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A virtual simulation is a category of simulation that uses simulation equipment to create a simulated world for the user. Virtual simulations allow users to interact with a virtual world . Virtual worlds operate on platforms of integrated software and hardware components.
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.
Modeling and simulation (M&S) is the use of models (e.g., physical, mathematical, behavioral, or logical representation of a system, entity, phenomenon, or process) as a basis for simulations to develop data utilized for managerial or technical decision making.
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.
GPR is a Bayesian non-linear regression method. A Gaussian process (GP) is a collection of random variables, any finite number of which have a joint Gaussian (normal) distribution. A GP is defined by a mean function and a covariance function, which specify the mean vectors and covariance matrices for each finite collection of the random variables.
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the outcome or response variable, or a label in machine learning parlance) and one or more error-free independent variables (often called regressors, predictors, covariates, explanatory ...
Usually, the underlying simulation model is stochastic, so that the objective function must be estimated using statistical estimation techniques (called output analysis in simulation methodology). Once a system is mathematically modeled, computer-based simulations provide information about its behavior.
A stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities. [1] Realizations of these random variables are generated and inserted into a model of the system. Outputs of the model are recorded, and then the process is repeated with a new set of random values.