Parametric statistics

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

Scenarios for Multistage Stochastic Programs

Abstract: A major issue in any application of multistage stochastic programming is the representation of the underlying random data process. We discuss the case when enough data paths can be generated according to an accepted parametric or nonparametric stochastic model. No assumptions on convexity with respect to the random parameters are required. We emphasize the notion of representative scenarios (or a representative scenario tree) relative to the problem being modeled.

Stochastic averaging: An approximate method of solving random vibration problems

Abstract: Results obtained by applying the method of stochastic averaging to random vibration problems are discussed. This method is applicable to a variety of problems involving the response of lightly damped systems to broad-band random excitations. Solutions pertaining to both linear and non-linear vibrations are reviewed, and it is shown that the technique enables, in the case of parametric excitation, stability criteria to be established. Some results which have been obtained relating to the first-passage reliability problems are also surveyed. Various applications of the theory to engineering problems are outlined.

Robust Point Matching via Vector Field Consensus

Abstract: In this paper, we propose an efficient algorithm, called vector field consensus, for establishing robust point correspondences between two sets of points. Our algorithm starts by creating a set of putative correspondences which can contain a very large number of false correspondences, or outliers, in addition to a limited number of true correspondences (inliers). Next, we solve for correspondence by interpolating a vector field between the two point sets, which involves estimating a consensus of inlier points whose matching follows a nonparametric geometrical constraint. We formulate this a maximum a posteriori (MAP) estimation of a Bayesian model with hidden/latent variables indicating whether matches in the putative set are outliers or inliers. We impose nonparametric geometrical constraints on the correspondence, as a prior distribution, using Tikhonov regularizers in a reproducing kernel Hilbert space. MAP estimation is performed by the EM algorithm which by also estimating the variance of the prior model (initialized to a large value) is able to obtain good estimates very quickly (e.g., avoiding many of the local minima inherent in this formulation). We illustrate this method on data sets in 2D and 3D and demonstrate that it is robust to a very large number of outliers (even up to 90%). We also show that in the special case where there is an underlying parametric geometrical model (e.g., the epipolar line constraint) that we obtain better results than standard alternatives like RANSAC if a large number of outliers are present. This suggests a two-stage strategy, where we use our nonparametric model to reduce the size of the putative set and then apply a parametric variant of our approach to estimate the geometric parameters. Our algorithm is computationally efficient and we provide code for others to use it. In addition, our approach is general and can be applied to other problems, such as learning with a badly corrupted training data set.

A mixture model combining logistic regression with proportional hazards regression

Abstract: SUMMARY A model is proposed for the analysis of censored data which combines a logistic formulation for the probability of occurrence of an event with a proportional hazards specification for the time of occurrence of the event. The proposed model is a semiparametric generalization of a parametric model due to Farewell (1982). Estimates of the regression parameters are obtained by maximizing a Monte Carlo approximation of a marginal likelihood and the EM algorithm is used to estimate the baseline survivor function. We present some simulation results to verify the validity of the suggested estimation procedure. It appears that the semiparametric estimates are reasonably efficient with acceptable bias whereas the parametric estimates can be highly dependent on the parametric assumptions.