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There are at least two main considerations when performing collocations. The first is the sampling pattern of the instrument. Measurements may be dense and regular, such as those from a cross-track scanning satellite instrument. In this case, some form of interpolation may be appropriate. On the other hand, the measurements may be sparse, such ...
Pickover developed an algorithm (which uses neither random perturbations nor natural laws) to create very complicated forms resembling invertebrate organisms. The iteration, or recursion, of mathematical transformations is used to generate biological morphologies. He called them "biomorphs."
Multiple-try Metropolis (MTM) is a sampling method that is a modified form of the Metropolis–Hastings method, first presented by Liu, Liang, and Wong in 2000. It is designed to help the sampling trajectory converge faster, by increasing both the step size and the acceptance rate.
A diagram of an alias table that represents the probability distribution〈0.25, 0.3, 0.1, 0.2, 0.15〉 In computing, the alias method is a family of efficient algorithms for sampling from a discrete probability distribution, published in 1974 by Alastair J. Walker.
An illustration of Monte Carlo integration. In this example, the domain D is the inner circle and the domain E is the square. Because the square's area (4) can be easily calculated, the area of the circle (π*1.0 2) can be estimated by the ratio (0.8) of the points inside the circle (40) to the total number of points (50), yielding an approximation for the circle's area of 4*0.8 = 3.2 ≈ π.
Lower case denotes the face and upper case denotes node; , , and refer to the "East," "West," and "Central" cell. (again, see Fig. 1 below). Defining variable F as convection mass flux and variable D as diffusion conductance = and =
In computational fluid dynamics QUICK, which stands for Quadratic Upstream Interpolation for Convective Kinematics, is a higher-order differencing scheme that considers a three-point upstream weighted by quadratic interpolation for the cell face values.
SGLD can be applied to the optimization of non-convex objective functions, shown here to be a sum of Gaussians. Stochastic gradient Langevin dynamics (SGLD) is an optimization and sampling technique composed of characteristics from Stochastic gradient descent, a Robbins–Monro optimization algorithm, and Langevin dynamics, a mathematical extension of molecular dynamics models.