3.22 Facultad de Matemáticas

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Browsing 3.22 Facultad de Matemáticas by Subject "519.542"

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    Flexible bayesian inference for families of random densities.
    (2020) Galasso Díaz, Bastián; González Burgos, Jorge Andrés; Pontificia Universidad Católica de Chile. Facultad de Matemáticas
    A main goal of this thesis is to propose and study novel flexible Bayesian models for setups that entail families of random densities. Two specific contexts will be examined: one involves phase-varying point processes, whereas the other involves functional principal component analysis. The common denominator underlying these contexts is the need to model families of random measures to each of which corresponds a different data generating process. On both contexts, prior processes will be used so to devise priors on the target objects of interest. In more detail, one context entails separating amplitude variation from phase variation in a multiple point process setting. In this framework, I pioneer the development of priors on spaces of warping maps by proposing a novel Bayesian semiparametric approach for modeling registration of multiple point processes. Specifically, I develop induced priors for warp maps via a Bernstein polynomial prior so to learn about the structural measure of the point process and about the phase variation in the process. Theoretical properties of the induced prior, including support and posterior consistency, are established under a fairly mild proviso. Also, numerical experiments are conducted to assess the performance of this new approach; finally, a real data application in climatology illustrates the proposed methodology. The other context that will be considered in this thesis involves modeling families of random densities using functional principal component analysis through the so-called Karhunen–Loève decomposition. For this, I develop a data-driven prior based on the Karhunen–Loève decomposition which can be used to borrowing strength across samples. The proposed approach defines a prior on the space of families of densities. Theoretical properties are developed to ensure that the trajectories from an infinite mixture belong to L 2 which is a necessary condition for the Karhunen–Loève decomposition to hold. Numerical experiments are conducted to assess the performance of the proposed approach against competing methods, and we offer an illustration by revisiting Galton’s height parents dataset.
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    Linking measurements : a bayesian nonparametric approach.
    (2019) Varas Cáceres, Inés María; González Burgos, Jorge Andrés; Pontificia Universidad Católica de Chile. Facultad de Matemáticas