Minimum mean-square-error criterion

Solutions for objects of finite extent are obtained through the familiar minimum mean-square-error criterion by selecting the Fourier components that minimize... 

Figure 4.10 (a solid line 1) shows the displacement distance along the loading axis to the center of the equivalent elastic element reference values modulus cesium. The same graph (Fig. 4.10, a-2) shows the radial displacements of atoms from the distance to the center of mass of nanoparticles r, for constant Poisson s ratio. The graphs show that these dependencies are not identical. Therefore, changing the modulus of elasticity, it is necessary to achieve data fusion curves (Fig. 4.10b), which is the criterion for the minimum mean square error. The mean square error is a pronounced minimum (Fig. 4.11). We calculate the bulk modulus of nanoparticles of cesium from the system (the Eq. (7)).

Equations (3) and (4) form the basis for the optimal Bayesian solution. Once the posterior density Z ) is known, an optimal state estimate with respect to any criterion can also be computed. For example, the Minimum Mean Square Error (MMSE) estimate is the conditional mean of ... 

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