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Dissertations / Theses on the topic 'Linear model'
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1
Brien, Christopher J. "Factorial linear model analysis." Title page, table of contents and summary only, 1992. http://thesis.library.adelaide.edu.au/public/adt-SUA20010530.175833.
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"February 1992" Bibliography: leaf 323-344. Electronic publication; Full text available in PDF format; abstract in HTML format. Develops a general strategy for factorial linear model analysis for experimental and observational studies, an iterative, four-stage, model comparison procedure. The approach is applicable to studies characterized as being structure-balanced, multitiered and based on Tjur structures unless the structure involves variation factors when it must be a regular Tjur structure. It covers a wide range of experiments including multiple-error, change-over, two-phase, superimposed and unbalanced experiments. Electronic reproduction.[Australia] :Australian Digital Theses Program,2001.
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Greenaway, Mark Jonathan. "Numerically Stable Approximate Bayesian Methods for Generalized Linear Mixed Models and Linear Model Selection." Thesis, The University of Sydney, 2019. http://hdl.handle.net/2123/20233.
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Approximate Bayesian inference methods offer methodology for fitting Bayesian models as fast alternatives to Markov Chain Monte Carlo methods that sometimes have only a slight loss of accuracy. In this thesis, we consider variable selection for linear models, and zero inflated mixed models. Variable selection for linear regression models are ubiquitous in applied statistics. We use the popular g-prior (Zellner, 1986) for model selection of linear models with normal priors where g is a prior hyperparameter. We derive exact expressions for the model selection Bayes Factors in terms of special functions depending on the sample size, number of covariates and R-squared of the model. We show that these expressions are accurate, fast to evaluate, and numerically stable. An R package blma for doing Bayesian linear model averaging using these exact expressions has been released on GitHub. We extend the Particle EM method of (Rockova, 2017) using Particle Variational Approximation and the exact posterior marginal likelihood expressions to derive a computationally efficient algorithm for model selection on data sets with many covariates. Our algorithm performs well relative to existing algorithms, completing in 8 seconds on a model selection problem with a sample size of 600 and 7200 covariates. We consider zero-inflated models that have many applications in areas such as manufacturing and public health, but pose numerical issues when fitting them to data. We apply a variational approximation to zero-inflated Poisson mixed models with Gaussian distributed random effects using a combination of VB and the Gaussian Variational Approximation (GVA). We also incorporate a novel parameterisation of the covariance of the GVA using the Cholesky factor of the precision matrix, similar to Tan and Nott (2018) to resolve associated numerical difficulties.
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Townsend, Shane Martin Joseph. "Non-linear model predictive control." Thesis, Queen's University Belfast, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301061.
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Waterman, Megan Janet Tuttle. "Linear Mixed Model Robust Regression." Diss., Virginia Tech, 2002. http://hdl.handle.net/10919/27708.
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Mixed models are powerful tools for the analysis of clustered data and many extensions of the classical linear mixed model with normally distributed response have been established. As with all parametric models, correctness of the assumed model is critical for the validity of the ensuing inference. Model robust regression techniques predict mean response as a convex combination of a parametric and a nonparametric model fit to the data. It is a semiparametric method by which incompletely or incorrectly specified parametric models can be improved through adding an appropriate amount of a nonparametric fit. We apply this idea of model robustness in the framework of the linear mixed model. The mixed model robust regression (MMRR) predictions we propose are convex combinations of predictions obtained from a standard normal-theory linear mixed model, which serves as the parametric model component, and a locally weighted maximum likelihood fit which serves as the nonparametric component. An application of this technique with real data is provided.Ph. D.
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Zurcher, James. "Model-based knowledge acquisition using adaptive piecewise linear models." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0018/NQ46956.pdf.
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Asterios, Geroukis. "Prediction of Linear Models: Application of Jackknife Model Averaging." Thesis, Uppsala universitet, Statistiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-297671.
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When using linear models, a common practice is to find the single best model fit used in predictions. This on the other hand can cause potential problems such as misspecification and sometimes even wrong models due to spurious regression. Another method of predicting models introduced in this study as Jackknife Model Averaging developed by Hansen & Racine (2012). This assigns weights to all possible models one could use and allows the data to have heteroscedastic errors. This model averaging estimator is compared to the Mallows’s Model Averaging (Hansen, 2007) and model selection by Bayesian Information Criterion and Mallows’s Cp. The results show that the Jackknife Model Averaging technique gives less prediction errors compared to the other methods of model prediction. This study concludes that the Jackknife Model Averaging technique might be a useful choice when predicting data.
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Overstall, Antony Marshall. "Default Bayesian model determination for generalised linear mixed models." Thesis, University of Southampton, 2010. https://eprints.soton.ac.uk/170229/.
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In this thesis, an automatic, default, fully Bayesian model determination strategy for GLMMs is considered. This strategy must address the two key issues of default prior specification and computation. Default prior distributions for the model parameters, that are based on a unit information concept, are proposed. A two-phase computational strategy, that uses a reversible jump algorithm and implementation of bridge sampling, is also proposed. This strategy is applied to four examples throughout this thesis.
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Sima, Adam. "Accounting for Model Uncertainty in Linear Mixed-Effects Models." VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/2950.
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Standard statistical decision-making tools, such as inference, confidence intervals and forecasting, are contingent on the assumption that the statistical model used in the analysis is the true model. In linear mixed-effect models, ignoring model uncertainty results in an underestimation of the residual variance, contributing to hypothesis tests that demonstrate larger than nominal Type-I errors and confidence intervals with smaller than nominal coverage probabilities. A novel utilization of the generalized degrees of freedom developed by Zhang et al. (2012) is used to adjust the estimate of the residual variance for model uncertainty. Additionally, the general global linear approximation is extended to linear mixed-effect models to adjust the standard errors of the parameter estimates for model uncertainty. Both of these methods use a perturbation method for estimation, where random noise is added to the response variable and, conditional on the observed responses, the corresponding estimate is calculated. A simulation study demonstrates that when the proposed methodologies are utilized, both the variance and standard errors are inflated for model uncertainty. However, when a data-driven strategy is employed, the proposed methodologies show limited usefulness. These methods are evaluated with a trial assessing the performance of cervical traction in the treatment of cervical radiculopathy.
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Vazirinejad, Shamsedin. "Model identification and parameter estimation of stochastic linear models." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/185037.
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It is well known that when the input variables of the linear regression model are subject to noise contamination, the model parameters can not be estimated uniquely. This, in the statistical literature, is referred to as the identifiability problem of the errors-in-variables models. Further, in linear regression there is an explicit assumption of the existence of a single linear relationship. The statistical properties of the errors-in-variables models under the assumption that the noise variances are either known or that they can be estimated are well documented. In many situations, however, such information is neither available nor obtainable. Although under such circumstances one can not obtain a unique vector of parameters, the space, Ω, of the feasible solutions can be computed. Additionally, assumption of existence of a single linear relationship may be presumptuous as well. A multi-equation model similar to the simultaneous-equations models of econometrics may be more appropriate. The goals of this dissertation are the following: (1) To present analytical techniques or algorithms to reduce the solution space, Ω, when any type of prior information, exact or relative, is available; (2) The data covariance matrix, Σ, can be examined to determine whether or not Ω is bounded. If Ω is not bounded a multi-equation model is more appropriate. The methodology for identifying the subsets of variables within which linear relations can feasibly exist is presented; (3) Ridge regression technique is commonly employed in order to reduce the ills caused by collinearity. This is achieved by perturbing the diagonal elements of Σ. In certain situations, applying ridge regression causes some of the coefficients to change signs. An analytical technique is presented to measure the amount of perturbation required to render such variables ineffective. This information can assist the analyst in variable selection as well as deciding on the appropriate model; (4) For the situations when Ω is bounded, a new weighted regression technique based on the computed upper bounds on the noise variances is presented. This technique will result in identification of a unique estimate of the model parameters.
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Sammut, Fiona. "Using generalized linear models to model compositional response data." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/89876/.
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This work proposes a multivariate logit model which models the influence of explanatory variables on continuous compositional response variables. This multivariate logit model generalizes an elegant method that was suggested previously by Wedderburn (1974) for the analysis of leaf blotch data in the special case of J = 2, leading to our naming this new approach as the generalized Wedderburn method. In contrast to the logratio modelling approach devised by Aitchison (1982, J. Roy Stat. Soc. B.), the multivariate logit model used under the generalized Wedderburn approach models the expectation of a compositional response variable directly and is also able to handle zeros in the data. The estimation of the parameters in the new model is carried out using the technique of generalized estimating equations (GEE). This technique relies on the specification of a working variance-covariance structure. A working variance-covariance structure which caters for the specific variability arising in compositional data is derived. The GEE estimator that is used to estimate the parameters of the multivariate logit model is shown to be invariant to the values of the correlation and dispersion parameters in the working variance-covariance structure. Due to this invariance property and the fact that the estimating equations used under the generalized Wedderburn method are linear and unbiased, the GEE estimator achieves full efficiency across a wide class of potential dispersion and correlation matrices for the compositional response variables. As for any other GEE estimator, the estimator used in the generalized Wedderburn method is also asymptotically unbiased and consistent, provided that the marginal mean model specification is correct. The theoretical results derived in this thesis are substantiated by simulation experiments, and properties of the new model are also studied empirically on some classic datasets from the literature.
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Veerapen, Parmaseeven Pillay. "Recurrence relationships and model monitoring for Dynamic Linear Models." Thesis, University of Warwick, 1991. http://wrap.warwick.ac.uk/109386/.
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This thesis considers the incorporation and deletion of information in Dynamic Linear Models together with the detection of model changes and unusual values. General results are derived for the Normal Dynamic Linear Model which naturally also relate to second order modelling such as occurs with the Kalman Filter, linear least squares and linear Bayes estimation. The incorporation of new information, the assessment of its influence and the deletion of old or suspect information are important features of all sequential models. Many dynamic sequential models exhibit conditioned, independence properties. Important results concerning conditional independence in normal models are established which provide the framework and the tools necessary to develop neat procedures and to obtain appropriate recurrence relationships for data incorporation and deletion. These are demonstrated in the context of dynamic linear models, with particularly simple procedures for discount regression models. Appropriate model and forecast monitoring mechanisms are required to detect model changes and unusual values. Cumulative Sum (Cusum) techniques widely used in quality control and in model and forecast monitoring have been the source of inspiration in this context. Bearing in mind that a single sided Cusum may be regarded essentially as a sequence of sequential tests, such a Cusum is, in many cases, equivalent to a Sequence of Sequential Probability Ratio Tests in many cases, as for example in the case of the Exponential Family. A relationship between Cusums and Bayesian decision is established for a useful class of linear loss functions. It is found to apply to the Normal and other important practical cases. For V- mask Cusum graphs, a particularly interesting result which emerges is the interpretation of the distance of the V vertex from the latest plotted point as the prior precision in terms of a number of equivalent observations.
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Gumedze, Freedom Nkhululeko. "A variance shilf model for outlier detection and estimation in linear and linear mixed models." Doctoral thesis, University of Cape Town, 2008. http://hdl.handle.net/11427/4381.
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Includes abstract.Includes bibliographical references.
Outliers are data observations that fall outside the usual conditional ranges of the response data.They are common in experimental research data, for example, due to transcription errors or faulty experimental equipment. Often outliers are quickly identified and addressed, that is, corrected, removed from the data, or retained for subsequent analysis. However, in many cases they are completely anomalous and it is unclear how to treat them. Case deletion techniques are established methods in detecting outliers in linear fixed effects analysis. The extension of these methods to detecting outliers in linear mixed models has not been entirely successful, in the literature. This thesis focuses on a variance shift outlier model as an approach to detecting and assessing outliers in both linear fixed effects and linear mixed effects analysis. A variance shift outlier model assumes a variance shift parameter, wi, for the ith observation, where wi is unknown and estimated from the data. Estimated values of wi indicate observations with possibly inflated variances relative to the remainder of the observations in the data set and hence outliers. When outliers lurk within anomalous elements in the data set, a variance shift outlier model offers an opportunity to include anomalies in the analysis, but down-weighted using the variance shift estimate wi. This down-weighting might be considered preferable to omitting data points (as in case-deletion methods). For very large values of wi a variance shift outlier model is approximately equivalent to the case deletion approach.
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Gumedze, Freedom Nkhululeko. "A variance shift model for outlier detection and estimation in linear and linear mixed models." Doctoral thesis, University of Cape Town, 2009. http://hdl.handle.net/11427/4380.
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Outliers are data observations that fall outside the usual conditional ranges of the response data.They are common in experimental research data, for example, due to transcription errors or faulty experimental equipment. Often outliers are quickly identified and addressed, that is, corrected, removed from the data, or retained for subsequent analysis. However, in many cases they are completely anomalous and it is unclear how to treat them. Case deletion techniques are established methods in detecting outliers in linear fixed effects analysis. The extension of these methods to detecting outliers in linear mixed models has not been entirely successful, in the literature. This thesis focuses on a variance shift outlier model as an approach to detecting and assessing outliers in both linear fixed effects and linear mixed effects analysis. A variance shift outlier model assumes a variance shift parameter, !i, for the ith observation, where !i is unknown and estimated from the data. Estimated values of !i indicate observations with possibly inflated variances relative to the remainder of the observations in the data set and hence outliers. When outliers lurk within anomalous elements in the data set, a variance shift outlier model offers an opportunity to include anomalies in the analysis, but down-weighted using the variance shift estimate Ë!i. This down-weighting might be considered preferable to omitting data points (as in case-deletion methods). For very large values of !i a variance shift outlier model is approximately equivalent to the case deletion approach. We commence with a detailed review of parameter estimation and inferential procedures for the linear mixed model. The review is necessary for the development of the variance shift outlier model as a method for detecting outliers in linear fixed and linear mixed models. This review is followed by a discussion of the status of current research into linear mixed model diagnostics. Different types of residuals in the linear mixed model are defined. A decomposition of the leverage matrix for the linear mixed model leads to interpretable leverage measures. ii A detailed review of a variance shift outlier model in linear fixed effects analysis is given. The purpose of this review is firstly, to gain insight into the general case (the linear mixed model) and secondly, to develop the model further in linear fixed effects analysis. A variance shift outlier model can be formulated as a linear mixed model so that the calculations required to estimate the parameters of the model are those associated with fitting a linear mixed model, and hence the model can be fitted using standard software packages. Likelihood ratio and score test statistics are developed as objective measures for the variance shift estimates. The proposed test statistics initially assume balanced longitudinal data with a Gaussian distributed response variable. The dependence of the proposed test statistics on the second derivatives of the log-likelihood function is also examined. For the single-case outlier in linear fixed effects analysis, analytical expressions for the proposed test statistics are obtained. A resampling algorithm is proposed for assessing the significance of the proposed test statistics and for handling the problem of multiple testing. A variance shift outlier model is then adapted to detect a group of outliers in a fixed effects model. Properties and performance of the likelihood ratio and score test statistics are also investigated. A variance shift outlier model for detecting single-case outliers is also extended to linear mixed effects analysis under Gaussian assumptions for the random effects and the random errors. The variance parameters are estimated using the residual maximum likelihood method. Likelihood ratio and score tests are also constructed for this extended model. Two distinct computing algorithms which constrain the variance parameter estimates to be positive, are given. Properties of the resulting variance parameter estimates from each computing algorithm are also investigated. A variance shift outlier model for detecting single-case outliers in linear mixed effects analysis is extended to detect groups of outliers or subjects having outlying profiles with random intercepts and random slopes that are inconsistent with the corresponding model elements for the remaining subjects in the data set. The issue of influence on the fixed effects under a variance shift outlier model is also discussed.
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Metz, Werner. "Linear barotropic simulation of atmospheric low-frequency variability." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-212307.
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A steady-state barotropic model, linearized about a GCM-derived 500 hPa basic state, is driven by a sample of \"observed\" forcing fields. lt tums out that the leading mode (LEOF) obtained from the sample of linear solutions matches weil with the leading EOF of low-frequency atmospheric variability actually occurring in the GCM. The response ofthe linear model is analysed in tenns of the singular modes of the model\'s linear operator. lt is found that about 50 percent ofthe spatial variance of the LEOF can be explained in tenns of the leading two singular modes. This finding is reflected also in the linear barotropic energy balance of the LEOF which shows that the mode is maintained through nearly equal contributions from i) the kinetic energy conversion of basic state kinetic energy (which is primarily due to the action of the singular modes) and ii) the forcing. The linear simulation of the GCM EOF fails if the linear model is linearized about a 300 hPa basic. This is explained by the fact that in this case the structure of the leading singular modes, which have a strong impact on the linear response, is much more dissimilar to the structure of the GCM EOF than in the 500 hPa caseEin stationäres barotropes Modell, das bezüglich eines (aus einem GCM Experiment abgeleiteten) 500 hPa Grundzustandes linearisiert ist, wird für einen Satz von "beobachteten" Antriebsfeldern gelöst. Dabei zeigt sich, daß die führende Mode der langperiodischen atmosphärischen Variabilität (EOF) im GCM Experiment durch das lineare Modell sehr gut simuliert wird. Weiterhin stellt sich heraus, daß hierfür die Antriebsfelder und die singulären Moden des linearen Modelloperators die gleiche Bedeutung besitzen. Auf die Wichtigkeit der Anwendung des Modells bezüglich des äquivalentbarotropen Niveaus wird hingewiesen
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Amhemad, Abdella Zidan. "Reprocessing and model analysis for linear and integer programming models." Thesis, Brunel University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.336657.
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Carlos, Monteiro Ponce de Leon Antonio. "Optimum experimental design for model discrimination and generalized linear models." Thesis, London School of Economics and Political Science (University of London), 1993. http://etheses.lse.ac.uk/2434/.
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The main subject of this thesis concerns the optimum design of experiments for discriminating between two rival mathematical models. In addition, optimality of designs for parameter estimation is investigated although restricted to binary response models. Optimal design theory and generalized linear models form the background for this work. The former provides the tools for construction of the optimum designs whereas the latter provides the framework in which the methods are developed. For model discrimination the procedures which are proposed may not only be applied to compare two regression models but also to compare two generalized linear models as long as they belong to the same subclass. The principle of the so called T-optimality criterion, originally introduced for discriminating between two regression models, is extended to other classes such as generalized linear models. Within each context a theorem based on the General Equivalence Theorem from the optimal design theory is shown to hold thus allowing both constructing and checking optimum designs. Optimum experimental designs to estimate the parameters of a binary response model is the other subject of this thesis. Initially, well known link functions such as logit, probit and complementary log-log are considered. Later, this range is widened by introducing a family of link functions which includes the logit and the complementary log-log links as particular members. One common feature of these two problems is that classical optimal designs depend on the unknown values of the model parameters. Therefore, only locally optimal designs can be obtained unless observations may be taken sequentially, in which case several methods to search for the optimum are available in the literature. As an alternative to locally and sequentially optimal experiments, Bayesian designs are introduced for both model discrimination and parameter estimation.
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Fong, W. N. W. "Model-based methods for linear and non-linear audio signal enhancement." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.599095.
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Owing to the random nature of audio signals, most of the enhancement methodologies reviewed in this work are based explicitly on a Bayesian model-based approach. Of these, the Kalman filter is the most commonly adopted enhancement strategy for a linear and Gaussian restoration problem. To copy with the general non-linear and non-Gaussian case, different filters such as the extended Kalman filter and the Gaussian sum filter have been proposed in the past few decades. As computing power increases, more computationally expensive simulation based approaches such as Monte Carlo methods have been suggested. The main focus of this work is on sequential estimation of the underlying clean signal and system parameters given some noisy observations under the Monte Carlo framework. This class of method is known as sequential Monte Carlo methods, also commonly referred to as the particle filter. In this work, different improvement strategies have been developed and described to improve on the generic particle filtering/smoothing algorithm. A block-based particle smoother is proposed to reduce the memory capacity required for the processing of lengthy datasets, such as audio signals. A Rao-Blackwellised particle smoother is developed to improve on the simulation results by reducing the dimension of the sampling space and thus the estimation variance. To cope with the non-linear restoration problem, a non-linear Rao-Blackwellised particle smoother is developed, which marginalises the parameter state, instead of the signal state as suggested earlier. Finally, we propose an efficient implementation of the suggested slow time-varying model under the sequential Monte Carlo framework for on-line joint signal and parameter estimation.
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Hagerud, Gustaf E. "A new non-linear GARCH model." Doctoral thesis, Stockholm : Economic Research Institute, Stockholm School of Economics [Ekonomiska forskningsinstitutet vid Handelshögsk.] (EFI), 1997. http://www.hhs.se/efi/summary/444.htm.
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Vasconcelos, Julio Cezar Souza. "Modelo linear parcial generalizado simétrico." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-26072017-105153/.
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Neste trabalho foi proposto o modelo linear parcial generalizado simétrico, com base nos modelos lineares parciais generalizados e nos modelos lineares simétricos, em que a variável resposta segue uma distribuição que pertence à família de distribuições simétricas, considerando um preditor linear que possui uma parte paramétrica e uma não paramétrica. Algumas distribuições que pertencem a essa classe são as distribuições: Normal, t-Student, Exponencial potência, Slash e Hiperbólica, dentre outras. Uma breve revisão dos conceitos utilizados ao longo do trabalho foram apresentados, a saber: análise residual, influência local, parâmetro de suavização, spline, spline cúbico, spline cúbico natural e algoritmo backfitting, dentre outros. Além disso, é apresentada uma breve teoria dos modelos GAMLSS (modelos aditivos generalizados para posição, escala e forma). Os modelos foram ajustados utilizando o pacote gamlss disponível no software livre R. A seleção de modelos foi baseada no critério de Akaike (AIC). Finalmente, uma aplicação é apresentada com base em um conjunto de dados reais da área financeira do Chile.In this work we propose the symmetric generalized partial linear model, based on the generalized partial linear models and symmetric linear models, that is, the response variable follows a distribution that belongs to the symmetric distribution family, considering a linear predictor that has a parametric and a non-parametric component. Some distributions that belong to this class are distributions: Normal, t-Student, Power Exponential, Slash and Hyperbolic among others. A brief review of the concepts used throughout the work was presented, namely: residual analysis, local influence, smoothing parameter, spline, cubic spline, natural cubic spline and backfitting algorithm, among others. In addition, a brief theory of GAMLSS models is presented (generalized additive models for position, scale and shape). The models were adjusted using the package gamlss available in the free R software. The model selection was based on the Akaike criterion (AIC). Finally, an application is presented based on a set of real data from Chile\'s financial area.
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Chen, Jinsong. "Semiparametric Methods for the Generalized Linear Model." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/28012.
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The generalized linear model (GLM) is a popular model in many research areas. In the GLM, each outcome of the dependent variable is assumed to be generated from a particular distribution function in the exponential family. The mean of the distribution depends on the independent variables. The link function provides the relationship between the linear predictor and the mean of the distribution function. In this dissertation, two semiparametric extensions of the GLM will be developed. In the first part of this dissertation, we have proposed a new model, called a semiparametric generalized linear model with a log-concave random component (SGLM-L). In this model, the estimate of the distribution of the random component has a nonparametric form while the estimate of the systematic part has a parametric form. In the second part of this dissertation, we have proposed a model, called a generalized semiparametric single-index mixed model (GSSIMM). A nonparametric component with a single index is incorporated into the mean function in the generalized linear mixed model (GLMM) assuming that the random component is following a parametric distribution.
In the first part of this dissertation, since most of the literature on the GLM deals with the parametric random component, we relax the parametric distribution assumption for the random component of the GLM and impose a log-concave constraint on the distribution. An iterative numerical algorithm for computing the estimators in the SGLM-L is developed. We construct a log-likelihood ratio test for inference. In the second part of this dissertation, we use a single index model to generalize the GLMM to have a linear combination of covariates enter the model via a nonparametric mean function, because the linear model in the GLMM is not complex enough to capture the underlying relationship between the response and its associated covariates. The marginal likelihood is approximated using the Laplace method. A penalized quasi-likelihood approach is proposed to estimate the nonparametric function and parameters including single-index coe±cients in the GSSIMM. We estimate variance components using marginal quasi-likelihood. Asymptotic properties of the estimators are developed using a similar idea by Yu (2008). A simulation example is carried out to compare the performance of the GSSIMM with that of the GLMM. We demonstrate the advantage of my approach using a study of the association between daily air pollutants and daily mortality adjusted for temperature and wind speed in various counties of North Carolina.Ph. D.
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Bai, Xue. "Robust linear regression." Kansas State University, 2012. http://hdl.handle.net/2097/14977.
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Master of ScienceDepartment of Statistics
Weixin Yao
In practice, when applying a statistical method it often occurs that some observations deviate from the usual model assumptions. Least-squares (LS) estimators are very sensitive to outliers. Even one single atypical value may have a large effect on the regression parameter estimates. The goal of robust regression is to develop methods that are resistant to the possibility that one or several unknown outliers may occur anywhere in the data. In this paper, we review various robust regression methods including: M-estimate, LMS estimate, LTS estimate, S-estimate, [tau]-estimate, MM-estimate, GM-estimate, and REWLS estimate. Finally, we compare these robust estimates based on their robustness and efficiency through a simulation study. A real data set application is also provided to compare the robust estimates with traditional least squares estimator.
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Zulj, Valentin. "On The Jackknife Averaging of Generalized Linear Models." Thesis, Uppsala universitet, Statistiska institutionen, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-412831.
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Frequentist model averaging has started to grow in popularity, and it is considered a good alternative to model selection. It has recently been applied favourably to gen- eralized linear models, where it has mainly been purposed to aid the prediction of probabilities. The performance of averaging estimators has largely been compared to that of models selected using AIC or BIC, without much discussion of model screening. In this paper, we study the performance of model averaging in classification problems, and evaluate performances with reference to a single prediction model tuned using cross-validation. We discuss the concept of model screening and suggest two methods of constructing a candidate model set; averaging over the models that make up the LASSO regularization path, and the so called LASSO-GLM hybrid. By means of a Monte Carlo simulation study, we conclude that model averaging does not necessarily offer any improvement in classification rates. In terms of risk, however, we see that both methods of model screening are efficient, and their errors are more stable than those achieved by the cross-validated model of comparison.
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Frühwirth-Schnatter, Sylvia. "Data Augmentation and Dynamic Linear Models." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1992. http://epub.wu.ac.at/392/1/document.pdf.
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We define a subclass of dynamic linear models with unknown hyperparameters called d-inverse-gamma models. We then approximate the marginal p.d.f.s of the hyperparameter and the state vector by the data augmentation algorithm of Tanner/Wong. We prove that the regularity conditions for convergence hold. A sampling based scheme for practical implementation is discussed. Finally, we illustrate how to obtain an iterative importance sampling estimate of the model likelihood. (author's abstract)Series: Forschungsberichte / Institut für Statistik
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Balabanov, Oleg. "Randomized linear algebra for model order reduction." Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/668906.
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Solutions to high-dimensional parameter-dependent problems are in great demand in the contemporary applied science and engineering. The standard approximation methods for parametric equations can require computational resources that are exponential in the dimension of the parameter space, which is typically refereed to as the curse of dimensionality. To break the curse of dimensionality one has to appeal to nonlinear methods that exploit the structure of the solution map, such as projection-based model order reduction methods.
This thesis proposes novel methods based on randomized linear algebra to enhance the efficiency and stability of projection-based model order reduction methods for solving parameter-dependent equations. Our methodology relies on random projections (or random sketching). Instead of operating with high-dimensional vectors we first efficiently project them into a low-dimensional space. The reduced model is then efficiently and numerically stably constructed from the projections of the reduced approximation space and the spaces of associated residuals.
Our approach allows drastic computational savings in basically any modern computational architecture. For instance, it can reduce the number of flops and memory consumption and improve the efficiency of the data flow (characterized by scalability or communication costs). It can be employed for improving the efficiency and numerical stability of classical Galerkin and minimal residual methods. It can also be used for the efficient estimation of the error, and post-processing of the solution of the reduced order model. Furthermore, random sketching makes computationally feasible a dictionary-based approximation method, where for each parameter value the solution is approximated in a subspace with a basis selected from a dictionary of vectors.
We also address the efficient construction (using random sketching) of parameter-dependent preconditioners that can be used to improve the quality of Galerkin projections or for effective error certification for problems with ill-conditioned operators.
For all proposed methods we provide precise conditions on the random sketch to guarantee accurate and stable estimations with a user-specified probability of success. A priori estimates to determine the sizes of the random matrices are provided as well as a more effective adaptive procedure based on a posteriori estimates.Cette thèse introduit des nouvelles approches basées sur l’algèbre linéaire aléatoire pour améliorer l’efficacité et la stabilité des méthodes de réduction de modèles basées sur des projections pour la résolution d’équations dépendant de paramètres. Notre méthodologie repose sur des techniques de projections aléatoires ("random sketching") qui consistent à projeter des vecteurs de grande dimension dans un espace de faible dimension. Un modèle réduit est ainsi construit de manière efficace et numériquement stable à partir de projections aléatoires de l’espace d’approximation réduit et des espaces des résidus associés. Notre approche permet de réaliser des économies de calcul considérables dans pratiquement toutes les architectures de calcul modernes. Par exemple, elle peut réduire le nombre de flops et la consommation de mémoire et améliorer l’efficacité du flux de données (caractérisé par l’extensibilité ou le coût de communication). Elle peut être utilisée pour améliorer l’efficacité et la stabilité des méthodes de projection de Galerkin ou par minimisation de résidu. Elle peut également être utilisée pour estimer efficacement l’erreur et post-traiter la solution du modèle réduit. De plus, l’approche par projection aléatoire rend viable numériquement une méthode d’approximation basée sur un dictionnaire, où pour chaque valeur de paramètre, la solution est approchée dans un sous-espace avec une base sélectionnée dans le dictionnaire. Nous abordons également la construction efficace (par projections aléatoires) de préconditionneurs dépendant de paramètres, qui peuvent être utilisés pour améliorer la qualité des projections de Galerkin ou des estimateurs d’erreur pour des problèmes à opérateurs mal conditionnés. Pour toutes les méthodes proposées, nous fournissons des conditions précises sur les projections aléatoires pour garantir des estimations précises et stables avec une probabilité de succès spécifiée par l’utilisateur. Pour déterminer la taille des matrices aléatoires, nous fournissons des bornes a priori ainsi qu’une procédure adaptative plus efficace basée sur des estimations a posteriori
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Sandberg, Henrik. "Model Reduction for Linear Time-Varying Systems." Doctoral thesis, Lund University, Department of Automatic Control, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-74698.
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The thesis treats model reduction for linear time-varying systems. Time-varying models appear in many fields, including power systems, chemical engineering, aeronautics, and computational science. They can also be used for approximation of time-invariant nonlinear models. Model reduction is a topic that deals with simplification of complex models. This is important since it facilitates analysis and synthesis of controllers. The thesis consists of two parts. The first part provides an introduction to the topics of time-varying systems and model reduction. Here, notation, standard results, examples, and some results from the second part of the thesis are presented. The second part of the thesis consists of four papers. In the first paper, we study the balanced truncation method for linear time-varying state-space models. We derive error bounds for the simplified models. These bounds are generalizations of well-known time-invariant results, derived with other methods. In the second paper, we apply balanced truncation to a high-order model of a diesel exhaust catalyst. Furthermore, we discuss practical issues of balanced truncation and approximative discretization. In the third paper, we look at frequency-domain analysis of linear time-periodic impulse-response models. By decomposing the models into Taylor and Fourier series, we can analyze convergence properties of different truncated representations. In the fourth paper, we use the frequency-domain representation developed in the third paper, the harmonic transfer function, to generalize Bode's sensitivity integral. This result quantifies limitations for feedback control of linear time-periodic systems.QC 20120206
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Almelid, Øyvind. "Pion Condensation in the Linear Sigma Model." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-12667.
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In this thesis we study the phase diagram of quantum chromodynamics in an effective low-energy theory at zero baryon chemical potential but finite temperature and isospin density. We investigate pion condensation at finite temperature and isospin chemical potential $mu_I$ in two different approximation schemes of the linear sigma model; the Large-$N$ and Hartree approximations at leading order. While being a simple model, the linear sigma model allows for phase transitions of both the first and second order, as well as crossover transitions at the physical point. The large-$N$ approximation yields results typical for mean-field approaches, including a second order phase transition with critical exponent $nu = frac{1}{2}$. At the physical point we find that pion condensation occurs below a threshold temperature $T_c(mu_I)$ only for $mu_I geq m_pi$. Due to the symmetry of the $O(N)$ expansion, the large-$N$ approximation also obeys Goldstone's theorem, yielding a massless Goldstone mode in the pion condensed phase.By contrast, we find a large violation of Goldstone's theorem in the Hartree approximation, with the Goldstone mode achieving a mass of $200 ~hbox{MeV} approx 1.4~ m_pi$. It is possible that the Hartree approximation's violation of symmetry makes the Goldstone mode tachyonic at low temperatures. However, it appears that the Hartree approximation yields a phase structure much more similar to what has been found in lattice studies, with a first order phase transition at high isospin densities and crossover transitions at lower densities. We have only been able to study the Hartree approximation under the condition that either the chiral condensate or the pion condensate is zero, however, and accurate probing of the phase diagram at the physical point is therefore not possible.
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FARINAS, MAYTE SUAREZ. "THE LINEAR LOCAL-GLOBAL NEURAL NETWORK MODEL." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2003. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=3694@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICONesta tese apresenta-se o Modelo de Redes Neurais Globais- Locais (RNGL) dentro do contexto de modelos de séries temporais. Esta formulação abrange alguns modelos não- lineares já existentes e admite também o enfoque de Mistura de Especialistas. Dedica-se especial atenção ao caso de especialistas lineares, e são discutidos extensivamente aspectos teóricos do modelo: condições de estacionariedade, identificabilidade do modelo, existência, consistência e normalidade assintótica dos estimadores dos parâmetros. Considera-se também uma estratégia de construção do modelo e são discutidos os procedimentos numéricos de estimação, apresentando uma solução para o cálculo de valores iniciais. Finalmente, ilustra-se a metodologia apresentada em duas séries temporais reais, amplamente utilizada na literatura de modelos não lineares.
In this thesis, the Local Global Neural Networks model is proposed within the context of time series models. This formulation encompasses some already existing nonlinear models and also admits the Mixture of Experts approach. We place emphasis on the linear expert case and extensively discuss the theoretical aspects of the model: stationary conditions, existence, consistency and asymptotic normality of the parameter estimates, and model identifiability. A model building strategy is also considered and the whole procedure is illustrated with two real time-series.
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FERNANDES, CRISTIANO AUGUSTO COELHO. "LINEAR GROWTH BAYESIAN MODEL USING DISCOUNT FACTORS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1985. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=9308@1.
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOO objetivo principal desta dissertação é descrever e discutir o Modelo Bayesiano de Crescimento Linear Sazonal, formulação Estados múltiplos, utilizando descontos. As idéias originais deste modelo foram desenvolvidas por Ameen e Harrison. Na primeira parte do trabalho (capítulos 2 e 3) apresentamos idéias bem gerais sobre Séries Temporais e os principais modelos da literatura. A segunda parte (capítulos 4, 5 e 6) é dedicada à Estatística Bayesiana (conceitos gerais), ao MDL na sua formulação original, e ao nosso modelo de interesse. São apresentadas algumas sugestões operacionais e um fluxograma de operação do modelo, com vistas a uma futura implementação computacional.
The aim of this thesis is to discuss in details the Multiprocess Linear Grawth Bayesian Model for seasonal and/or nonseasonal series, using discount factors. The original formulation of this model was put forward recently by Ameen and Harrison. In the first part of the thesis (chapters 2 and 3) we show some general concepts related to time series and time series modelling, whereas in the second (chapters 4, 5 and 6) we formally presented / the Bayesian formulation of the proposed model. A flow chart and some optional parameter setings aiming a computational implementation is also presented.
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Mariotto, Angela Bacellar. "Empirical Bayes inference and the linear model." Thesis, Imperial College London, 1989. http://hdl.handle.net/10044/1/47557.
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Gu, Wei. "Gauged Linear Sigma Model and Mirror Symmetry." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90892.
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This thesis is devoted to the study of gauged linear sigma models (GLSMs) and mirror symmetry. The first chapter of this thesis aims to introduce some basics of GLSMs and mirror symmetry. The second chapter contains the author's contributions to new exact results for GLSMs obtained by applying supersymmetric localization. The first part of that chapter concerns supermanifolds. We use supersymmetric localization to show that A-twisted GLSM correlation functions for certain supermanifolds are equivalent to corresponding Atwisted GLSM correlation functions for hypersurfaces. The second part of that chapter defines associated Cartan theories for non-abelian GLSMs by studying partition functions as well as elliptic genera. The third part of that chapter focuses on N=(0,2) GLSMs. For those deformed from N=(2,2) GLSMs, we consider A/2-twisted theories and formulate the genuszero correlation functions in terms of Jeffrey-Kirwan-Grothendieck residues on Coulomb branches, which generalize the Jeffrey-Kirwan residue prescription relevant for the N=(2,2) locus. We reproduce known results for abelian GLSMs, and can systematically calculate more examples with new formulas that render the quantum sheaf cohomology relations and other properties manifest. We also include unpublished results for counting deformation parameters. The third chapter is about mirror symmetry. In the first part of the third chapter, we propose an extension of the Hori-Vafa mirrror construction [25] from abelian (2,2) GLSMs they considered to non-abelian (2,2) GLSMs with connected gauge groups, a potential solution to an old problem. We formally show that topological correlation functions of B-twisted mirror LGs match those of A-twisted gauge theories. In this thesis, we study two examples, Grassmannians and two-step flag manifolds, verifying in each case that the mirror correctly reproduces details ranging from the number of vacua and correlations functions to quantum cohomology relations. In the last part of the third chapter, we propose an extension of the Hori-Vafa construction [25] of (2,2) GLSM mirrors to (0,2) theories obtained from (2,2) theories by special tangent bundle deformations. Our ansatz can systematically produce the (0,2) mirrors of toric varieties and the results are consistent with existing examples which were produced by laborious guesswork. The last chapter briefly discusses some directions that the author would like to pursue in the future.Doctor of Philosophy
In this thesis, I summarize my work on gauged linear sigma models (GLSMs) and mirror symmetry. We begin by using supersymmetric localization to show that A-twisted GLSM correlation functions for certain supermanifolds are equivalent to corresponding A-twisted GLSM correlation functions for hypersurfaces. We also define associated Cartan theories for non-abelian GLSMs. We then consider N =(0,2) GLSMs. For those deformed from N =(2,2) GLSMs, we consider A/2-twisted theories and formulate the genus-zero correlation functions on Coulomb branches. We reproduce known results for abelian GLSMs, and can systematically compute more examples with new formulas that render the quantum sheaf cohomology relations and other properties are manifest. We also include unpublished results for counting deformation parameters. We then turn to mirror symmetry, a duality between seemingly-different two-dimensional quantum field theories. We propose an extension of the Hori-Vafa mirror construction [25] from abelian (2,2) GLSMs to non-abelian (2,2) GLSMs with connected gauge groups, a potential solution to an old problem. In this thesis, we study two examples, Grassmannians and two-step flag manifolds, verifying in each case that the mirror correctly reproduces details ranging from the number of vacua and correlations functions to quantum cohomology relations. We then propose an extension of the HoriVafa construction [25] of (2,2) GLSM mirrors to (0,2) theories obtained from (2,2) theories by special tangent bundle deformations. Our ansatz can systematically produce the (0,2) mirrors of toric varieties and the results are consistent with existing examples. We conclude with a discussion of directions that we would like to pursue in the future.
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Zhao, Yonggang. "The general linear model for censored data." The Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=osu1054781042.
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Alabiso, Audry. "Linear Mixed Model Selection by Partial Correlation." Bowling Green State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1587142724497829.
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Dixon, Cheryl Annette. "Power Analysis for the Mixed Linear Model." VCU Scholars Compass, 1996. http://scholarscompass.vcu.edu/etd/4525.
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Power analysis is becoming standard in inference based research proposals and is used to support the proposed design and sample size. The choice of an appropriate power analysis depends on the choice of the research question, measurement procedures, design, and analysis plan. The "best" power analysis, however, will have many features of a sound data analysis. First, it addresses the study hypothesis, and second, it yields a credible answer.
Power calculations for standard statistical hypotheses based on normal theory have been defined for t-tests through the univariate and multivariate general linear models. For these statistical methods, the approaches to power calculations have been presented based on the exact or approximate distributions of the test statistics in question. Through the methods proposed by O'Brien and Muller (1993), the noncentrality parameter for the noncentral distribution of the test statistics for the univariate and multivariate general linear models is expressed in terms of its distinct components. This in tum leads to methods for calculating power which are efficient and easy to implement.
As more complex research questions are studied, more involved methods have been proposed to analyze data. One such method includes the mixed linear model. This research extends the approach to power calculation used for the general linear model to the mixed linear model. Power calculations for the mixed linear model will be based on the approximate F statistic for testing the mixed model's fixed effects proposed by Helms (1992). The noncentrality parameter of the approximate noncentral F for the mixed model will be written in terms of its distinct components so that a useful and efficient method for calculating power in the mixed model setting will be achieved. In this research, it has been found that the rewriting of the noncentrality parameter varies depending on study design. Thus, the noncentrality parameter for three specific cases of study design are derived.
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Friedbaum, Jesse Robert. "Model Predictive Linear Control with Successive Linearization." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/7063.
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Robots have been a revolutionizing force in manufacturing in the 20th and 21st century but have proven too dangerous around humans to be used in many other fields including medicine. We describe a new control algorithm for robots developed by the Brigham Young University Robotics and Dynamics and Robotics Laboratory that has shown potential to make robots less dangerous to humans and suitable to work in more applications. We analyze the computational complexity of this algorithm and find that it could be a feasible control for even the most complicated robots. We also show conditions for a system which guarantee local stability for this control algorithm.
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Randell, David. "Bayes linear variance learning for mixed linear temporal models." Thesis, Durham University, 2012. http://etheses.dur.ac.uk/3646/.
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Modelling of complex corroding industrial systems is ritical to effective inspection and maintenance for ssurance of system integrity. Wall thickness and corrosion rate are modelled for multiple dependent corroding omponents, given observations of minimum wall thickness per component. At each inspection, partial observations of the system are considered. A Bayes Linear approach is adopted simplifying parameter estimation and avoiding often unrealistic distributional assumptions. Key system variances are modelled, making exchangeability assumptions to facilitate analysis for sparse inspection time-series. A utility based criterion is used to assess quality of inspection design and aid decision making. The model is applied to inspection data from pipework networks on a full-scale offshore platform.
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Hernandez, Erika Lyn. "Parameter Estimation in Linear-Linear Segmented Regression." Diss., CLICK HERE for online access, 2010. http://contentdm.lib.byu.edu/ETD/image/etd3551.pdf.
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Orukpe, Patience Ebehiremen. "Model predictive control for linear time invariant systems using linear matrix inequality techniques." Thesis, Imperial College London, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509510.
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Abraham, Anita Ann Edwards Lloyd J. "Model selection methods in the linear mixed model for longitudinal data." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2008. http://dc.lib.unc.edu/u?/etd,1859.
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Thesis (DrPH)--University of North Carolina at Chapel Hill, 2008.Title from electronic title page (viewed Dec. 11, 2008). "... in partial fulfillment of the requirements for the degree of Doctor of Public Health in the Department of Biostatistics, School of Public Health." Discipline: Biostatistics; Department/School: Public Health.
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Ten, Eyck Patrick. "Problems in generalized linear model selection and predictive evaluation for binary outcomes." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/6003.
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This manuscript consists of three papers which formulate novel generalized linear model methodologies.
In Chapter 1, we introduce a variant of the traditional concordance statistic that is associated with logistic regression. This adjusted c − statistic as we call it utilizes the differences in predicted probabilities as weights for each event/non- event observation pair. We highlight an extensive comparison of the adjusted and traditional c-statistics using simulations and apply these measures in a modeling application.
In Chapter 2, we feature the development and investigation of three model selection criteria based on cross-validatory c-statistics: Model Misspecification Pre- diction Error, Fitting Sample Prediction Error, and Sum of Prediction Errors. We examine the properties of the corresponding selection criteria based on the cross- validatory analogues of the traditional and adjusted c-statistics via simulation and illustrate these criteria in a modeling application.
In Chapter 3, we propose and investigate an alternate approach to pseudo- likelihood model selection in the generalized linear mixed model framework. After outlining the problem with the pseudo-likelihood model selection criteria found using the natural approach to generalized linear mixed modeling, we feature an alternate approach, implemented using a SAS macro, that obtains and applies the pseudo-data from the full model for fitting all candidate models. We justify the propriety of the resulting pseudo-likelihood selection criteria using simulations and implement this new method in a modeling application.
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Yam, Ho-kwan, and 任浩君. "On a topic of generalized linear mixed models and stochastic volatility model." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B29913342.
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Frühwirth-Schnatter, Sylvia. "Bayesian Model Discrimination and Bayes Factors for Normal Linear State Space Models." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1993. http://epub.wu.ac.at/108/1/document.pdf.
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It is suggested to discriminate between different state space models for a given time series by means of a Bayesian approach which chooses the model that minimizes the expected loss. Practical implementation of this procedures requires a fully Bayesian analysis for both the state vector and the unknown hyperparameters which is carried out by Markov chain Monte Carlo methods. Application to some non-standard situations such as testing hypotheses on the boundary of the parameter space, discriminating non-nested models and discrimination of more than two models is discussed in detail. (author's abstract)Series: Forschungsberichte / Institut für Statistik
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Yousef, Mohammed A. "Two-Stage SCAD Lasso for Linear Mixed Model Selection." Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1558431514460879.
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Gory, Jeffrey J. "Marginally Interpretable Generalized Linear Mixed Models." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1497966698387606.
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Metz, Werner. "Linear barotropic simulation of atmospheric low-frequency variability." Universität Leipzig, 1995. https://ul.qucosa.de/id/qucosa%3A15014.
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A steady-state barotropic model, linearized about a GCM-derived 500 hPa basic state, is driven by a sample of \'observed\' forcing fields. lt tums out that the leading mode (LEOF) obtained from the sample of linear solutions matches weil with the leading EOF of low-frequency atmospheric variability actually occurring in the GCM. The response ofthe linear model is analysed in tenns of the singular modes of the model\''s linear operator. lt is found that about 50 percent ofthe spatial variance of the LEOF can be explained in tenns of the leading two singular modes. This finding is reflected also in the linear barotropic energy balance of the LEOF which shows that the mode is maintained through nearly equal contributions from i) the kinetic energy conversion of basic state kinetic energy (which is primarily due to the action of the singular modes) and ii) the forcing. The linear simulation of the GCM EOF fails if the linear model is linearized about a 300 hPa basic. This is explained by the fact that in this case the structure of the leading singular modes, which have a strong impact on the linear response, is much more dissimilar to the structure of the GCM EOF than in the 500 hPa case.Ein stationäres barotropes Modell, das bezüglich eines (aus einem GCM Experiment abgeleiteten) 500 hPa Grundzustandes linearisiert ist, wird für einen Satz von 'beobachteten' Antriebsfeldern gelöst. Dabei zeigt sich, daß die führende Mode der langperiodischen atmosphärischen Variabilität (EOF) im GCM Experiment durch das lineare Modell sehr gut simuliert wird. Weiterhin stellt sich heraus, daß hierfür die Antriebsfelder und die singulären Moden des linearen Modelloperators die gleiche Bedeutung besitzen. Auf die Wichtigkeit der Anwendung des Modells bezüglich des äquivalentbarotropen Niveaus wird hingewiesen.
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Emond, Mary Jane. "Efficient estimation in the generalized semilinear model /." Thesis, Connect to this title online; UW restricted, 1993. http://hdl.handle.net/1773/9543.
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AMARAL, LUIZ FELIPE MOREIRA DO. "USING LINEAR AND NON-LINEAR APPROACHES TO MODEL THE BRAZILIAN ELECTRICITY SPOT PRICE SERIES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2003. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=3727@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORNesta dissertação, estratégias de modelagem são apresentadas envolvendo modelos de séries temporais lineares e não lineares para modelar a série do preço spot no mercado elétrico brasileiro. Foram usados, dentre os lineares, os modelos ARIMA(p,d,q) proposto por Box, Jenkins e Reinsel (1994) e os modelos de regressão dinâmica. Dentre os não lineares, o modelo escolhido foi o STAR desenvolvido, inicialmente, por Chan e Tong (1986) e, posteriormente, por Teräsvista (1994). Para este modelo, testes do tipo Multiplicador de Lagrange foram usados para testar linearidade, bem como para avaliar os modelos estimados. Além disso, foi também utilizada uma proposta para os valores iniciais do algoritmo de otimização, desenvolvido por Franses e Dijk (2000). Estimativas do filtro de Kalman suavizado foram usadas para substituir os valores da série de preço durante o racionamento de energia ocorrido no Brasil.
In this dissertation, modeling strategies are presented involving linear and non-linear time series models to model the spot price of Brazil s electrical energy market. It has been used, among the linear models, the modeling approach of Box, Jenkins and Reinsel (1994) i.e., ARIMA(p,d,q) models, and dynamic regression. Among the non-linear ones, the chosen model was the STAR developed, initially, by Chan and Tong (1986) and, later, by Teräsvirta (1994). For this model, the Lagrange Multipliers test, to measure the degree of non linearity of the series , as well as to evaluate the estimated model was used. Moreover, it was also used a proposal for the initial values of the optimization algorithm, developed by Franses and Dijk (2000). The smoothed Kalman filter estimates were used in order to provide values for the spot price series during the energy shortage period.
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McPhee, Craig. "Development and characterisation of synthetic model lipid membranes under linear and non-linear microscopy." Thesis, Cardiff University, 2016. http://orca.cf.ac.uk/111884/.
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Lipid domains provide a framework for localised functionality of the cellular membrane through transient coordination of certain lipids and membrane proteins into structurally distinct, stabilised heterogeneous membrane regions. Present experimental studies fall short of conclusively proving lipid domain existence within the plasma membrane due to the lack of label-free, chemically sensitive nanoscale detection. Herein, I present my progress towards developing novel, label-free optical microscopy techniques to over- come these limitations. Giant unilamellar vesicles (GUVs) represent a simple model of cellular membranes and are well suited for the study of lipid domains. In this thesis, I discuss the demonstration of a novel, label free method to directly assess GUV lamellarity: Quantitative differential interference contrast microscopy (qDIC). Under qDIC, a contrast image is produced which encodes the difference in optical phase (hence optical path length) after propagation through two adjacent points of the sample. I show that, with appropriate data analysis applied to qDIC contrast images, we are able to measure membrane lamellarity directly with sub-nm precision. I then demonstrate the application of this method to static synthetic membranes exhibiting lipid domains: Planar Lipid Bilayer Patches (PLBPs). Sub-nm thickness differences (∼9Å) attributable to coexisting lipid domains are resolved and quantified. Overall, these results demonstrate that label free qDIC is a rapid, non-perturbing, sensitive and accurate method, providing an alternative to fluorescence microscopy, for quantitative studies of lipid domains in model membranes. Furthermore, I discuss correlative qDIC and Coherent Anti-Stokes Ra- man scattering microscopy (CARS) of PLBPs with lipid domains. CARS microscopy has emerged in the last decade as a powerful, chemically specific multi-photon imaging method which overcomes the sensitivity and speed limitations of spontaneous Raman scattering, and enables rapid quantitative analysis of lipids label-free. I demonstrate application of broadband hyper-spectral CARS imaging over the CH 2,3 stretching vibrational resonances, combined with in-house developed phase-corrected Kramers Krönig (PCKK) analysis, which allowed us to resolve and quantify the chemical components of lipid domains at the single bilayer level. Stimulated Raman loss (SRL) microscopy is an alternative, chemically specific, non-linear imaging modality recently implemented within our research group. In contrast to CARS microscopy, SRL rejects non-resonant background providing high contrast imaging of single lipid bilayers comparable to fluorescence imaging. I demonstrate early application of SRL at the single bilayer level across the CH 2,3 stretch region. During this project a number of notable achievements have been made. A novel qDIC method has been developed and utilised. CARS microscopy has been applied to determine lipid liquid phase at both single frequency and hyper-spectral imaging modalities. SRL microscopy has then been applied, demonstrating superior contrast to that seen under CARS. These studies form the foundation for further chemically specific investigation.
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Frankel, Joe. "Linear dynamic models for automatic speech recognition." Thesis, University of Edinburgh, 2004. http://hdl.handle.net/1842/1087.
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The majority of automatic speech recognition (ASR) systems rely on hidden Markov models (HMM), in which the output distribution associated with each state is modelled by a mixture of diagonal covariance Gaussians. Dynamic information is typically included by appending time-derivatives to feature vectors. This approach, whilst successful, makes the false assumption of framewise independence of the augmented feature vectors and ignores the spatial correlations in the parametrised speech signal. This dissertation seeks to address these shortcomings by exploring acoustic modelling for ASR with an application of a form of state-space model, the linear dynamic model (LDM). Rather than modelling individual frames of data, LDMs characterize entire segments of speech. An auto-regressive state evolution through a continuous space gives a Markovian model of the underlying dynamics, and spatial correlations between feature dimensions are absorbed into the structure of the observation process. LDMs have been applied to speech recognition before, however a smoothed Gauss-Markov form was used which ignored the potential for subspace modelling. The continuous dynamical state means that information is passed along the length of each segment. Furthermore, if the state is allowed to be continuous across segment boundaries, long range dependencies are built into the system and the assumption of independence of successive segments is loosened. The state provides an explicit model of temporal correlation which sets this approach apart from frame-based and some segment-based models where the ordering of the data is unimportant. The benefits of such a model are examined both within and between segments. LDMs are well suited to modelling smoothly varying, continuous, yet noisy trajectories such as found in measured articulatory data. Using speaker-dependent data from the MOCHA corpus, the performance of systems which model acoustic, articulatory, and combined acoustic-articulatory features are compared. As well as measured articulatory parameters, experiments use the output of neural networks trained to perform an articulatory inversion mapping. The speaker-independent TIMIT corpus provides the basis for larger scale acoustic-only experiments. Classification tasks provide an ideal means to compare modelling choices without the confounding influence of recognition search errors, and are used to explore issues such as choice of state dimension, front-end acoustic parametrization and parameter initialization. Recognition for segment models is typically more computationally expensive than for frame-based models. Unlike frame-level models, it is not always possible to share likelihood calculations for observation sequences which occur within hypothesized segments that have different start and end times. Furthermore, the Viterbi criterion is not necessarily applicable at the frame level. This work introduces a novel approach to decoding for segment models in the form of a stack decoder with A* search. Such a scheme allows flexibility in the choice of acoustic and language models since the Viterbi criterion is not integral to the search, and hypothesis generation is independent of the particular language model. Furthermore, the time-asynchronous ordering of the search means that only likely paths are extended, and so a minimum number of models are evaluated. The decoder is used to give full recognition results for feature-sets derived from the MOCHA and TIMIT corpora. Conventional train/test divisions and choice of language model are used so that results can be directly compared to those in other studies. The decoder is also used to implement Viterbi training, in which model parameters are alternately updated and then used to re-align the training data.
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Kim, Tae-Hyoung. "Robust model predictive control for constrained linear systems." 京都大学 (Kyoto University), 2006. http://hdl.handle.net/2433/143898.
Full textAbstract:
Kyoto University (京都大学)0048
新制・課程博士
博士(情報学)
甲第12450号
情博第204号
新制||情||44(附属図書館)
24286
UT51-2006-J441
京都大学大学院情報学研究科システム科学専攻
(主査)教授 杉江 俊治, 教授 酒井 英昭, 教授 熊本 博光
学位規則第4条第1項該当
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Khan, Md Jafar Ahmed. "Robust linear model selection for high-dimensional datasets." Thesis, University of British Columbia, 2006. http://hdl.handle.net/2429/31082.
Full textAbstract:
This study considers the problem of building a linear prediction model when the number of candidate covariates is large and the dataset contains a fraction of outliers and other contaminations that are difficult to visualize and clean. We aim at predicting the future non-outlying cases. Therefore, we need methods that are robust and scalable at the same time.
We consider two different strategies for model selection: (a) one-step model building and (b) two-step model building. For one-step model building, we robustify the step-by-step algorithms forward selection (FS) and stepwise (SW), with robust partial F-tests as stopping rules.
Our two-step model building procedure consists of sequencing and segmentation. In sequencing, the input variables are sequenced to form a list such that the good predictors are likely to appear in the beginning, and the first m variables of the list form a reduced set for further consideration. For this step we robustify Least Angle Regression (LARS) proposed by Efron, Hastie, Johnstone and Tibshirani (2004). We use bootstrap to stabilize the results obtained by robust LARS, and use "learning curves" to determine the size of the reduced set.
The second step (of the two-step model building procedure) - which we call segmentation - carefully examines subsets of the covariates in the reduced set in order to select the final prediction model. For this we propose a computationally suitable robust cross-validation procedure. We also propose a robust bootstrap procedure for segmentation, which is similar to the method proposed by Salibian-Barrera and Zamar (2002) to conduct robust inferences in linear regression.
We introduce the idea of "multivariate-Winsorization" which we use for robust data cleaning (for the robustification of LARS). We also propose a new correlation estimate which we call the "adjusted-Winsorized correlation estimate". This estimate is consistent and has bounded influence, and has some advantages over univariate-Winsorized correlation estimate (Huber 1981 and Alqallaf 2003).Science, Faculty of
Statistics, Department of
Graduate