Presentaremos distintos métodos de estimación no-paramétrica para la densidad con soporte compacto o dominio con geometría que puede ser compleja. Veremos como se fue afectado la calidad de estimadores clásicos al borde del dominio. En particular se propondrá un nuevo estimador basados en polinomios locales para estimar la densidad en un punto x. Veremos que este estimador puede adaptarse a distintas geometrías y que tiene propiedades optímales en términos del error cuadrático medio y de la regularidad de la función a estimar. Compararemos este método al método sparr que es una alternativa popular para la estimación de densidad en dominios a geometría complicada.
The proliferation of large-scale geospatial data from sources such as satellite remote sensing and cellular phone networks has created a need for new statistical methods capable of handling massive datasets and complex spatial domains, as classical techniques often face prohibitive computational burdens and restrictive assumptions. In this talk, I discuss recent advances that directly address some of these challenges, primarily through the development of a scalable model that reduces computational complexity from cubic to near-linear in the number of observations. Further, we explore some of its applications. Beyond scalability, progress has been made in tailoring methods for complex domains by defining a process using appropriate distance metrics. The synthesis of these scalable and geometrically aware methods empowers practitioners to extract meaningful insights from vast and intricate spatial data. Again, we revisit applications in other spatial domains. FAPEMIG and CNPq partially funded these works.This is a joint work with Carlos Gonzáles, Dipak K. Dey, Harvard Rue, Heitor Ramos, Lucas Godoy, Lucas Michelin, Jun Yan and Zaida Quiroz
Imperfect repairs (IRs) are widely applicable in reliability engineering since most equipment is not completely replaced after failure. In this sense, it is necessary to develop methodologies that can describe failure processes and predict the reliability of systems under this type of repair. One of the challenges in this context is to establish reliability models for multiple repairable systems considering unobserved heterogeneity associated with systems failure times and their failure intensity after performing IRs. Thus, in this work, frailty models are proposed to identify unobserved heterogeneity in these failure processes. In this context, we consider the arithmetic reduction of age (ARA) and arithmetic reduction of intensity (ARI) classes of IR models, with constant repair efficiency and a Power-Law Process (PLP) distribution to model failure times and a univariate Gamma distributed frailty by all systems failure times. Classical inferential methods are used to estimate the parameters and reliability predictors of systems under IRs. An extensive simulation study is carried out under different scenarios to investigate the suitability of the models and the asymptotic consistency and efficiency properties of the maximum likelihood estimators. Finally, we illustrate the practical relevance of the proposed models on a real data set of sugarcane harvesters.
Joint work with: Éder S. Brito, Vera L. D. Tomazella, Paulo H. Ferreira, Francisco Louzada Neto, Oilson A. Gonzatto Junior.
El uso de distintos Sistemas de Gestión de Aprendizaje o plataformas educativas se ha convertido en una herramienta clave en el ámbito educativo. Estos sistemas generan diariamente un enorme volumen de datos tanto de estudiantes como de docentes. Transformar estos datos en información relevante para la toma de decisiones representa un gran desafío, debido a la complejidad de su estructura y a la dificultad de resumir el proceso de aprendizaje a partir de los registros disponibles.
En este trabajo se presentan métodos para transformar los datos de plataformas educativas en información relevante y explorar cómo esta puede utilizarse para predecir el desempeño académico en educación primaria pública en Uruguay. Se aplican métodos de aprendizaje estadístico Bayesianos para predecir rendimiento académico a partir de los patrones de uso de la plataforma Little Bridge, así como variables sociodemográficas y datos a nivel institucional. Específicamente, se utiliza el modelo BART (Bayesian Additive Regression Trees) y se compara su desempeño predictivo con Random Forest. El enfoque Bayesiano es seleccionado debido a la capacidad de incorporar efectos aleatorios a nivel de escuela, lo cual permite analizar los procesos de aprendizaje en múltiples niveles.
Los resultados pueden aplicarse tanto a nivel individual —para la identificación temprana de estudiantes en riesgo— como a nivel institucional, para destacar centros educativos que requieren intervención o aquellos que pueden servir como modelos de éxito.
Assessing agreement between instruments is fundamental in clinical and observational studies to evaluate how similarly two methods measure the same set of subjects. In this talk, we present two extensions of a widely used coefficient for assessing agreement between continuous variables. The first extension introduces a novel agreement coefficient for lattice sequences observed over the same areal units, motivated by the comparison of poverty measurement methodologies in Chile. The second extension proposes a new coefficient, denoted as ρ1, designed to measure agreement between continuous measurements obtained from two instruments observing the same experimental units. Unlike traditional approaches, ρ1 is based on L1 distances, providing robustness to outliers and avoiding dependence on nuisance parameters. Both proposals are supported by theoretical results, an inference framework, and simulation studies that illustrate their performance and practical relevance.
The dynamics of a rain forest is extremely complex involving births, deaths and growth
of trees with complex interactions between trees, animals, climate, and environment. We
consider the patterns of recruits (new trees) and dead trees between rain forest censuses.
For a current census we specify regression models for the conditional intensity of recruits
and the conditional probabilities of death given the current trees and spatial covariates. We
estimate regression parameters using conditional composite likelihood functions that only
involve the conditional first order properties of the data. When constructing assumption
lean estimators of covariance matrices of parameter estimates we only need mild assumptions
of decaying conditional correlations in space while assumptions regarding correlations over
time are avoided by exploiting conditional centering of composite likelihood score functions.
Time series of point patterns from rain forest censuses are quite short while each point
pattern covers a fairly big spatial region. To obtain asymptotic results we therefore use a
central limit theorem for the fixed timespan - increasing spatial domain asymptotic setting.
This also allows us to handle the challenge of using stochastic covariates constructed from
past point patterns. Conveniently, it suffices to impose weak dependence assumptions on
the innovations of the space-time process. We investigate the proposed methodology by
simulation studies and an application to rain forest data.
Matrix-variate distributions are powerful tools for modeling three-way datasets that often arise in longitudinal and multidimensional spatio-temporal studies. However, observations in these datasets can be missing or subject to some detec- tion limits because of the restriction of the experimental apparatus. Here, we develop an efficient EM-type algorithm for maximum likelihood estimation of parameters, in the context of interval-censored and/or missing data, utilizing the matrix-variate normal distribution. This algorithm provides closed-form expres- sions that rely on truncated moments, offering a reliable approach to parameter estimation under these conditions. Results obtained from the analysis of both simulated data and real case studies concerning water quality monitoring are reported to demonstrate the effectiveness of the proposed method.
For large, clustered survival studies, usual parametric and semi-parametric regression are inappropriate and inadequate when the appropriate functional forms of the covariates and their interactions in hazard functions are unknown, and random cluster effects as well as some unknown cluster-level covariates are spatially correlated. We present a general nonparametric method for such studies under the Bayesian ensemble learning paradigm called Soft Bayesian Additive Regression Trees (SBART in short).Our additional methodological and computational challenges include large number of clusters, variable cluster sizes, and proper statistical augmentation of the unobservable cluster-level covariate using a data registry different from the main survival study. We use an innovative 3-step computational tool based on latent variables to address our computational challenges. Using two different data resources, we illustrate the practical implementation of our method and its advantages over existing methods by assessing the impacts of intervention in some cluster/county level and patient-level covariates to mitigate existing disparity in breast cancer survival in 67 Florida counties (clusters) . Florida Cancer Registry (FCR) is used to obtain clustered survival data with patient-level covariates, and the Behavioral Risk Factor Surveillance Survey (BRFSS) is used as to obtain further data information on an unobservable county-level covariate of Screening Mammography Utilization (SMU).
Neal (1996) demostró que las redes neuronales Bayesianas (BNN) de una capa infinitamente anchas convergen a un proceso Gaussiano (GP), cuando los pesos tienen una previa de varianza finita. Cho & Saul (2009) presentaron una fórmula recursiva para procesos de kernel profundos, relacionando la matriz de covarianza de una capa con la matriz de covarianza de la capa anterior. Más aún, obtuvieron una fórmula explícita para la recursión con algunas funciones de activación comunes, incluyendo la ReLU. Trabajos posteriores han fortalecido estos resultados a arquitecturas más complejas, obteniendo límites similares para redes más profundas. A pesar de esto, trabajos recientes, incluyendo Aitchison et al. (2021), destacan como los kernels de covarianza obtenidos de esta forma son determinísticos y así imposibilitan el aprendizaje de las represenciones de la red límite, lo cual equivale a aprender un kernel posterior que sea no-degenerado dadas las observaciones. Para abordar esto proponen añadir un ruido artifical y así que el kernel retenga estocasticidad. Sin embargo, este ruido artifical puede criticarse pues no emerge del límite de la arquitectura de una BNN. Buscando evitar esto, demostramos que una red neuronal Bayesiana profunda, donde la anchura de cada capa va a infinito, y todos los pesos tienen distribución conjunta elíptica con varianza infinita, convergen a un proceso con marginales α-estable en cada capa que tengan una representación condicionalmente Gaussiana. Estas covarianzas aleatorias pueden relacionarse recursivamente en la manera de Cho & Saul (2009), a pesar de que los procesos tengan comportamiento estable, y por tanto las covarianzas no están necesariamente definidas. Nuestros resultados proveen generalizaciones a nuestro trabajo previo de Loría & Bhadra (2024) en redes de una capa, a redes de múltiples capas y evitando la intensa carga computacional. Las ventajas computacionales y estadísticas resaltan sobre otros métodos en simulaciones y en bases de datos de referencia.