Latin hypercube sampling better than monte carlo

Latin hypercube sampling better than monte carlo full#

Where 'x' is the parameter value, is the parameter minimum, is the parameter maximum, and is the standard uniform value.Д¬onverting LHS output from Standard Normal to Parameter Space _ Each random sample can be converted to parameter values via the following equations:Д¬onverting LHS output from Standard Uniform to Parameter Space _ This code outputs samples for the standard uniform and standard normal distributions. Posterior Distribution вЂ“ the resulting statistical distribution of the model outputДЄn example implementation of a LHS algorithm is below. Prior Distribution вЂ“ the statistical distribution of the input parameters to a model Due to the possibility of clustering (LHS sample with points close together) of sample points, a nearest neighbour restriction can be imposed. This is best visualized in a 2D space with the following figure:ДЄs seen in Figure 1, there is only one sample in each row and column in (X,Y) space. Once a suitable CDF sample is made, the sample CDF value is inversely mapped back to a parameter value.ДЄ requirement for LHS is that each region of the CDF can only be sampled once for each parameter.

Latin hypercube sampling better than monte carlo full#

By representing each variable as its Cumulative Distribution Function (CDF) (prior distribution) and partitioning the CDF into N regions and taking a single sample from each region, this increases the likelihood that the full range of the posterior distribution is sampled. LHS typically requires less samples and converges faster than Monte Carlo Simple Random Sampling (MCSRS) methods when used in uncertainty analysis. Latin Hypercube Sampling (LHS) is a method of sampling a model input space, usually for obtaining data for training metamodels or for uncertainty analysis. 3.2 Converting LHS output from Standard Normal to Parameter Space.3.1 Converting LHS output from Standard Uniform to Parameter Space.