Showing papers on "Parametric statistics published in 2002"

Nonparametric permutation tests for functional neuroimaging: A primer with examples

Abstract: Requiring only minimal assumptions for validity, nonparametric permutation testing provides a flexible and intuitive methodology for the statistical analysis of data from functional neuroimaging experiments, at some computational expense. Introduced into the functional neuroimaging literature by Holmes et al. ([1996]: J Cereb Blood Flow Metab 16:7-22), the permutation approach readily accounts for the multiple comparisons problem implicit in the standard voxel-by-voxel hypothesis testing framework. When the appropriate assumptions hold, the nonparametric permutation approach gives results similar to those obtained from a comparable Statistical Parametric Mapping approach using a general linear model with multiple comparisons corrections derived from random field theory. For analyses with low degrees of freedom, such as single subject PET/SPECT experiments or multi-subject PET/SPECT or fMRI designs assessed for population effects, the nonparametric approach employing a locally pooled (smoothed) variance estimate can outperform the comparable Statistical Parametric Mapping approach. Thus, these nonparametric techniques can be used to verify the validity of less computationally expensive parametric approaches. Although the theory and relative advantages of permutation approaches have been discussed by various authors, there has been no accessible explication of the method, and no freely distributed software implementing it. Consequently, there have been few practical applications of the technique. This article, and the accompanying MATLAB software, attempts to address these issues. The standard nonparametric randomization and permutation testing ideas are developed at an accessible level, using practical examples from functional neuroimaging, and the extensions for multiple comparisons described. Three worked examples from PET and fMRI are presented, with discussion, and comparisons with standard parametric approaches made where appropriate. Practical considerations are given throughout, and relevant statistical concepts are expounded in appendices.

Statistical Models and Methods for Lifetime Data

Abstract: Basic Concepts and Models. Observation Schemes, Censoring and Likelihood. Some Nonparametric and Graphical Procedures. Inference Procedures for Parametric Models. Inference procedures for Log-Location-Scale Distributions. Parametric Regression Models. Semiparametric Multiplicative Hazards Regression Models. Rank-Type and Other Semiparametric Procedures for Log-Location-Scale Models. Multiple Modes of Failure. Goodness of Fit Tests. Beyond Univariate Survival Analysis. Appendix A. Glossary of Notation and Abbreviations. Appendix B. Asymptotic Variance Formulas, Gamma Functions and Order Statistics. Appendix C. Large Sample Theory for Likelihood and Estimating Function Methods. Appendix D. Computational Methods and Simulation. Appendix E. Inference in Location-Scale Parameter Models. Appendix F. Martingales and Counting Processes. Appendix G. Data Sets. References.

Unsupervised learning of finite mixture models

Abstract: This paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data. The adjective "unsupervised" is justified by two properties of the algorithm: 1) it is capable of selecting the number of components and 2) unlike the standard expectation-maximization (EM) algorithm, it does not require careful initialization. The proposed method also avoids another drawback of EM for mixture fitting: the possibility of convergence toward a singular estimate at the boundary of the parameter space. The novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models; instead, we seamlessly integrate estimation and model selection in a single algorithm. Our technique can be applied to any type of parametric mixture model for which it is possible to write an EM algorithm; in this paper, we illustrate it with experiments involving Gaussian mixtures. These experiments testify for the good performance of our approach.

Fiber-based optical parametric amplifiers and their applications

Abstract: An applications-oriented review of optical parametric amplifiers in fiber communications is presented. The emphasis is on parametric amplifiers in general and single pumped parametric amplifiers in particular. While a theoretical framework based on highly efficient four-photon mixing is provided, the focus is on the intriguing applications enabled by the parametric gain, such as all-optical signal sampling, time-demultiplexing, pulse generation, and wavelength conversion. As these amplifiers offer high gain and low noise at arbitrary wavelengths with proper fiber design and pump wavelength allocation, they are also candidate enablers to increase overall wavelength-division-multiplexing system capacities similar to the more well-known Raman amplifiers. Similarities and distinctions between Raman and parametric amplifiers are also addressed. Since the first fiber-based parametric amplifier experiments providing net continuous-wave gain in the for the optical fiber communication applications interesting 1.5-/spl mu/m region were only conducted about two years ago, there is reason to believe that substantial progress may be made in the future, perhaps involving "holey fibers" to further enhance the nonlinearity and thus the gain. This together with the emergence of practical and inexpensive high-power pump lasers may in many cases prove fiber-based parametric amplifiers to be a desired implementation in optical communication systems.

Parametric shape analysis via 3-valued logic

Abstract: Shape analysis concerns the problem of determining "shape invariants" for programs that perform destructive updating on dynamically allocated storage. This article presents a parametric framework for shape analysis that can be instantiated in different ways to create different shape-analysis algorithms that provide varying degrees of efficiency and precision. A key innovation of the work is that the stores that can possibly arise during execution are represented (conservatively) using 3-valued logical structures. The framework is instantiated in different ways by varying the predicates used in the 3-valued logic. The class of programs to which a given instantiation of the framework can be applied is not limited a priori (i.e., as in some work on shape analysis, to programs that manipulate only lists, trees, DAGS, etc.); each instantiation of the framework can be applied to any program, but may produce imprecise results (albeit conservative ones) due to the set of predicates employed.

Robust stability and stabilization for singular systems with state delay and parameter uncertainty

Abstract: Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method.

Shape Priors for Level Set Representations

Abstract: Level Set Representations, the pioneering framework introduced by Osher and Sethian [14] is the most common choice for the implementation of variational frameworks in Computer Vision since it is implicit, intrinsic, parameter and topology free. However, many Computer vision applications refer to entities with physical meanings that follow a shape form with a certain degree of variability. In this paper, we propose a novel energetic form to introduce shape constraints to level set representations. This formulation exploits all advantages of these representations resulting on a very elegant approach that can deal with a large number of parametric as well as continuous transformations. Furthermore, it can be combined with existing well known level set-based segmentation approaches leading to paradigms that can deal with noisy, occluded and missing or physically corrupted data. Encouraging experimental results are obtained using synthetic and real images.

The time-rescaling theorem and its application to neural spike train data analysis

Abstract: Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model's validity prior to using it to make inferences about a particular neural system. Assessing goodness-of-fit is a challenging problem for point process neural spike train models, especially for histogram-based models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The time-rescaling theorem is a well-known result in probability theory, which states that any point process with an integrable conditional intensity function may be transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodness-of-fit tests for both parametric and histogram-based point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the supplementary eye field of a macque monkey and a comparison of temporal and spatial smoothers, inhomogeneous Poisson, inhomogeneous gamma, and inhomogeneous inverse gaussian models of rat hippocampal place cell spiking activity. To help make the logic behind the time-rescaling theorem more accessible to researchers in neuroscience, we present a proof using only elementary probability theory arguments. We also show how the theorem may be used to simulate a general point process model of a spike train. Our paradigm makes it possible to compare parametric and histogram-based neural spike train models directly. These results suggest that the time-rescaling theorem can be a valuable tool for neural spike train data analysis.

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods

Abstract: We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

Cointegration Vector Estimation by Panel Dols and Long-Run Money Demand

Abstract: We study the panel DOLS estimator of a homogeneous cointegration vector for a balanced panel of N individuals observed over T time periods. Allowable heterogeneity across individuals include individual-specific time trends, individual-specific fixed effects and time-specific effects. The estimator is fully parametric, computationally convenient, and more precise than the single equation estimator. For fixed N as T approaches infinity, the estimator converges to a function of Brownian motions and the Wald statistic for testing a set of linear constraints has a limiting chi-square distribution. The estimator also has a Gaussian sequential limit distribution that is obtained first by letting T go to infinity then letting N go to infinity. In a series of Monte Carlo experiments, we find that the asymptotic distribution theory provides a reasonably close approximation to the exact finite sample distribution. We use panel dynamic OLS to estimate coefficients of the long-run money demand function from a panel of 19 countries with annual observations that span from 1957 to 1996. The estimated income elasticity is 1.08 (asymptotic s.e.=0.26) and the estimated interest rate semi-elasticity is -0.02 (asymptotic s.e.=0.01).

A parametric model for the distribution of the angle of arrival and the associated correlation function and power spectrum at the mobile station

Abstract: One of the main assumptions in Clarke's classic channel model is isotropic scattering, i.e., uniform distribution for the angle of arrival (AOA) of multipath components at the mobile station. However, in many mobile radio channels we encounter nonisotropic scattering, which strongly affects the correlation function and power spectrum of the complex envelope at the mobile receiver. We propose the use of the versatile von Mises (1918) angular distribution, which includes and/or closely approximates important distributions like uniform, impulse, cardioid, Gaussian, and wrapped Gaussian, for modeling the nonuniform AOAs at the mobile. Based on this distribution, the associated correlation function and. power spectrum of the complex envelope at the mobile receiver are derived. The utility of the new results is demonstrated by comparison with the correlation function estimates of measured data.

Three-dimensional modeling of the friction stir-welding process

Abstract: This paper presents an attempt to model the stir-welding process using three-dimensional visco-plastic modeling. The scope of the project is focused on butt joints for aluminum thick plates. Parametric studies have been conducted to determine the effect of tool speeds on plate temperatures and to validate the model predictions with available measurements. In addition, forces acting on the tool have been computed for various welding and rotational speeds. It is found that pin forces increase with increasing welding speeds, but the opposite effect is observed for increasing rotational speeds. Numerical models such as the one presented here will be useful in designing welding tools which will yield desired thermal gradients and avoid tool breakage.

Coordinated Reinforcement Learning

Abstract: We present several new algorithms for multiagent reinforcement learning. A common feature of these algorithms is a parameterized, structured representation of a policy or value function. This structure is leveraged in an approach we call coordinated reinforcement learning, by which agents coordinate both their action selection activities and their parameter updates. Within the limits of our parametric representations, the agents will determine a jointly optimal action without explicitly considering every possible action in their exponentially large joint action space. Our methods differ from many previous reinforcement learning approaches to multiagent coordination in that structured communication and coordination between agents appears at the core of both the learning algorithm and the execution architecture.

Parametric Mixture Models for Multi-Labeled Text

Abstract: We propose probabilistic generative models, called parametric mixture models (PMMs), for multiclass, multi-labeled text categorization problem. Conventionally, the binary classification approach has been employed, in which whether or not text belongs to a category is judged by the binary classifier for every category. In contrast, our approach can simultaneously detect multiple categories of text using PMMs. We derive efficient learning and prediction algorithms for PMMs. We also empirically show that our method could significantly outperform the conventional binary methods when applied to multi-labeled text categorization using real World Wide Web pages.

On-Off Intermittency in a Human Balancing Task

Abstract: Motion analysis in three dimensions demonstrate that the fluctuations in the vertical displacement angle of a stick balanced at the fingertip obey a scaling law characteristic of on-off intermittency and that >98% of the corrective movements occur fast compared to the measured time delay. These experimental observations are reproduced by a model for an inverted pendulum with time-delayed feedback in which parametric noise forces a control parameter across a particular stability boundary. Our observations suggest that parametric noise is an essential, but up until now underemphasized, component of the neural control of balance.

Effect of cubic nonlinearity on auto-parametrically amplified resonant MEMS mass sensor

Abstract: Parametric resonance has been well established in many areas of science, including the stability of ships, the forced motion of a swing and Faraday surface wave patterns on water. We have previously investigated a linear parametrically driven torsional oscillator and along with other groups have mentioned applications including mass sensing, parametric amplification, and others. Here, we thoroughly investigate the design of a highly sensitive mass sensor. The device we use to carry out this study is an in-plane parametrically resonant oscillator. We show that in this configuration, the nonlinearities (electrostatic and mechanical) have a large impact on the dynamic response of the structure. This result is not unique to this oscillator—many MEMS oscillators display nonlinearities of equal importance (including the very common parallel plate actuator). We report the effects of nonlinearity on the behavior of parametric resonance of a micro-machined oscillator. A nonlinear Mathieu equation is used to model this problem. Analytical results show that nonlinearity significantly changes the stability characteristics of parametric resonance. Experimental frequency response around the first parametric resonance is well validated by theoretical analysis. Unlike parametric resonance in the linear case, the jumps (very critical for mass sensor application) from large response to zero happen at additional frequencies other than at the boundary of instability area. The instability area of the first parametric resonance is experimentally mapped. Some important parameters, such as damping co-efficient, cubic stiffness and linear electrostatic stiffness are extracted from the nonlinear response of parametric resonance and agree very well with normal methods.

An MCMC Approach to Classical Estimation

Abstract: This paper studies computationally and theoretically attractive estimators referred here as to the Laplace type estimators (LTE). The LTE include means and quantiles of Quasi-posterior distributions defined as transformations of general (non-likelihood-based) statistical criterion functions, such as those in GMM, nonlinear IV, empirical likelihood, and minimum distance methods. The approach generates an alternative to classical extremum estimation and also falls outside the parametric Bayesian approach. For example, it offers a new attractive estimation method for such important semi-parametric problems as censored and instrumental quantile regression, nonlinear IV, GMM, and value-at-risk, models. The LTE's are computed using Markov Chain Monte Carlo methods, which help circumvent the computational curse of dimensionality. A large sample theory is obtained and illustrated for regular cases.

Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems

Abstract: This paper presents a robust adaptive neural control design for a class of perturbed strict feedback nonlinear system with both completely unknown virtual control coefficients and unknown nonlinearities. The unknown nonlinearities comprise two types of nonlinear functions: one naturally satisfies the "triangularity condition" and can be approximated by linearly parameterized neural networks, while the other is assumed to be partially known and consists of parametric uncertainties and known "bounding functions." With the utilization of iterative Lyapunov design and neural networks, the proposed design procedure expands the class of nonlinear systems for which robust adaptive control approaches have been studied. The design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. Leakage terms are incorporated into the adaptive laws to prevent parameter drifts due to the inherent neural-network approximation errors. It is proved that the proposed robust adaptive scheme can guarantee the uniform ultimate boundedness of the closed-loop system signals.. The control performance can be guaranteed by an appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach.

Intrinsic Dimension Estimation Using Packing Numbers

Abstract: We propose a new algorithm to estimate the intrinsic dimension of data sets. The method is based on geometric properties of the data and requires neither parametric assumptions on the data generating model nor input parameters to set. The method is compared to a similar, widely-used algorithm from the same family of geometric techniques. Experiments show that our method is more robust in terms of the data generating distribution and more reliable in the presence of noise.

The neuro-m method for fitting neural network parametric pedotransfer functions

Abstract: Parametric pedotransfer functions (PTFs), which predict parameters of a model from basic soil properties are useful in deriving continuous functions of soil properties, such as water retention curves. The common method for deriving parametric water retention PTFs involves estimating the parameters of a soil hydraulic model by fitting the model to the data, and then forming empirical relationships between basic soil properties and parameters. The latter step usually utilizes multiple linear regression or artificial neural networks. Neural network analysis is a powerful tool and has been shown to perform better than multiple linear regression. However neural-network PTFs are usually trained with an objective function that fits the estimated parameters of a soil hydraulic model. We called this the neuro-p method. The estimated parameters may carry errors and since the aim is to be able to estimate water retention, it is sensible to train the network to fit the measured water content. We propose a new objective function for neural network training, which predicts the parameters of the soil hydraulic model and optimizes the PTF to match the measured and observed water content, we called this neuro-m method. This method was used to predict the parameters of the van Genuchten model. Using Australian soil hydraulic data as a training set, neuro-m predicted the water retention from bulk density and particle-size distribution with a mean accuracy of 0.04 m 3 m 3 . The relative improvement of neuro-m over neural networks that was optimized to fit the parameters (neuro-p) is 13%. Compared with a published neural network PTF, the new method is 30% more accurate and less biased.

Spatial autocorrelation and statistical tests in ecology

Abstract: The presence of positive spatial autocorrelation in ecological data causes parametric statistical tests to give more apparently significant results than the data justify, which is a serious problem

A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties

Abstract: A new learning control approach is developed in this note to address a class of nonlinear systems with time-varying parametric uncertainties. The concept of composite energy function (CEF), which provides the system information along both time and learning repetition horizons, is introduced in the analysis of learning control. CEF consists of two parts. The first part is a standard Lyapunov function,. which is used to access system behavior along time horizon during each learning cycle. The second part is an L/sup 2/ norm of parametric learning errors which reflects the variation of the system status when the control system is updated on the basis of learning cycles. The proposed learning control algorithm achieves asymptotical convergence along a learning repetition horizon. At the same time, the boundedness and pointwise convergence of the tracking error along time horizon is guaranteed. The proposed learning control strategy is applicable to quite general classes of nonlinear systems without requiring the global Lipschitz continuity condition and zero relative degree condition.

Robust Kalman filters for linear time-varying systems with stochastic parametric uncertainties

Abstract: We present a robust recursive Kalman filtering algorithm that addresses estimation problems that arise in linear time-varying systems with stochastic parametric uncertainties. The filter has a one-step predictor-corrector structure and minimizes an upper bound of the mean square estimation error at each step, with the minimization reduced to a convex optimization problem based on linear matrix inequalities. The algorithm is shown to converge when the system is mean square stable and the state space matrices are time invariant. A numerical example consisting of equalizer design for a communication channel demonstrates that our algorithm offers considerable improvement in performance when compared with conventional Kalman filtering techniques.

Parametric profiling using optical spectroscopic systems

Abstract: A gallery of seed profiles is constructed and the initial parameter values associated with the profiles are selected using manufacturing process knowledge of semiconductor devices. Manufacturing process knowledge may also be used to select the best seed profile and the best set of initial parameter values as the starting point of an optimization process whereby data associated with parameter values of the profile predicted by a model is compared to measured data in order to arrive at values of the parameters. Film layers over or under the periodic structure may also be taken into account. Different radiation parameters such as the reflectivities Rs, Rp and ellipsometric parameters may be used in measuring the diffracting structures and the associated films. The above-described techniques may be supplied to a track/stepper and etcher to control the lithographic and etching processes in order to compensate for any errors in the profile parameters.

Hierarchical Estimation and Segmentation of Dense Motion Fields

Abstract: In this paper we present a comprehensive energy-based framework for the estimation and the segmentation of the apparent motion in image sequences. The robust cost functions and the associated hierarchical minimization techniques that we propose mix efficiently non-parametric (dense) representations, local interacting parametric representations, and global non-interacting parametric representations related to a partition into regions. Experimental comparisons, both on synthetic and real images, demonstrate the merit of the approach on different types of photometric and kinematic contents ranging from moving rigid objects to moving fluids.