Bayesian nonparametric (BNP) statistics is a relative new area of statistics. The intersection of
Bayesian and non-parametric statistics was almost empty until the sixties and seventies where
the first advances were made, primarily on the mathematical for
In this thesis, we propose novel stationary time series models that can be used when the observations are taken on irregularly spaced times. First, we present a model with a first-order moving average structure, and then we generalized it to consider an autoregressive component. We called the fir...
En esta tesis, se propone modelos de series de tiempo estacionarios que pueden ser usados cuando las observaciones son tomadas en tiempos irregularmente espaciados. Primero, se presenta un modelo con estructura de promedios móviles de primer orden, para posteriormente considerar componentes autor...
El analisis estad ´ ´ıstico de formas, y de variedades diferenciables mas generales, es un ´ area de ´
creciente interes en investigaci ´ on, el que se explica por la necesidad de trabajar con datos que ´
poseen una estructura geometrica compleja. Este ti
This thesis is divided in two chapters, which are independent and can be read separately.
In the rst chapter we provide a converse theorem for a certain class of non-holomorphic automorphic
forms, called Jacobi{Maass forms. This new type of automorphic f
En esta tesis, se propone un nuevo procedimiento Bayesiano no-paramétrico para prueba de hipótesis cuando los datos están correlacionados. Inicialmente, se presenta una propuesta para comparar distribuciones en muestras pareadas. Luego, se propone un procedimiento para realizar prueba de hipótesi...
In this thesis, we propose novel Bayesian Nonparametric hypothesis testing procedures
for correlated data. First, we develop and study a proposal for comparing the
distributions of paired samples. Next, we propose and analyze a hypothesis testing
procedure for longitudinal data analysis. Both ...
En esta tesis primero estudiamos la dinámica global de campos vectoriales planners en distintas situaciones: (I) el camp vectorial es polynomial homogéneo de grado cuatro; (II) el campo vectorial es dado por una función Hamiltonian polynomial con simetría (con respecto a la reflexión (x; y) -> (-...
In this thesis firstly we study the global dynamics of planar vector fields in different situations: (I) the vector field is a homogeneous polynomial of degree four; (II) the vector field is given by a symmetric (with respect to the reflection (x; y) -> (-x; y)) polynomial Hamiltonian function of...
Stochastic Partial Differential Equations are an essential tool for
the analysis of scaling limits of a diverse array of microscopic
models coming from other fields such as physics and chemistry.
This type of equations correspond to classical partial differential
equations to which one has added ...
El objetivo de esta tesis es contribuir al desarrollo de métodos numéricos para resolver ecuaciones provenientes del modelado de dispositivos de recolección de energía solar.
El diseño óptimo de una celda solar fotovoltaica requiere de técnicas numéricas eficientes que proporcionen aproximaciones...
The goal of this thesis is to contribute to the development of numerical methods for solving equations arising from modeling light harvesting devices.
The optimal design of a photovoltaic solar cell requires efficient solvers that provide accurate approximations of the solution of Maxwell or H...
Esta tesis tiene como objetivo estudiar condiciones suficientes para la existencia, unicidad, representación (explícita e implícita) y regularidad de soluciones para una cierta clase de ecuaciones de Schrödinger de tipo homogéneas, lineales y no lineales determinadas por el operador Laplaciano fr...
This thesis aims to study sufficient conditions for the existence, uniqueness, representation (explicit
and implicit) and regularity of solutions for a certain class of equations of Schr¨odinger of homogeneous, linear and non-linear type determined by the operator Fractional Laplacian. This rese...
