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The Fourier-wavelet method of Elliott et al. is investigated and compared with other methods, all of which are evaluated in terms of their ability to sample the stochastic process over a large number of decades for a given computational cost.
Hence, to apply Equation (1), which assumes constant time steps, it is necessary to sample the stochastic time series at regular time intervals.
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In the case considered here, a very common approach exploiting features of the Gaussian processes is employed; thus, we assume that our target function (the generalization capabilities of the SVM with RBF kernel applied to the prediction of the activity of chemical compounds) f is a sample of the stochastic process.
Traditionally, this method has been applied by using Monte Carlo (MC) sampling to generate the samples of the stochastic variables.
Traditionally, this method has been applied by using the Monte Carlo sampling technique to generate the samples of the stochastic variables.
This work presents an alternative approach to robust optimization, where the robustness of each design is assessed through multiple sampling of the stochastic variables at each design point.
To create approximations to the distribution of Pr values we computed 214 samples from the stochastic map, after discarding a brief initial transient.
By meticulously blending sharpness-promised interval eigenvalue analysis with stochastic sampling techniques, the stochastic profiles (i.e., probability density functions (PDFs) and the cumulative distribution functions (CDFs)) of the extreme bounds of the structural natural frequencies can be rigorously established by utilizing the adequate statistical inference methods.
Monte Carlo simulation is employed to obtain a few samples of the stochastic temperature and displacement fields, from which lower and upper bounds of expected value and second order moment are computed.
For instance, a merit of SFA is that particularly high observed efficiency values (abnormal values) are obtained compared to other samples and the stochastic production frontier can absorb a significant part of the impact of these abnormal values, symmetrically, in the error term.
For the convergence of the results, we ran these simulations for 1000 samples, and considered the average of sample realizations of the stochastic process to generate infection curves.
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