<div>The multi-armed bandit (MAB) problem refers to the task of sequentially assigning treatments to experimental units so as to identify the best treatment(s) while controlling the opportunity cost of further investigation. Many algorithms have been developed that attempt to balance this trade-off between exploiting the seemingly optimum treatment and exploring the other treatments. The selection of an MAB algorithm for implementation in a particular context is often performed by comparing candidate algorithms in terms of their abilities to control the expected regret of exploration versus exploitation. This singular criterion of mean regret is insufficient for many practical problems, and therefore an additional criterion that should be considered is control of the variance, or risk, of regret.</div><div>This work provides an overview of how the existing prominent MAB algorithms handle both criteria. We additionally investigate the effects of incorporating prior information into an algorithm's model, including how sharing information across treatments affects the mean and variance of regret.</div><div>A unified and accessible framework does not currently exist for constructing MAB algorithms that control both of these criteria. To this end, we develop such a framework based on the two elementary concepts of dismemberment of treatments and a designed learning phase prior to dismemberment. These concepts can be incorporated into existing MAB algorithms to effectively yield new algorithms that better control the expectation and variance of regret. We demonstrate the utility of our framework by constructing new variants of the Thompson sampler that involve a small number of simple tuning parameters. As we illustrate in simulation and case studies, these new algorithms are implemented in a straightforward manner and achieve improved control of both regret criteria compared to the traditional Thompson sampler. Ultimately, our consideration of additional criteria besides expected regret illuminates novel insights into the multi-armed bandit problem.</div><div>Finally, we present visualization methods, and a corresponding R Shiny app for their practical execution, that can yield insights into the comparative performances of popular MAB algorithms. Our visualizations illuminate the frequentist dynamics of these algorithms in terms of how they perform the exploration-exploitation trade-off over their populations of realizations as well as the algorithms' relative regret behaviors. The constructions of our visualizations facilitate a straightforward understanding of complicated MAB algorithms, so that our visualizations and app can serve as unique and interesting pedagogical tools for students and instructors of experimental design.</div>

La realidad mixta, unificación de la realidad virtual y la realidad aumentada, posee muchas expectativas debido a las grandes tendencias que han surgido desde su creación y la forma en que ha fusionado casi en su totalidad a nuestro mundo real con el mundo digital, con la proyección de objetos digitales que estimulan los sentidos, logrando obtener una percepción similar a los objetos del entorno real y llevando su uso a múltiples posibilidades. En la investigación se identificó la problemática que aborda la necesidad de profundizar sobre las propiedades de la realidad mixta y los objetivos a trazar para cubrir con dicha necesidad. Durante el proyecto se logró recolectar información y crear un catálogo sobre los distintos tipos de aplicaciones, dispositivos y soluciones tecnológicas implementadas referente a la tecnología. Se investigó acerca de la parte teórica de la realidad mixta en base a las distintas definiciones del autor seminal y de expertos en la materia, además de las definiciones sobre las tecnologías con funcionalidades similares. Además, se procesó la información obtenida, identificando los rubros de negocio en donde se desempeña la realidad Mixta. Finalmente, se logró crear una taxonomía de realidad mixta y un gráfico estadístico de la participación de cada rubro de negocio en el mercado, con el fin de poder tener un panorama claro de la adopción y el valor comercial de cada rubro en donde se ejerce dicha tecnología y que pueda ser utilizado como referencia para la creación de proyectos de tecnología. / Mixed reality, the union of virtual reality and augmented reality, has high expectations due to the biggest trends that have emerged since its inception and the way in which it has almost entirely merged the real world with the digital world with the projection of digital objects that stimulate the senses, achieving a perception similar to the objects in the real environment and taking their use to multiple possibilities. The research identified the problem that addresses the need to delve into the properties of mixed reality and the objectives to be set in order to meet this need. During the project, information was collected in order to create a catalog on the different types of applications, devices and technological solutions implemented regarding that technology. The theoretical part of mixed reality was researched based on the different definitions given by authors and experts in the field, in addition to the definitions of technologies with similar functionalities. Moreover, the information obtained was processed, identifying the business areas where the mixed reality operates. Finally, it was possible to create a mixed reality taxonomy and a statistical graph of the participation of each business area in the market, for the purpose of being able to have a clear overview of the adoption and commercial value of each area where said technology is used and that can be employed as a reference for the creation of future technology projects. / Tesis

Statistical and scientific computing applications exhibit characteristics that are fundamentally different from classical database system application domains. The CROSS-DB data model presented in this paper is optimized for use in such applications by providing advanced data modelling methods and application-oriented query facilities, thus providing a framework for optimized data management procedures. CROSS-DB (which stands for Classification-oriented, Redundancy-based Optimization of Statistical and Scientific DataBases) is based on a multidimensional data view. The model differs from other approaches by o~ering two complementary rnechanisrnsfor structuring qualifying information, classification and feature description. Using these mechanisms results in a normalized, low-dimensional database schema which ensures both, modelling uniqueness and understandability while providing enhanced modelling flexibility.