Topic
Parametric statistics
About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.
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23 May 1990TL;DR: In this article, a method for parameter set estimation for a system wich contains both parametric and nonparametric uncertainty prior nformation is available about both types of uncertainty, but only the parametric type is further refined from the measured data.
Abstract: A method is presented for parameter set estimation for a system wich contains both parametric and nonparametric uncertainty Prior nformation is available about both types of uncertainty, but only the parametric type is further refined from the measured data
132 citations
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TL;DR: In this paper, the nonlinear dynamics of a hinged-hinged pipe conveying pulsatile fluid subjected to combination and principal parametric resonance in the presence of internal resonance is investigated.
132 citations
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01 Mar 2002
TL;DR: This thesis proposes a two-step solution to construct a probabilistic approximation to the posterior of Gaussian processes, and combines the sparse approximation with an extension to the Bayesian online algorithm that allows multiple iterations for each input and thus approximating a batch solution.
Abstract: In recent years there has been an increased interest in applying non-parametric methods to real-world problems. Significant research has been devoted to Gaussian processes (GPs) due to their increased flexibility when compared with parametric models. These methods use Bayesian learning, which generally leads to analytically intractable posteriors. This thesis proposes a two-step solution to construct a probabilistic approximation to the posterior. In the first step we adapt the Bayesian online learning to GPs: the final approximation to the posterior is the result of propagating the first and second moments of intermediate posteriors obtained by combining a new example with the previous approximation. The propagation of em functional forms is solved by showing the existence of a parametrisation to posterior moments that uses combinations of the kernel function at the training points, transforming the Bayesian online learning of functions into a parametric formulation. The drawback is the prohibitive quadratic scaling of the number of parameters with the size of the data, making the method inapplicable to large datasets. The second step solves the problem of the exploding parameter size and makes GPs applicable to arbitrarily large datasets. The approximation is based on a measure of distance between two GPs, the KL-divergence between GPs. This second approximation is with a constrained GP in which only a small subset of the whole training dataset is used to represent the GP. This subset is called the em Basis Vector, or BV set and the resulting GP is a sparse approximation to the true posterior. As this sparsity is based on the KL-minimisation, it is probabilistic and independent of the way the posterior approximation from the first step is obtained. We combine the sparse approximation with an extension to the Bayesian online algorithm that allows multiple iterations for each input and thus approximating a batch solution. The resulting sparse learning algorithm is a generic one: for different problems we only change the likelihood. The algorithm is applied to a variety of problems and we examine its performance both on more classical regression and classification tasks and to the data-assimilation and a simple density estimation problems.
132 citations
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TL;DR: This work proposes a second-order linear time-varying autoregressive (TVAR) process for parametric representation of the electroencephalogram (EEG) signals using the coefficients of the Fourier-Bessel series expansion.
132 citations
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TL;DR: In this article, a parametric stiffness analysis of the Orthoglide was performed and a compliant modeling and a symbolic expression of the stiffness matrix were conducted. Butler et al. presented a simple systematic analysis for the influence of the geometric design parameters and identified the critical link parameters.
132 citations