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Simulation can be used to predict the performance of an existing or planned system and to compare alternative solutions for a particular design problem. [68] Another important goal of simulation in manufacturing systems is to quantify system performance. Common measures of system performance include the following: [69]
However, the simulation outputs are weighted to correct for the use of the biased distribution, and this ensures that the new importance sampling estimator is unbiased. The weight is given by the likelihood ratio , that is, the Radon–Nikodym derivative of the true underlying distribution with respect to the biased simulation distribution.
Modeling and simulation are important in research. Representing the real systems either via physical reproductions at smaller scale, or via mathematical models that allow representing the dynamics of the system via simulation, allows exploring system behavior in an articulated way which is often either not possible, or too risky in the real world.
For simulation with black-box models subset simulation and line sampling can also be used. Under these headings are a variety of specialized techniques; for example, particle transport simulations make extensive use of "weight windows" and "splitting/Russian roulette" techniques, which are a form of importance sampling.
Monte Carlo simulation: Drawing a large number of pseudo-random uniform variables from the interval [0,1] at one time, or once at many different times, and assigning values less than or equal to 0.50 as heads and greater than 0.50 as tails, is a Monte Carlo simulation of the behavior of repeatedly tossing a coin.
Though computational statistics is widely used today, it actually has a relatively short history of acceptance in the statistics community. For the most part, the founders of the field of statistics relied on mathematics and asymptotic approximations in the development of computational statistical methodology.
It is often more important to be able to access the data produced by the simulation and to discover logic defects in the design or the sequence of events. A continuous dynamic simulation performs numerical solution of differential-algebraic equations or differential equations (either partial or ordinary). Periodically, the simulation program ...
SimDec, or Simulation decomposition, is a hybrid uncertainty and sensitivity analysis method, for visually examining the relationships between the output and input variables of a computational model. SimDec maps multivariable scenarios onto the distribution of the model output. [ 1 ]