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The book addresses the problem of calculation of d-dimensional integrals (conditional expectations) in filter problems. It develops new methods of deterministic numerical integration, which can be used to speed up and stabilize filter algorithms. With the help of these methods, better estimates and predictions of latent variables are made possible in the fields of economics, engineering and physics. The resulting procedures are tested within four detailed simulation studies.

Statistics. --- Computer mathematics. --- Vibration. --- Dynamical systems. --- Dynamics. --- Econometrics. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Computational Mathematics and Numerical Analysis. --- Vibration, Dynamical Systems, Control. --- Statistical Physics and Dynamical Systems. --- Cubature formulas. --- Numerical integration. --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Definite integrals --- Interpolation --- Numerical analysis --- Formulas, Cubature --- Numerical integration --- Computer science --- Statistical physics. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Mathematics. --- Physics --- Mathematical statistics --- Cycles --- Mechanics --- Sound --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Economics, Mathematical --- Statistics --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Statistics . --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Statics