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In many situations the number of code runs available to build the Gaussian process approximation is limited.
Based on the D-partition method and FOPDT (First Order plus Dead Time) process approximation, a software tool is designed that allows for tuning subject to phase and gain margins.
For instance, Artificial Neural Network (ANN) in [7 9], ANN with Gaussian process approximation and adaptive Bayesian learning in [10], combination of wavelet transform with ANN [11], fuzzy logic methods in [5, 12], Kalman filter in [13], support vector machine in [14], and adaptive neuro-fuzzy inference system (ANFIS) in [15] have been proposed for wind power prediction.
By using analytic models described by the Langevin equations driven by Gaussian white noise and Poissonian white shot noise, we verify our theoretical error estimates and discuss the non-Gaussianity effect in the error estimates when the Gaussian process approximation does not hold exactly.
It is possible to derive an expression for the global invasion threshold in a branching process approximation [39], [40].
The probability that a typical infective generates a local epidemic is computed by using a branching process approximation [12] for the initial stages of the epidemic, and equating 'epidemic' with the event that the branching process does not become extinct.
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The proposed approach is applied to the simulated Williams-Otto reactor, considering three GNM process approximations.
The first terms in these expansions are familiar stationary Gaussian process approximations and the first non-zero correction terms represent first order corrections to these Gaussian process approximations.
The linking solution approach uses traffic process approximations to analyze the performance of sub-models corresponding to individual tiers (semi-open queues) and the vertical transfer units (open queues).
Since the functional forms of these first order correction terms are fixed and unique, corrections to the familiar stationary Gaussian process approximations of probability density and exceedance rate functions are predicted to have fixed functional forms for fractionally small variance fluctuations.
This is appropriate for most non-spatial models, for which branching process approximations can be applied (Ball, 1983; Davis et al., 2008), showing that early growth is exponential, with the nth generation of infectives ∝ λ * n, and with infectious numbers of each type in the ratios of the corresponding right eigen-vector.
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