MATH-710: Data Analysis for Science and Engineering

Summary

An overview course intended for scientists and engineers who need to use statistical methods as part of their research, who have already attended a course at the second-year EPFL undergraduate level, and need revision and deepening of their knowledge at a more conceptual level.

Official source

https://edu.epfl.ch/coursebook/en/data-analysis-for-science-and-engineering-MATH-710

Moodle Page

http://go.epfl.ch/MATH-710

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Instructors (4)

Related concepts (143)

Related courses (86)

Related MOOCs (9)

Stephan Morgenthaler

ACADEMIC POSITIONS Professor of Applied Statistics, EPFL, 1988-present Associate Professor of Statistics, Yale University, 1987-1988 Assistant Professor of Statistics, Yale University, 1983-1987 Instructor of Mathematics, Massachusetts Institute of Technology, 1983-1984

Anthony Christopher Davison

Anthony Davison has published on a wide range of topics in statistical theory and methods, and on environmental, biological and financial applications. His main research interests are statistics of extremes, likelihood asymptotics, bootstrap and other resampling methods, and statistical modelling, with a particular focus on the first currently. Statistics of extremes concerns rare events such as storms, high winds and tides, extreme pollution episodes, sporting records, and the like. The subject has a long history, but under the impact of engineering and environmental problems has been an area of intense development in the past 20 years. Davison''s PhD work was in this area, in a project joint between the Departments of Mathematics and Mechanical Engineering at Imperial College, with the aim of modelling potential high exposures to radioactivity due to releases from nuclear installations. The key tools developed, joint with Richard Smith, were regression models for exceedances over high thresholds, which generalized earlier work by hydrologists, and formed the basis of some important later developments. This has led to an ongoing interest in extremes, and in particular their application to environmental and financial data. A major current interest is the development of suitable methods for modelling rare spatio-temporal events, particularly but not only in the context of climate change. Likelihood asymptotics too have undergone very substantial development since 1980. Key tools here have been saddlepoint and related approximations, which can give remarkably accurate approximate distribution and density functions even for very small sample sizes. These approximations can be used for wide classes of parametric models, but also for certain bootstrap and resampling problems. The literature on these methods can seem arcane, but they are potentially widely applicable, and Davison wrote a book joint with Nancy Reid and Alessandra Brazzale intended to promote their use in applications. Bootstrap methods are now used in many areas of application, where they can provide a researcher with accurate inferences tailor-made to the data available, rather than relying on large-sample or other approximations of doubtful validity. The key idea is to replace analytical calculations of biases, variances, confidence and prediction intervals, and other measures of uncertainty with computer simulation from a suitable statistical model. In a nonparametric situation this model consists of the data themselves, and the simulation simply involves resampling from the existing data, while in a parametric case it involves simulation from a suitable parametric model. There is a wide range of possibilities between these extremes, and the book by Davison and Hinkley explores these for many data examples, with the aim of showing how and when resampling methods succeed and why they can fail. He was Editor of Biometrika (2008-2017), Joint Editor of Journal of the Royal Statistical Society, series B (2000-2003), editor of the IMS Lecture Notes Monograph Series (2007), Associate Editor of Biometrika (1987-1999), and Associate Editor of the Brazilian Journal of Probability and Statistics (1987 2006). Currently he on the editorial board of Annual Reviews of Statistics and its Applications. He has served on committees of Royal Statistical Society and of the Institute of Mathematical Statistics. He is an elected Fellow of the American Statistical Assocation and of the Institute of Mathematical Statistics, an elected member of the International Statistical Institute, and a Chartered Statistician. In 2009 he was awarded a laurea honoris causa in Statistical Science by the University of Padova, in 2011 he held a Francqui Chair at Hasselt University, and in 2012 he was Mitchell Lecturer at the University of Glasgow. In 2015 he received the Guy Medal in Silver of the Royal Statistical Society and in 2018 was a Medallion Lecturer of the Institute of Mathematical Statistics.

Victor Panaretos

Darlene Goldstein

Log-linear model

A log-linear model is a mathematical model that takes the form of a function whose logarithm equals a linear combination of the parameters of the model, which makes it possible to apply (possibly multivariate) linear regression. That is, it has the general form in which the fi(X) are quantities that are functions of the variable X, in general a vector of values, while c and the wi stand for the model parameters. The term may specifically be used for: A log-linear plot or graph, which is a type of semi-log plot.

Scientific method

The scientific method is an empirical method for acquiring knowledge that has characterized the development of science since at least the 17th century (with notable practitioners in previous centuries; see the article history of scientific method for additional detail.) It involves careful observation, applying rigorous skepticism about what is observed, given that cognitive assumptions can distort how one interprets the observation.

Gaussian process

In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g.

Generalized additive model

In statistics, a generalized additive model (GAM) is a generalized linear model in which the linear response variable depends linearly on unknown smooth functions of some predictor variables, and interest focuses on inference about these smooth functions. GAMs were originally developed by Trevor Hastie and Robert Tibshirani to blend properties of generalized linear models with additive models. They can be interpreted as the discriminative generalization of the naive Bayes generative model.

Poisson point process

In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field.