit les cdfs de lвЂ™Г©chantillonnage alГ©atoire Monte Carlo (RS-MC), les cdfs de sortie obtenues avec des tailles dвЂ™Г©chantillons LHS-MC de 100, 300 et 500 ainsi quвЂ™un Г©chantillon RS-MC de taille 10,000 sont comparГ©es en utilisant les tests de Kolmogoroff-Smirnoff Г deux Г©chantillons. a systemic sampling of the uncertain distributions, Latin Hypercube Sampling (LHS) technique was used to sample data. JSTOR 2670057.Dans le but de faciliter lвЂ™analyse dвЂ™incertitude dвЂ™un modГЁle MOFAT de transport Г Г©lГ©ments finis polyphasГ© et Г multicomposantes, cet article se veut un guide pour la sГ©lection de la dimension de lвЂ™Г©chantillonnage latin hypercube Monte Carlo (LHS-MC). Journal of the American Statistical Association. 'Orthogonal column Latin hypercubes and their application in computer experiments'. 'Orthogonal arrays for computer experiments, integration and visualization'. 'Orthogonal Array-Based Latin Hypercubes'. Latin hypercube sampling (program user's guide). Introduction, input variable selection and preliminary variable assessment'. 'An approach to sensitivity analysis of computer models, Part 1. However, uncertainty analysis using conventional methods such as standard Monte Carlo or Latin Hypercube Sampling may not be efficient, or even feasible. 'New approach to the design of multifactor experiments'. 'A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code'. Thus, orthogonal sampling ensures that the set of random numbers is a very good representative of the real variability, LHS ensures that the set of random numbers is representative of the real variability whereas traditional random sampling (sometimes called brute force) is just a set of random numbers without any guarantees. All sample points are then chosen simultaneously making sure that the total set of sample points is a Latin hypercube sample and that each subspace is sampled with the same density. In orthogonal sampling, the sample space is divided into equally probable subspaces.Such configuration is similar to having N rooks on a chess board without threatening each other. In Latin hypercube sampling one must first decide how many sample points to use and for each sample point remember in which row and column the sample point was taken.One does not necessarily need to know beforehand how many sample points are needed. In random sampling new sample points are generated without taking into account the previously generated sample points.In two dimensions the difference between random sampling, Latin hypercube sampling, and orthogonal sampling can be explained as follows: Another advantage is that random samples can be taken one at a time, remembering which samples were taken so far. This sampling scheme does not require more samples for more dimensions (variables) this independence is one of the main advantages of this sampling scheme. When sampling a function of N, to be equal for each variable. A Latin hypercube is the generalisation of this concept to an arbitrary number of dimensions, whereby each sample is the only one in each axis-aligned hyperplane containing it. In the context of statistical sampling, a square grid containing sample positions is a Latin square if (and only if) there is only one sample in each row and each column.

Latin hypercube sampling uncertainty analysis manuals#

Detailed computer codes and manuals were later published. LHS is a stratified random sampling method where the distribution is divided. An independently equivalent technique was proposed by EglДЃjs in 1977. A good alternative to pure random sampling is Latin Hypercube Sampling (LHS) 2. LHS was described by Michael McKay of Los Alamos National Laboratory in 1979. The sampling method is often used to construct computer experiments or for Monte Carlo integration. Latin hypercube sampling ( LHS) is a statistical method for generating a near-random sample of parameter values from a multidimensional distribution.