Latin Hypercube Sampling Software Mac
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Parallelization Computation time is often the bottle neck for modeling applications. Especially when parameteres are estimated it is important the single estimation runs converge as quick as possible.
This allows a interactive workflow when the ideal structure of a model is known jet. In the parameter estimation the model has to be evaluated many times.
Often, a single model evaluation requires serveral numerical solutions of the ODE systems. Since these evaluation are all independent this is the ideal level for applying parallel computing without communication overhead between parallel ODE solver calls. The Data 2 Dynamics software package applies parallelization based on multi-threading using the pthread package. The number of threads that are executed in parallel can be set by the function arSetParallelThreads(n) where the default for n is the number of cores of machine time two.
Under every combination we've tested, the sample means are much, much closer together with the Latin Hypercube sampling method than with the Monte Carlo method. If you'd like to know more about the theory of Monte Carlo and Latin Hypercube sampling methods, please look at the technical appendices of the @RISK manual.
Multi-threaded calculations can entirely be switched off by setting the flag ar.config.useParallel = false. For Unix type operating system, for instance Linux or Mac OS X, the pthread package is usally installed an can be used mmediately. On Windows systems the pthread-w32 package can be installed. Two addition.dll files need to be placed in the C: Windows folder: pthreadGC2.dll and pthreadVC2.dll. The files can be found in the code subfolder arFramework3 pthreads-w322.9.1 dll for your convenience. The arCheck.m function will notify you when these files are not available and will disable multi-threading. We use the example application that contains 24 different experimental conditions as demonstation and 500 randonly drawn, via Latin Hypercube Sampling, sets of parameters.
Latin Hypercube Sampling Matlab
In a recent post on Linked In, David Vose argues that the advantages of Latin Hypercube sampling (LHS) over Monte Carlo are so minimal that “LHS does not deserve a place in modern simulation software.” He makes some interesting points, yet products like Analytica and Crystal Ball still provide LHS and even offer it as their default method. Importance Sampling Even with Latin hypercube sampling, Monte Carlo analysis requires a HUGE number of sampling points Example: rare event estimation The theoretical answer for P(x ≤ -5) is equal to 2.87×10-7 100M sampling points are required if we attempt to estimate this probability by random sampling.
The 24 different experimental conditions correspond to 24 different variants of the original ODE system that have to be numerically simulated for one evaluation of the complete model, using a maximum of 24 independent threads. The figure below shows the statistics of computation acceleration on a 12 core machine if the number of thread is increased up to 24, compare to sequential computation on the same machine. This figure can be reproduces using the function arCheckParallelSpeedUp. The figure indicates that acceleration scales as excepted with increasing number of threads. After using as many cores as available on this machine (dashed horizontal line) the acceleration can not increase much. Please note that some threads, i.e. Some experimental conditions, can be computationally more demanding that others.
This can lead to an overall decrease of acceleration compared to the theoretical possible acceleration (red line). Updated 2014-01-08.
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