Showing papers on "Parametric model published in 2009"

Gaussian Mixture Models.

Abstract: Definition A Gaussian Mixture Model (GMM) is a parametric probability density function represented as a weighted sum of Gaussian component densities. GMMs are commonly used as a parametric model of the probability distribution of continuous measurements or features in a biometric system, such as vocal-tract related spectral features in a speaker recognition system. GMM parameters are estimated from training data using the iterative Expectation-Maximization (EM) algorithm or Maximum A Posteriori (MAP) estimation from a well-trained prior model.

Nonlinear Robust Adaptive Control of Flexible Air-Breathing Hypersonic Vehicles

Abstract: This paper describes the design of a nonlinear robust adaptive controller for a flexible air-breathing hypersonic vehicle model. Because of the complexity of a first-principle model of the vehicle dynamics, a control-oriented model is adopted for design and stability analysis. This simplified model retains the dominant features of the higher-fidelity model, including the nonminimum phase behavior of the flight-path angle dynamics, the flexibility effects, and the strong coupling between the engine and flight dynamics. A combination of nonlinear sequential loop closure and adaptive dynamic inversion is adopted for the design of a dynamic state-feedback controller that provides stable tracking of the velocity and altitude reference trajectories and imposes a desired set point for the angle of attack. A complete characterization of the internal dynamics of the model is derived for a Lyapunov-based stability analysis of the closed-loop system, which includes the structural dynamics. The proposed methodology addresses the issue of stability robustness with respect to both parametric model uncertainty, which naturally arises when adopting reduced-complexity models for control design, and dynamic perturbations due to the flexible dynamics. Simulation results from the full nonlinear model show the effectiveness of the controller.

Non-parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps

Abstract: We consider a stochastic process driven by diffusions and jumps Given a discrete record of observations, we devise a technique for identifying the times when jumps larger than a suitably defined threshold occurred This allows us to determine a consistent non-parametric estimator of the integrated volatility when the infinite activity jump component is Levy Jump size estimation and central limit results are proved in the case of finite activity jumps Some simulations illustrate the applicability of the methodology in finite samples and its superiority on the multipower variations especially when it is not possible to use high frequency data

Break detection in the covariance structure of multivariate time series models

Abstract: In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very flexible as it can be applied, for example, to many of the multivariate GARCH models established in the literature, and also works well in the case of high dimensionality of the underlying data. Since it is nonparametric, the procedure avoids the difficulties associated with parametric model selection, model fitting and parameter estimation. We provide the theoretical foundation for the test and demonstrate its applicability via a simulation study and an analysis of financial data. Extensions to multiple changes and the case of infinite fourth moments are also discussed.

GP-BayesFilters: Bayesian filtering using Gaussian process prediction and observation models

Abstract: Bayesian filtering is a general framework for recursively estimating the state of a dynamical system. Key components of each Bayes filter are probabilistic prediction and observation models. This paper shows how non-parametric Gaussian process (GP) regression can be used for learning such models from training data. We also show how Gaussian process models can be integrated into different versions of Bayes filters, namely particle filters and extended and unscented Kalman filters. The resulting GP-BayesFilters can have several advantages over standard (parametric) filters. Most importantly, GP-BayesFilters do not require an accurate, parametric model of the system. Given enough training data, they enable improved tracking accuracy compared to parametric models, and they degrade gracefully with increased model uncertainty. These advantages stem from the fact that GPs consider both the noise in the system and the uncertainty in the model. If an approximate parametric model is available, it can be incorporated into the GP, resulting in further performance improvements. In experiments, we show different properties of GP-BayesFilters using data collected with an autonomous micro-blimp as well as synthetic data.

Parameter estimation from time-series data with correlated errors: a wavelet-based method and its application to transit light curves

Abstract: We consider the problem of fitting a parametric model to time-series data that are afflicted by correlated noise. The noise is represented by a sum of two stationary Gaussian processes: one that is uncorrelated in time, and another that has a power spectral density varying as 1/f γ. We present an accurate and fast [O(N)] algorithm for parameter estimation based on computing the likelihood in a wavelet basis. The method is illustrated and tested using simulated time-series photometry of exoplanetary transits, with particular attention to estimating the mid-transit time. We compare our method to two other methods that have been used in the literature, the time-averaging method and the residual-permutation method. For noise processes that obey our assumptions, the algorithm presented here gives more accurate results for mid-transit times and truer estimates of their uncertainties.

Model Learning with Local Gaussian Process Regression

Abstract: Precise models of robot inverse dynamics allow the design of significantly more accurate, energy-efficient and compliant robot control. However, in some cases the accuracy of rigid-body models does not suffice for sound control performance due to unmodeled nonlinearities arising from hydraulic cable dynamics, complex friction or actuator dynamics. In such cases, estimating the inverse dynamics model from measured data poses an interesting alternative. Nonparametric regression methods, such as Gaussian process regression (GPR) or locally weighted projection regression (LWPR), are not as restrictive as parametric models and, thus, offer a more flexible framework for approximating unknown nonlinearities. In this paper, we propose a local approximation to the standard GPR, called local GPR (LGP), for real-time model online learning by combining the strengths of both regression methods, i.e., the high accuracy of GPR and the fast speed of LWPR. The approach is shown to have competitive learning performance for...

Modelling pedestrian trajectory patterns with Gaussian processes

Abstract: We propose a non-parametric model for pedestrian motion based on Gaussian Process regression, in which trajectory data are modelled by regressing relative motion against current position. We show how the underlying model can be learned in an unsupervised fashion, demonstrating this on two databases collected from static surveillance cameras. We furthermore exemplify the use of model for prediction, comparing the recently proposed GP-Bayesfilters with a Monte Carlo method. We illustrate the benefit of this approach for long term motion prediction where parametric models such as Kalman Filters would perform poorly.

Spatial Variation of Seismic Ground Motions: Modeling and Engineering Applications

Abstract: Introduction Stochastic estimation of spatial variability Basic definitions Stochastic processes Bi-variate stochastic processes Coherency Multi-variate stochastic processes and stochastic fields Parametric modeling of spatial variability Parametric power spectral densities Early studies on spatial variability Dependence of coherency on physical parameters Parametric coherencymodeling Parametric cross spectrum modeling Physical characterization of spatial variability Frequency-wavenumber (F-K) spectra Amplitude and phase variability Seismic ground-surface strains Semi-empirical estimation of the propagation velocity Estimation of the surface strain field Accuracy of single-station strain estimation Incoherence vs propagation effects in surface strains Displacement gradient estimation from array data Considerations in the estimation of seismic ground strains Random vibrations for multi-support excitations Introduction to random vibrations Discrete-parameter systems Distributed-parameter systems Analysis of rms lifeline response Additional random vibration considerations Simulations of spatially variable ground motions Simulation of random processes Simulation of random fields Simulation ofmulti-variate stochastic vector processes Conditionally simulated ground motions Conditional simulation of random processes Processing of simulated acceleration time series Example applications Engineering Applications Large, mat, rigid foundations Dams Suspension and cable-stayed bridges Highway bridges Some concluding remarks References

Model-free estimation of the psychometric function

Abstract: A subject's response to the strength of a stimulus is described by the psychometric function, from which summary measures, such as a threshold or a slope, may be derived. Traditionally, this function is estimated by fitting a parametric model to the experimental data, usually the proportion of successful trials at each stimulus level. Common models include the Gaussian and Weibull cumulative distribution functions. This approach works well if the model is correct, but it can mislead if not. In practice, the correct model is rarely known. Here, a nonparametric approach based on local linear fitting is advocated. No assumption is made about the true model underlying the data, except that the function is smooth. The critical role of the bandwidth is identified, and its optimum value is estimated by a cross-validation procedure. As a demonstration, seven vision and hearing data sets were fitted by the local linear method and by several parametric models. The local linear method frequently performed better and never worse than the parametric ones. Supplemental materials for this article can be downloaded from app.psychonomic-journals.org/content/supplemental.

Predicting software reliability with neural network ensembles

Abstract: Software reliability is an important factor for quantitatively characterizing software quality and estimating the duration of software testing period. Traditional parametric software reliability growth models (SRGMs) such as nonhomogeneous Poisson process (NHPP) models have been successfully utilized in practical software reliability engineering. However, no single such parametric model can obtain accurate prediction for all cases. In addition to the parametric models, non-parametric models like neural network have shown to be effective alternative techniques for software reliability prediction. In this paper, we propose a non-parametric software reliability prediction system based on neural network ensembles. The effects of system architecture on the performance are investigated. The comparative studies between the proposed system with the single neural network based system and three parametric NHPP models are carried out. The experimental results demonstrate that the system predictability can be significantly improved by combing multiple neural networks.

Nonparametric Transition-Based Tests for Jump Diffusions

Abstract: We develop a specification test for the transition density of a discretely sampled continuous-time jump-diffusion process, based on a comparison of a nonparametric estimate of the transition density or distribution function with their corresponding parametric counterparts assumed by the null hypothesis. As a special case, our method applies to pure diffusions. We provide a direct comparison of the two densities for an arbitrary specification of the null parametric model using three different discrepancy measures between the null and alternative transition density and distribution functions. We establish the asymptotic null distributions of proposed test statistics and compute their power functions. We investigate the finite-sample properties through simulations and compare them with those of other tests. This article has supplementary material online.

Bayesian Emulation and Calibration of a Stochastic Computer Model of Mitochondrial DNA Deletions in Substantia Nigra Neurons

Abstract: This article considers the problem of parameter estimation for a stochastic biological model of mitochondrial DNA population dynamics using experimental data on deletion mutation accumulation. The stochastic model is an attempt to describe the hypothesized link between deletion accumulation and neuronal loss in the substantia nigra region of the human brain. Inference for the parameters of the model is complicated by the fact that the model is both analytically intractable and slow to sample from. We show how the stochastic model can be approximated using a simple parametric statistical model with smoothly varying parameters. These parameters are treated as unknown functions and modeled using Gaussian process priors. Several simplifications of our Bayesian model are implemented to ease the computational burden. Throughout the article, we validate our models using predictive simulations. We demonstrate the validity of our fitted model on an independent dataset of substantia nigra neuron survival.

Phase II Monitoring of Nonlinear Profiles

Abstract: In many practical cases, the quality of a product or process is characterized by multiple measurements constituting a line or curve that is referred to as a profile In this article, we develop two approaches for monitoring process and product nonlinear profiles The first approach consists of control chart methods to monitor nonlinear profiles using parametric estimates of regression model In order to avoid the problems arising from complexity of coefficient estimation of nonlinear profiles, the second approach, which consists of using metrics to measure deviation from a reference curve, is proposed The performance of the methods is evaluated through a numerical example using average run length criterion The effect of sample size on the performance of both approaches is also investigated in this article

A New Training Approach for Parametric Modeling of Microwave Passive Components Using Combined Neural Networks and Transfer Functions

Abstract: This paper presents a novel technique to develop combined neural network and transfer function models for parametric modeling of passive components. In this technique, the neural network is trained to map geometrical variables onto coefficients of transfer functions. A major advance is achieved in resolving the discontinuity problem of numerical solutions of the coefficients with respect to the geometrical variables. Minimum orders of transfer functions for different regions of geometrical parameter space are identified. Our investigations show that varied orders used for different regions result in the discontinuity of coefficients. The gaps between orders are bridged by a new order-changing module, which guarantees the continuity of coefficients and simultaneously maintains the modeling accuracy through a neural network optimization process. This technique is also expanded to include bilinear transfer functions. Once trained, the model provides accurate and fast prediction of the electromagnetic behavior of passive components with geometrical parameters as variables. Compared to conventional training methods, the proposed method allows better accuracy in challenging applications involving high-order transfer functions, wide frequency range, and large geometrical variations. Three examples including parametric modeling of slotted patch antennas, bandstop microstrip filters, and bandpass coupled-line filters are examined to demonstrate the validity of this technique.

Alternatives to the normal model of stock returns: Gaussian mixture, generalised logF and generalised hyperbolic models

Abstract: Simple parametric models of the marginal distribution of stock returns are an essential building block in many areas of applied finance. Even though it is well known that the normal distribution fails to represent most of the “stylised” facts characterising return distributions, it still dominates much of the applied work in finance. Using monthly S&P 500 stock index returns (1871–2005) as well as daily returns (2001–2005), we investigate the viability of three alternative parametric families to represent both the stylised and empirical facts: the generalised hyperbolic distribution, the generalised logF distribution, and finite mixtures of Gaussians. For monthly return data, all three alternatives give reasonable fits for all sub-periods. However, the generalised hyperbolic distribution fails to describe some features of the marginal distributions in some sub-periods. The daily return data are much more symmetric and expose another problem for all three distributions: the parameters describing the behaviour of the tails also influence the scale so that simpler alternatives or restricted parameterisations are called for.

Efficient estimation of auto-regression parameters and innovation distributions for semiparametric integer-valued AR(p) models

Abstract: Summary. Integer-valued auto-regressive (INAR) processes have been introduced to model non-negative integer-valued phenomena that evolve over time. The distribution of an INAR(p) process is essentially described by two parameters: a vector of auto-regression coefficients and a probability distribution on the non-negative integers, called an immigration or innovation distribution. Traditionally, parametric models are considered where the innovation distribution is assumed to belong to a parametric family. The paper instead considers a more realistic semiparametric INAR(p) model where there are essentially no restrictions on the innovation distribution. We provide an (semiparametrically) efficient estimator of both the auto-regression parameters and the innovation distribution.

Frequency-Domain Identification of Linear Time-Periodic Systems using LTI Techniques

Abstract: A variety of systems can be faithfully modeled as linear with coefficients that vary periodically with time or Linear Time-Periodic (LTP). Examples include anisotropic rotor-bearing systems, wind turbines and nonlinear systems linearized about a periodic trajectory; all of these have been treated analytically in the literature. However, few methods exist for experimentally characterizing LTP systems. This paper presents a set of tools that can be used to experimentally characterize an LTP system, using a frequency domain approach and utilizing existing algorithms to perform parameter identification. One of the approaches is based on lifting the response to obtain an equivalent Linear Time-Invariant (LTI) form and the other based on Fourier series expansion. The development focuses on the pre-processing steps needed to apply LTI identification to the measurements, the post-processing needed to reconstruct the LTP model from the identification results and the interpretation of the measurements. This approach elucidates the similarities between LTP and LTI identification, allowing the experimentalist to transfer insight from time-invariant systems to the LTP identification problem. The approach determines the model order of the system, and post processing reveals the shapes of the time-periodic functions comprising the LTP model. Further post-processing is also presented that allows one to generate the full state transition matrix and the time-varying state matrix of the system from the parametric model if the measurement set is adequate. The experimental techniques are demonstrated on simulated measurements from a Jeffcott rotor mounted on an anisotropic, flexible shaft, supported by anisotropic bearings.

Ensemble of neural networks with associative memory (ENNA) for estimating software development costs

Abstract: Companies usually have limited amount of data for effort estimation. Machine learning methods have been preferred over parametric models due to their flexibility to calibrate the model for the available data. On the other hand, as machine learning methods become more complex, they need more data to learn from. Therefore the challenge is to increase the performance of the algorithm when there is limited data. In this paper, we use a relatively complex machine learning algorithm, neural networks, and show that stable and accurate estimations are achievable with an ensemble using associative memory. Our experimental results show that our proposed algorithm (ENNA) produces significantly better results than neural network (NN) in terms of accuracy and robustness. We also analyze the effect of feature subset selection on ENNA's estimation performance in a wrapper framework. We show that the proposed ENNA algorithm that use the features selected by the wrapper does not perform worse than those that use all available features. Therefore, measuring only company specific key factors is sufficient to obtain accurate and robust estimates about software cost estimation using ENNA.

Parametric Model-Checking of Stopwatch Petri Nets

Abstract: At the border between control and verification, parametric verification can be used to synthesize constraints on the parameters to ensure that a system verifies given specifications. In this paper we propose a new framework for the parametric verification of time Petri nets with stopwatches. We first introduce a parametric exten- sion of time Petri nets with inhibitor arcs (ITPNs) with temporal parameters and we define a symbolic representation of the parametric state-space based on the classical state-class graph method. Then, we propose semi-algorithms for the parametric model- checking of a subset of parametric TCTL formulae on ITPNs. These results have been implemented in the tool Romeo and we illustrate them in a case-study based on a scheduling problem.

Likelihood ridges and multimodality in population growth rate models

Abstract: A central problem in population ecology is to use time series data to estimate the form of density dependence in the per capita growth rate (pgr). This is often accomplished with phenomenological models such as the theta-Ricker or generalized Beverton-Holt. Using the theta-Ricker model as a simple but flexible description of density dependence, we apply theory and simulations to show how multimodality and ridges in the likelihood surface can emerge even in the absence of model misspecification or observation error. The message for model fitting of real data is to consider the likelihood surface in detail, check whether the best- fit model is located on a likelihood ridge and, if so, evaluate predictive differences of biologically plausible models along the ridge. We present a detailed analysis of a focal data set showing how multimodality and ridges emerge in practice for fits of several parametric models, including a state-space model with explicit accommodation of observation error. Best-fit models for these data are biologically dubious beyond the range of the data, and likelihood ratio confidence regions include a wide range of more biologically plausible models. We demonstrate the broad relevance of these findings by presenting analyses of 25 additional data sets spanning a wide range of taxa. The results here are relevant to information-theoretic and Bayesian methods, which also rely on likelihoods. Beyond presentation of best-fit models and confidence regions around individual parameters, effort toward understanding features of the likelihood surface will help ensure the most robust translation from statistical analysis to biological interpretation.

Predictive feedback in human simulated pendulum balancing

Abstract: In studies of human balance, it is common to fit stimulus-response data by tuning the time-delay and gain parameters of a simple delayed feedback model. Many interpret this fitted model, a simple delayed feedback model, as evidence that predictive processes are not required to explain existing data on standing balance. However, two questions lead us to doubt this approach. First, does fitting a delayed feedback model lead to reliable estimates of the time-delay? Second, can a non-predictive controller provide an explanation compatible with the independently estimated time delay? For methodological and experimental clarity, we study human balancing of a simulated inverted pendulum via joystick and screen. A two-step approach to data analysis is used: firstly a non-parametric model—the closed-loop impulse response—is estimated from the experimental data; second, a parametric model is fitted to the non-parametric impulse-response by adjusting time-delay and controller parameters. To support the second step, a new explicit formula relating controller parameters to closed-loop impulse response is derived. Two classes of controller are investigated within a common state-space context: non-predictive and predictive. It is found that the time-delay estimate arising from the second step is strongly dependent on which controller class is assumed; in particular, the non-predictive control assumption leads to time-delay estimates that are smaller than those arising from the predictive assumption. Moreover, the time-delays estimated using the non-predictive control assumption are not consistent with a lower-bound on the time-delay of the non-parametric model whereas the corresponding predictive result is consistent. Thus while the goodness of fit only marginally favoured predictive over non-predictive control, if we add the additional constraint that the model must reproduce the non-parametric time delay, then the non-predictive control model fails. We conclude (1) the time-delay should be estimated independently of fitting a low order parametric model, (2) that balance of the simulated inverted pendulum could not be explained by the non-predictive control model and (3) that predictive control provided a better explanation than non-predictive control.

Identifying Optimal Prognostic Parameters from Data: A Genetic Algorithms Approach

Abstract: The ultimate goal of most prognostic systems is accurate prediction of the remaining useful life of individual systems or components based on their use and performance. This class of prognostic algorithms is termed Effects-Based or Type III Prognostics. Traditional individual- based prognostics involve identifying an appropriate degradation measure to characterize the system's progression to failure. These degradation measures may be sensed measurements, such as temperature or vibration level, or inferred measurements, such as model residuals or physics-based model predictions using other sensed measurements. Often, it is beneficial to combine several measures of degradation to develop a single parameter, called a prognostic parameter. A parametric model is fit to this parameter and then extrapolated to some predefined critical failure threshold to estimate the system's remaining useful life. Commonly, identification of a prognostic parameter is accomplished through visual inspection of the available information and engineering judgment. However, a set of metrics to characterize the suitability of prognostic parameters has been proposed. These metrics include monotonicity, prognosability, and trendability. Monotonicity characterizes a parameter's general increasing or decreasing nature. Prognosability measures the spread of the parameter's failure value for a population of systems. Finally, trendability indicates whether the parameters for a population of systems have the same underlying trend,and hence can be described by the same parametric function. This research formalizes these metrics in a way that is robust to the noise found in real world systems. The metrics are used in conjunction with a Genetic Algorithms optimization routine to identify an optimal prognostic parameter for the Prognostics and Health Management (PHM) Challenge data from the 2008 PHM conference.

Sinusoidal order estimation using angles between subspaces

Abstract: We consider the problem of determining the order of a parametric model from a noisy signal based on the geometry of the space. More specifically, we do this using the nontrivial angles between the candidate signal subspace model and the noise subspace. The proposed principle is closely related to the subspace orthogonality property known from the MUSIC algorithm, and we study its properties and compare it to other related measures. For the problem of estimating the number of complex sinusoids in white noise, a computationally efficient implementation exists, and this problem is therefore considered in detail. In computer simulations, we compare the proposed method to various well-known methods for order estimation. These show that the proposed method outperforms the other previously published subspace methods and that it is more robust to the noise being colored than the previously published methods.