Inferencia estatística

Titulación: Grao en Enxeñaría Informática -- Materia: EstatísticaAs bases da probabilidade e a estatística, segundo a Association for Computing Machinery e a IEEE Computer Society, subxacen aos conceptos de fiabilidade, seguridade e dependencia, factores fundamentais no ámbito da Enxeñaría en xeral e da Enxeñaría Informática, en particular. Con esta premisa, as devanditas asociacións elaboraron unhas guías para o deseño dos currículos formativos nos Graos en Enxeñaría Informática, onde se establece como obxectivo fundamental que o alumnado destes títulos adquira coñecementos dos modelos de probabilidade discretos e continuos, das distribucións na mostraxe, dos métodos de estimación e contraste e do modelado a través da regresión. No currículo do Grao en Enxeñaría Informática da Universidade de Santiago de Compostela (USC), a Estatística é unha materia do segundo semestre do primeiro curso, pertencente ao módulo de Matemáticas xunto con Álxebra, Fundamentos de Matemáticas, Matemática Discreta (primeiro semestre) e Cálculo e Análise Numérica (segundo semestre). Todas estas son materias básicas e polo tanto de carácter xeral, nas que se debe realizar unha tarefa de nivelación dos coñecementos do alumnado, proporcionando asemade os alicerces metodolóxicos para desenvolvementos posteriores noutras áreas como a representación gráfica ou a xestión empresarial. Nesta unidade didáctica presentaranse inicialmente os obxectivos da UD III (Inferencia Estatística), detallando a continuación os contidos máis relevantes da mesma considerando á súa vez tres bloques temáticos diferenciados (introdución á Inferencia Estatística, estimación de parámetros e contraste de hipóteses). Para unha selección adecuada dos contidos a incluír na UD, debe terse presente que o obxectivo final da Inferencia Estatística é tirar conclusións sobre una poboación (conxunto homoxéneo de individuos sobre os que se estudan características observables). Estas conclusións sobre o comportamento da poboación poden referirse a aspectos paramétricos, a comportamentos globais da distribución ou a comparativas con outras poboacións ou entre grupos dentro da mesma. Así, as técnicas da Inferencia Estatística poderían clasificarse en dous tipos, atendendo ao seu obxectivo final, se ben ambos os dous están estreitamente relacionados: a estimación de parámetros, de maneira puntual ou mediante intervalos, e o contraste de hipóteses. Abordar estes problemas dende un enfoque xeral presenta unha gran dificultade matemática, que excedería os coñecementos do alumnado de primeiro curso, polo que os contidos desta UD restrinxiranse, nun primeiro termo, a poboacións normais e ao estudo de proporcións. Malia a imposibilidade dun tratamento amplo do problema da estimación de parámetros, incluiranse algunhas breves mencións ás metodoloxías xerais de estimación, rematando esta UD con algunhas nocións sobre contrastes non paramétricos. Os contidos desta UD atópanse distribuídos en tres bloques temáticos, consecutivos no tempo, dado que cada un deles senta as bases do seguinte. As gráficas presentadas foron elaboradas co software estatístico R. No Anexo, inclúese unha breve presentación da libraría rpanel, en concreto, da utilidade rpcartoons que permite realizar algunhas ilustracións gráficas relacionadas cos contidos desta UD.Universidade de Santiago de Compostela. Servizo de Normalización Lingüístic

An introduction to statistical methods for circular data

Angles, directions, events, occurrences along time... all of them can be viewed as data on a circle (circular data). The particular nature of this type of data requires specific and adapted inferential and modelling procedures. Although there are quite a few references on this topic, and despite circular data are quite common in many applied sciences, they are frequently overlooked. This brief introduction aims to give the reader just some basic ideas on circular data analysis (with some mentions to the general case of spherical or directional data), providing some relevant references and tools for their application in practiceS

Nonparametric estimation of directional highest density regions

Highest density regions (HDRs) are defined as level sets containing sample points of relatively high density. Although Euclidean HDR estimation from a random sample, generated from the underlying density, has been widely considered in the statistical literature, this problem has not been contemplated for directional data yet. In this work, directional HDRs are formally defined and plug-in estimators based on kernel smoothing and associated confidence regions are proposed. We also provide a new suitable bootstrap bandwidth selector for plug-in HDRs estimation based on the minimization of an error criteria that involves the Hausdorff distance between the boundaries of the theoretical and estimated HDRs. An extensive simulation study shows the performance of the resulting estimator for the circle and for the sphere. The methodology is applied to analyze two real data sets in animal orientation and seismologyOpen Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. R.M. Crujeiras and P. Saavedra-Nieves acknowledge the financial support of Ministerio de Economía y Competitividad and Ministerio de Ciencia e Innovación of the Spanish government under grants MTM2016-76969P, MTM2017-089422-P, PID2020-118101GB-I00 and PID2020-116587GB-I00 and ERDF. Authors also thank Elena Vázquez Abal for her help, Prof. Felicita Scapini for providing the sandhoppers data (collected under the support of the European Project ERB ICI8-CT98-0270), the computational resources of the CESGA Supercomputing Center and the referees for the constructive comments which have improved the paperS

A circular nonhomogeneous hidden Markov field for the spatial segmentation of wildfire occurrences

This is the pre-peer reviewed version of the following article: Ameijeiras‐Alonso, J, Lagona, F, Ranalli, M, Crujeiras, RM. A circular nonhomogeneous hidden Markov field for the spatial segmentation of wildfire occurrences. Environmetrics. 2019; 30:e2501. https://doi.org/10.1002/env.2501, which has been published in final form at https://doi.org/10.1002/env.2501. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived VersionsMotivated by studies of wildfire seasonality, we propose a nonhomogeneous hidden Markov random field to model the spatial distribution of georeferenced fire occurrences during the year, by representing occurrence times as circular data. The model is based on a mixture of Kato–Jones circular densities, whose parameters vary across space according to a latent nonhomogeneous Potts model, modulated by georeferenced covariates. It allows us to segment fire occurrences according to a finite number of latent classes that represent the conditional distributions of the data under specific periods of the year, simultaneously accounting for unobserved heterogeneity and spatial autocorrelation. Further, it parsimoniously accommodates specific features of wildfire occurrence data such as multimodality, skewness, and kurtosis. Due to the numerical intractability of the likelihood function, estimation of the parameters is based on composite likelihood methods. It reduces to a computationally efficient expectation–maximization algorithm that iteratively alternates the maximization of a weighted composite likelihood function with weights updating. The proposal is illustrated in a study of wildfire occurrences in the Iberian Peninsula during a decadeJose Ameijeiras‐Alonso and Rosa M. Crujeiras gratefully acknowledge the support of Project MTM2016‐76969‐P (Spanish State Research Agency, AEI), co‐funded by the European Regional Development Fund (ERDF), IAP network from Belgian Science Policy. Part of the research was carried out by Jose Ameijeiras‐Alonso during his visit to University of Roma Tre, supported by Grants BES‐2014‐071006 and EEBB‐I‐17‐12716 from the Spanish Ministry of Economy, Industry and Competitiveness. Francesco Lagona is supported by the 2015 PRIN supported project “Environmental processes and human activities: capturing their interactions via statistical methods”, funded by the Italian Ministry of Education, University and Scientific ResearchNO

Gamestorming for the Conceptual Design of Products and Processes in the context of engineering education

Creating an ideal environment to develop creativity and innovation in engineering education is a real challenge. One alternative approach can be based in the application of Gamestorming methodology that considers the use of games in the process of brainstorming. Presenting the problem in a game format eludes the conventional lecturing and frees the participants to think creatively to solve problems. In this contribution, the adaptation of the Gamestorming methodology was applied in different Bachelor and Master courses of Chemical Engineering and Environmental Engineering in the University of Santiago de Compostela (Spain). The aim of this initiative was to develop students’ creativity and teamwork, where the class divided in working groups propose and assess alternatives in the Conceptual Design of Products and Processes. Specifically, two examples of the application of the methodology are provided: (i) a wood box for wine storage was remodeled according to a number of requisites: functionality, savings of energy consumption and reduction of environmental impact; (ii) the conceptual design of a treatment system for the removal of pollutants present in a gaseous stream to accomplish the targets of wide applicability and efficiency as well as reduced cost and environmental impact. A total of 129 students from 4 different academic years participated and the survey performed after completing the activity rated this methodology as a mechanism to foster their creativity in the progress of teamwork toward decision making processS

Mode testing, critical bandwidth and excess mass

This is a post-peer-review, pre-copyedit version of an article published in TEST. The final authenticated version is available online at: https://doi.org/10.1007/s11749-018-0611-5The identification of peaks or maxima in probability densities, by mode testing or bump hunting, has become an important problem in applied fields. For real random variables, this task has been approached in the statistical literature from different perspectives, with the proposal of testing procedures which are based on kernel density estimators or on the quantification of excess mass. However, none of the existing proposals for testing the number of modes provides a satisfactory performance in practice. In this work, a new procedure which combines the previous approaches (smoothing and excess mass) is presented together with a revision on the previous proposals. The new method is compared with the existing ones in an extensive simulation study, showing a superior behaviour, with good calibration and power results. Theoretical justification for its performance is also obtained. A real data example on philatelic data is also included for illustration purposes, revising previous approaches and discussing the results with the new procedureThe authors gratefully acknowledge the support of Projects MTM2016-76969-P (Spanish State Research Agency, AEI) and MTM2013-41383-P (Spanish Ministry of Economy, Industry and Competitiveness), both co-funded by the European Regional Development Fund (ERDF), IAP network from Belgian Science Policy. Work of J. Ameijeiras-Alonso has been supported by the Ph.D. Grant BES-2014-071006 from the Spanish Ministry of Economy, Industry and CompetitivenessS

Estadística no paramétrica: pasado, presente y futuro

La estadística no paramétrica engloba una serie de técnicas de inferencia cuya característica principal es la ausencia de un modelo paramétrico de distribución subyacente. Sin pretender revisar todos y cada uno de los conceptos e ideas que conforman este planteamiento, es nuestro objetivo que el lector se familiarice con términos como técnicas de suavizado, Bootstrap, verosimilitud empírica o datos funcionales, su porqué, su utilidad, su relevancia en la estadística actual y la posible proyección hacia el futuroS

On the second order properties of the multidimensional periodogram for regularly spaced data

Recently there is growing interest in improving the level of knowledge of spatial and spatio-temporal processes using spectral techniques. The properties of the estimator of the spectral density, the periodogram, have been broadly studied under different asymptotic assumptions that imply a valuable loss of information about the behavior of the underlying process that is often observed on a grid of small size and with sparse data. In this scheme, neither increasing domain nor shrinking asymptotics applies. The goal of this paper is to study the properties of the multidimensional periodogram, under both cases of tapering and no tapering, and the assumption of finite dimensionality of the regular lattice where the process is observed. We present some theoretical results regarding the second order properties of the multidimensional periodogram. Furthermore, we show that, independent of the tapering procedure, periodogram values present a dependence structure which is not stationary and which particularly depends on weights which are proportional to the Bartlett kernel or the chosen taperThis work was supported by the Spanish Ministry of Science and Education project MTM2005-0020 and grants MTM2004-06231 and BES2003-0581, and by Xunta de Galicia projects PGIDIT06PXIB207009PR and PGIDIT03PXIC20702PNS

Un nuevo método para analizar y representar las variaciones de temperatura del suelo en ambientes fríos. Los Andes Fueguinos, Tierra del Fuego, Argentina

The thermal response of soils in cold environments has been investigated in numerous studies. The data considered here were obtained in a study carried out in Tierra del Fuego, Argentina, as part of the IV International Polar Year. Temperature sensors were installed at ground level (0) and depths of -10, -20 and -60 cm in the study area, with the aim of characterizing the thermal response by detecting diurnal and annual variations. The study has two main aims. The first is to present and discuss the study findings regarding the thermal response of a soil in a sub-Antarctic environment by using classical descriptive analysis. The second, closely related, aim is to apply some novel statistical tools that would help improve this description. The study of freeze-thaw patterns can be approached from a non-parametric perspective, while taking into account the cyclical nature of the data. Data are considered cyclical when they can be represented on a unit circle, as with the hours in which certain events occur throughout a day (e.g. freezing and thawing). Analysis of this type of data is very different from the analysis of scalar data, as regards both descriptive and graphical measures. The application in this study of methods used to represent and analyse cyclical data improved visualization of the data and interpretation of the analytical findings. The main contribution of the present study is the use of estimators of the nuclear type density and derived techniques, such as the CircSiZer map, which enabled identification of significant freeze-thaw patterns. In addition, the relationships between the temperature recordings at different points were analysed using Taylor diagramsLos resultados de las investigaciones sobre la respuesta térmica del suelo en ambientes fríos han sido recogidos en un gran número de artículos. Las muestras de datos consideradas en este trabajo pertenecen también a un ambiente frío y se han obtenido de una investigación realizada en Tierra del Fuego, Argentina, bajo los auspicios del Año Polar Internacional. Con el fin de caracterizar la respuesta térmica, se instalaron diferentes sensores de temperatura a 0, -10, -20 y -60 cm de profundidad, permitiendo la detección de variaciones anuales y diarias. Este trabajo persigue un doble objetivo. Por un lado, la presentación de resultados y discusión sobre los mismos en relación al comportamiento térmico del suelo en un ambiente subantártico. Por otro lado, y apoyando al objetivo anterior, se introducen algunas herramientas estadísticas novedosas en este contexto, si bien el estudio se acompaña de análisis descriptivos clásicos. El estudio de patrones de congelación y descongelación puede enfocarse desde una perspectiva no paramétrica, a la vez que se tiene en cuenta la naturaleza circular (cíclica) de los datos. Una muestra de datos se considera circular cuando puede representarse sobre un círculo de radio unidad. Esto ocurre, por ejemplo, con las horas en las que suceden determinados eventos a lo largo de un día (por ejemplo, congelaciones y descongelaciones). El análisis de este tipo de datos es radicalmente distinto del que se realiza sobre datos escalares, tanto en lo que se refiere a medidas descriptivas como a métodos gráficos. El uso de representaciones y herramientas propias del análisis de datos circulares realizado en este trabajo permite una mejor visualización de los datos y de los resultados de su análisis. Como principal aportación, cabe destacar el uso de estimadores de la densidad tipo núcleo y técnicas derivadas, como el mapa CircSiZer, que identifica patrones significativos de congelación/descongelación. Además, el análisis de las relaciones entre registros de temperaturas en distintos puntos se presenta a través del uso de Diagramas de TaylorThis research was funded by the Ministry of Education and Science (Spain) projects (POL2006-09071) as a contribution to the fourth International Polar Year. Research by M. Oliveira, R.M. Crujeiras and A. Rodríguez was partially supported by grants MTM2013-41383P and MTM2016-76929P awarded by the Ministry of Economy and Competitiveness and AEI/FEDER, SpainS