Browsing by Subject "Gaussian process"

Now showing 1 - 3 of 3
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    Gaussian Processes in Semi-Parametric Models
    (2023-06) Thompson, Marten
    Gaussian processes provide a flexible, non-parametric prior for function estimation. We investigate the applicability of Gaussian processes in semi-parametric models to relax otherwise restrictive assumptions. Our first application of this perspective is climate time series, where we see both the advantage of Gaussian processes in semi-parametric models as well as their computational restrictions. Next, we use Gaussian processes to relax the assumed error distribution of traditional small area models. Finally, we turn our attention to stripping away assumptions on Gaussian processes themselves: can data be used to inform their parameterization? We detail our work on each of these problems and provide software for future researchers.
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    Topics on Climate Model Output Analyses
    (2021-10) Gong, Kaibo
    Comparison of two different data samples, and of paired data samples, is a well known problem in Statistics. Specifically, there is a wide range of applications in the fields of climate study. In this thesis, we provide a brief review on the ensemble of climate models and the need of probabilistic evaluation of model outputs, which is equivalent to the comparison between two models. Based on recent advancements in the context of evaluating climate model outputs, we develop two different approaches for comparing two functional time series. The first one is based on wavelet decomposition and the second one by comparing the local spectral density of non-stationary series. For the last chapter, we conduct a brief review on Gaussian Process and a framework for Bayesian Optimization, which establishes a theoretical framework and algorithmic properties of t-process based spatio-temporal modeling, for further use in modeling climate and neuroscience data.
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    Understanding Gaussian Process Fits and Some Model Building Tools Using an Approximate Form of the Restricted Likelihood
    (2016-07) Bose, Maitreyee
    Gaussian processes (GPs) are widely used in statistical modeling, often as random effects in a linear mixed model, with their unknowns estimated by maximizing the restricted likelihood or doing a Bayesian analysis, which are closely related. However, it is unclear how a GP's variance and range and the error variance are fit to features in the data. To get a better understanding of that, we applied the spectral approximation to the intercept-only GP. The restricted likelihood from this approximate model has a simple interpretable form, which is identical to the likelihood arising from a gamma-errors generalized linear model with the identity link. If there are covariates in the model, we regress them out and approximate the residuals using an intercept-only GP. Incorporating ideas from linear models, we propose a few tools for systematic model building in linear mixed models where the random effect is a Gaussian process. We present analyses of simulated data and forest inventory data using the spectral basis representation together with added variable plots as diagnostic tools for identifying missing covariates and assessing general goodness of fit.