Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 20 for “"Covariance functions"”.
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Modeling spatial covariance functions
<p>Covariance modeling plays a key role in the spatial data analysis as it provides important information about the dependence structure of underlying processes and determines performance of spatial prediction. Various parametric models have been developed to accommodate the idiosyncratic features …
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TESTING THE EQUALITY OF SEVERAL COVARIANCE FUNCTIONS FOR FUNCTIONAL DATA
… researchers in recent decades. And the equal-covariance assumption is commonly assumed in these equal-mean function testing problems. So it is of interest to check whether this assumption holds or not. In this thesis, we discuss three types of methods, i.e., the L2-norm based test, the …
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Non-Parametric Spatial Models
<p>Covariance functions play a central role in spatial statistics. Parametric covariance functions have been used in most of the existing works on the analysis of spatial data. The primary reason for this is that the classes of parametric covariance functions guarantee that the fitted covariance …
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The best truncation point for the estimated spectral density function of a stationary time series
… truncation point. Two different types of weight functions, both of which give consistent estimators of the spectral density function, are presented in this dissertation. Both of the weight functions have related truncation functions. For the problem of determining the best truncation function one …
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Models and Methods for Random Fields in Spatial Statistics with Computational Efficiency from Markov Properties
… A variation of the method using wavelet basis functions is proposed and using a simulation-based study, the wavelet approximations are compared with two of the most popular methods for efficient approximations of Gaussian fields. A new class of spatial models, including the Gaussian Matérn …
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Advances in Probabilistic Modelling: Sparse Gaussian Processes, Autoencoders, and Few-shot Learning
… Gaussian process approximations and invariant covariance functions, learning flexible priors for variational autoencoders, and probabilistic approaches for few-shot learning. As inference is rarely tractable, we discuss variational inference methods as a secondary theme. First, we disentangle …
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Gaussian process models for SCADA data based wind turbine performance/condition monitoring
… similarity between subsequent data points (via covariance functions) to fit and or estimate the future value from a training dataset. GP models have been applied to numerous multivariate and multi-task problems including spatial and spatiotemporal contexts.;Furthermore, GP models have been …
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Transforms for prediction residuals based on prediction inaccuracy modeling
… as the energy compaction property. Given the covariance function of the signal, the linear transform with the best energy compaction property is the Karhunen Loeve transform. In this thesis, we develop a new set of transforms for prediction residuals. We observe that the prediction process in …
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Improved Gaussian process approximations for spatial and flow fields
… broad class of priors - stationary priors whose covariance functions have well-defined spectral densities. Since many spatial fields are highly non-stationary, in Chapter 4 I construct a new class of non-stationary priors based on multiresolution (discrete wavelet) approximations, with a …
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Probabilistic Modelling in Function Space
… themselves as powerful tools for inferring functions from data. They provide a flexible framework for defining distributions over functions, enabling closed form solutions and principled handling of uncertainty. However, their application is often hindered by the difficulty of formulating …
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Hierarchical Gaussian models for wind field estimation and path planning
… we extract empirical estimates of the mean and covariance functions. The associated covariance matrices are anisotropic and non-stationary, and capture interactions among the wind vectors at all points in a discretization of the domain. We make the further assumption that, given a particular …
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Studies on the generalisation of Gaussian processes and Bayesian neural networks
… stochastic processes described by four different covariance functions. We also explain the early, linearly-decreasing behaviour of the curves and we investigate the asymptotic behaviour of the upper bounds. The effect of the noise and the characteristic lengthscale of the stochastic process on the …
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Topics in Bayesian Spatiotemporal Prediction of Environmental Exposure
… of 2017. To account for these patterns, we use covariance models over space, circles, and time. We review relevant existing covariance models and develop new classes of nonseparable covariance models appropriate for seasonal data collected at many locations. We compare the predictive performance …
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Non-linear dynamics identification using Gaussian process prior models within a Bayesian context.
… models, including various choices of classes of covariance functions, is also described in detail. Despite its good predictive nature, Gaussian regression is often limited by several O(N3) operations and O(N2) memory requirements during optimisation and prediction. Several fast and memory …
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Modelagem da produção de leite de cabras das raças Alpina e Saanen utilizando regressão aleatória
Foram analisados 17.356 registros de produção de leite no dia do controle (PLDC) de 642 primeiras lactações de cabras da raça Alpina e 13.278 registros de 470 cabras da raça Saanen do rebanho da Universidade Federal de Viçosa. O objetivo foi modelar variações na PLDC durante a primeira lactação de …
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Stochastic methods for uncertainty quantification in radiation transport
… a second-order random process with known covariance function in terms of a set of uncorrelated random variables and the eigenmodes of the covariance function. The flux and, in multiplying materials, the k-eigenvalue, which are the problem unknowns, are always expanded in a gPC expansion …
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Structural performance evaluation of concrete arch dams using ambient vibration monitoring and GNNS systems
… In Gaussian process regression, the choice of a covariance function is very important in producing good results. The ability of the different covariance functions in Gaussian process regression models, to predict natural frequencies and dam deformations, was studied. The performance of Gaussian …
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Randomized estimates in power spectral analysis
… the usual procedure is to use estimated auto-covariance functions ρ̂(τ), computed from a set of observations X(t<sub>i</sub>) from which φ(ω) is approximated by numerical integration. This gives φ̂(ω) = 1/W [ρ̂(0)+2∑<sub> j=1</sub><sup>m-1</sup> ρ̂[jπ/W]cos(ωjπ/W) + ρ̂[mπ/W]cos(ωmπ/W)] where …
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Implementation of gaussian process models for non-linear system identification
… modelling approach for repeated inversion of a covariance matrix whose size is dictated by the number of points included in the training dataset. Therefore, in order to maintain the computational viability of the approach, a number of different strategies have been proposed to lessen the …
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Flexible models and methods for longitudinal and multilevel functional data
… random subject-specific curves, the associated covariance function that represents between-subject variation, and the variance function of the residual measurement errors (which represents within-subject variation). The proposed methods offer flexible estimation of both the population- and …