20 research outputs found
Fooled by bursts. A Goal per Minute model for the World Cup
On the occasion of the last FIFA World Cup in Brazil, The Economist published
a plot depicting how many goals have been scored in all World Cup competitions
until present, minute by minute. The plot was followed by a naive and poorly
grounded qualitative analysis. In the present article we use The Economist
dataset to check its conclusions, update previous results from literature and
offer a new model. In particular, it will be shown that first and second half
game have different scoring rates. In the first half the scoring rate can be
considered constant. In the second it increases linearly with time
Functional linear models
This work aims at the exposition of two different results we have obtained in Functional Data Analysis. The first is a variable selection method in Functional Regression which is an adaptation of the well known Lasso technique.
The second is a brand new Random Walk test for Functional Time Series.
Being the results afferent to different areas of Functional Data Analysis, as well as of general Statistics, the introduction will be divided in three parts.
Firstly we expose the fundamentals of Functional Data Analysis. Then we will recall some variable selection methods in ordinary Linear Regression.
Finally we will review some basics of Time Series analysis and brie y review some existing Random Walk tests. These introductory sections will motivate our research putting it in a general framework. Since Functional Data Analysis can be seen as a data reduction method we will talk incidentally of Big Data and we will provide some comments on the current definition of it.
All results of our research are supported by extensive computer simulations and in general, all of FDA is based on extensive computer deployment so some attention will be given to software and computation methods. The Lasso has been used in Functional Regression before this work, our contribution is twofold, we provide a reduction of Lasso in Functional Regression from a functional optimization problem to a numerical one via algebraic manipulations, no sampling is required. Then, we augment the Lasso with a post hoc analysis method which helps deciding which regressors have to be dropped, we called this augmented strategy The Shaked Lasso. About testing if a Functional Autoregressive Process can be considered a Random
Walk, our proposed test, as far as we could establish, is the first one in
literature.En esta tesis se abordan dos problemas relacionados con el análisis de datos funcionales. El primero consiste en selección de variables en un problema de regresión con respuesta funcional adaptando la técnica conocida como Lasso. El segundo problema pretende abrir una línea nueva de investigación proponiendo un test para contrastar si una serie temporal funcional puede ser considerada como un camino aleatorio.
Como los resultados que se muestran en esta tesis están relacionados con áreas diferentes del análisis de datos funcionales y de la estadística en general, la Introducción está dividida en tres partes. En primer lugar, se exponen los fundamentos del análisis de datos funcionales. En la segunda sección se revisan algunos métodos de selección de variables en regresión lineal y por último, se recopilan brevemente las bases de series temporales así como los contrastes de hipótesis que se han utilizado en la literatura para contrastar caminos aleatorios. Estas secciones introductorias ayudan a motivar las aportaciones de la tesis encuadrándolas en su entorno de investigación. Además, ya que el análisis de datos funcionales se puede ver como un método de reducción de la dimensión de los datos, se incluirán algunos comentarios sobre Big Data y sus definiciones.
Todos los resultados de nuestra investigación están soportados por un extenso trabajo de simulación y, puesto que en los métodos estadísticos aplicados a datos funcionales es esencial la parte de computación, se ha prestado especial atención a todos los aspectos relacionados con el software y la modelización. El procedimiento Lasso de selección de variables se ha aplicado anteriormente en la literatura de regresión funcional pero no a los modelos que se analizan en la tesis. Las contribuciones en este aspecto son dos: por una parte se proporciona un método de selección de variables Lasso para un problema de regresión con respuesta funcional convirtiendo un problema de optimización funcional a un problema de optimización numérica vía manipulaciones algebraicas y sin necesidad de remuestreo. Después de ejecutar el problema de optimización, como segunda contribución se propone un análisis de las soluciones para decidir los regresores que deben ser eliminados. Este segundo análisis se ha denominado The Shaked Lasso porque se basa en alterar un parámetro del proceso de optimización para observar cómo se mueven las soluciones. Respecto al segundo capítulo de contribuciones de la tesis, se propone un contraste de hipótesis para testear si un proceso autoregresivo funcional se puede considerar como un camino aleatorio. Hasta lo que nosotros conocemos en la literatura en este campo, es el primer test de este tipo que se propone en la literatura.Programa Oficial de Doctorado en Ingeniería MatemáticaPresidente: Francisco Javier Prieto Fernández.- Secretario: Eva Senra Díaz.- Vocal: Ana Justel Eusebi
A Random Walk Test for Functional Time Series
In this paper we introduce a Random Walk test for Functional Autoregressive Processes of Order One. The test is non parametric, based on Bootstrap and Functional Principal Components. The power of the test is shown through an extensive Montecarlo simulation. We apply the test to two real dataset, Bitcoin prices and electrical energy consumption in France.The authors acknowledge financial support from the Spanish Ministry of
Economy and Competition, research project ECO2012-38442
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On the use of plume models to estimate the flux in volcanic gas plumes.
Many of the standard volcanic gas flux measurement approaches involve absorption spectroscopy in combination with wind speed measurements. Here, we present a new method using video images of volcanic plumes to measure the speed of convective structures combined with classical plume theory to estimate volcanic fluxes. We apply the method to a nearly vertical gas plume at Villarrica Volcano, Chile, and a wind-blown gas plume at Mount Etna, Italy. Our estimates of the gas fluxes are consistent in magnitude with previous reported fluxes obtained by spectroscopy and electrochemical sensors for these volcanoes. Compared to conventional gas flux measurement techniques focusing on SO2, our new model also has the potential to be used for sulfur-poor plumes in hydrothermal systems because it estimates the H2O flux
Lasso variable selection in functional regression
Functional Regression has been an active subject of research in the last two decades but
still lacks a secure variable selection methodology. Lasso is a well known effective
technique for parameters shrinkage and variable selection in regression problems. In this
work we generalize the Lasso technique to select variables in the functional regression
framework and show it performs well. In particular, we focus on the case of functional
regression with scalar regressors and functional response. Reduce the associated
functional optimization problem to a convex optimization on scalars. Find its solutions
and stress their interpretability. We apply the technique to simulated data sets as well as
to a new real data set: car velocity functions in low speed car accidents, a frequent cause
of whiplash injuries. By “Functional Lasso” we discover which car characteristics influence
more car speed and which can be considered not relevantThis research was
supported in part by Spanish Ministry of Education and Science grants MEC 2009/00035/001,
ECO2011-25706 and SEJ200
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On the use of plume models to estimate the flux in volcanic gas plumes.
Many of the standard volcanic gas flux measurement approaches involve absorption spectroscopy in combination with wind speed measurements. Here, we present a new method using video images of volcanic plumes to measure the speed of convective structures combined with classical plume theory to estimate volcanic fluxes. We apply the method to a nearly vertical gas plume at Villarrica Volcano, Chile, and a wind-blown gas plume at Mount Etna, Italy. Our estimates of the gas fluxes are consistent in magnitude with previous reported fluxes obtained by spectroscopy and electrochemical sensors for these volcanoes. Compared to conventional gas flux measurement techniques focusing on SO2, our new model also has the potential to be used for sulfur-poor plumes in hydrothermal systems because it estimates the H2O flux
Stokes settling and particle-laden plumes: implications for deep-sea mining and volcanic eruption plumes
Turbulent buoyant plumes moving through density
stratified environments transport large volumes of
fluid vertically. Eventually, the fluid reaches its
neutral buoyancy level at which it intrudes into the
environment. For single-phase plume, the well known
theory of Morton, Taylor and Turner [1] describes the
height of the intrusion with great accuracy. However,
in multiphase plumes, such as descending particle
plumes formed from the surface vessel during deep-
sea mining operations, or ascending volcanic plumes,
consisting of hot gas and dense ash particles, the
sedimentation of particles can change the buoyancy of
the fluid very significantly. Even if the plume speed
far exceeds the sedimentation speed, the ultimate
intrusion height of the fluid may be significantly
affected by particle sedimentation. We explore this
process, illustrating the phenomena with a series of
analogue experiments and some simple modelling,
and we discuss the applications in helping to quantify
some environmental impacts of deep-sea mining and
in helping to assess the eruption conditions leading to
the formation of large laterally spreading ash clouds
in the atmosphere
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The ventilation of buildings and other mitigating measures for COVID-19: a focus on wintertime.
The year 2020 has seen the emergence of a global pandemic as a result of the disease COVID-19. This report reviews knowledge of the transmission of COVID-19 indoors, examines the evidence for mitigating measures, and considers the implications for wintertime with a focus on ventilation.This work was undertaken as a contribution to the Rapid Assistance in Modelling the Pandemic (RAMP) initiative, coordinated by the Royal Society
Steady-state particle transport in a displacement-ventilated enclosure
Non UBCUnreviewedAuthor affiliation: BP Institute for Multiphase Flow, University of CambridgeGraduat
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Video-based measurements of the entrainment, speed and mass flux in a wind-blown eruption column at Eyjafjallajökull volcano, Iceland
On May 4 2010 a wind-blown ash plume issued from Eyjafjallajökull volcano in Iceland. Analysis of a 17-minute long video recording of the eruption suggests that within km of the vent, the flow was moving with the wind and rising under buoyancy, following a trajectory directly analogous with laboratory experiments of turbulent buoyant plumes in a cross-flow. The visible radius of the time-averaged ash cloud grew with height at a rate , corresponding to an entrainment coefficient of , again consistent with laboratory experiments. By analysing the frames in the video and comparing the shape of the plume to that predicted by the model, we estimate that during the 17 minutes recorded, the eruption rate gradually decreased by about 43 from an initial eruption rate of kg/s to kg/s. The analysis reported herein opens the way to assess eruption rates and eruption column processes from video recordings during explosive volcanic eruptions