Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

Random vibration of hysteretic systems under bi-directional ground motions

Abstract: A random vibration method is developed for the response analysis of hysteretic structural systems under stochastic two-dimensional earthquake excitations. The biaxial hysteretic restoring force is modelled by coupled non-linear differential equations; the response statistics are obtained using the equivalent linearization technique. The validity of the proposed model is appraised using available biaxial loading tests of reinforced concrete columns. A parametric study was performed to examine the significance of the effects of biaxial interaction under earthquake excitations. A practical method to evaluate the extreme response statistics is also presented.

Accurate detection of outliers and subpopulations with Pmetrics, a nonparametric and parametric pharmacometric modeling and simulation package for R

Abstract: Introduction:Nonparametric population modeling algorithms have a theoretical superiority over parametric methods to detect pharmacokinetic and pharmacodynamic subgroups and outliers within a study population.Methods:The authors created “Pmetrics,” a new Windows and Unix R software package that updat

Estimating motion in image sequences

Abstract: We have reviewed the estimation of 2D motion from time-varying images, paying particular attention to the underlying models, estimation criteria, and optimization strategies. Several parametric and nonparametric models for the representation of motion vector fields and motion trajectory fields have been discussed. For a given region of support, these models determine the dimensionality of the estimation problem as well as the amount of data that has to be interpreted or transmitted thereafter. Also, the interdependence of motion and image data has been addressed. We have shown that even ideal constraints may not provide a well-defined estimation criterion. Therefore, the data term of an estimation criterion is usually supplemented with a smoothness term that can be expressed explicitly or implicitly via a constraining motion model. We have paid particular attention to the statistical criteria based on Markov random fields. Because the optimization of an estimation criterion typically involves a large number of unknowns, we have presented several fast search strategies.

Internal statistics of a single natural image

Abstract: Statistics of ‘natural images’ provides useful priors for solving under-constrained problems in Computer Vision. Such statistics is usually obtained from large collections of natural images. We claim that the substantial internal data redundancy within a single natural image (e.g., recurrence of small image patches), gives rise to powerful internal statistics, obtained directly from the image itself. While internal patch recurrence has been used in various applications, we provide a parametric quantification of this property. We show that the likelihood of an image patch to recur at another image location can be expressed parametricly as a function of the spatial distance from the patch, and its gradient content. This “internal parametric prior” is used to improve existing algorithms that rely on patch recurrence. Moreover, we show that internal image-specific statistics is often more powerful than general external statistics, giving rise to more powerful image-specific priors. In particular: (i) Patches tend to recur much more frequently (densely) inside the same image, than in any random external collection of natural images. (ii) To find an equally good external representative patch for all the patches of an image, requires an external database of hundreds of natural images. (iii) Internal statistics often has stronger predictive power than external statistics, indicating that it may potentially give rise to more powerful image-specific priors.