MATH-463: Mathematical modelling of behavior

Summary

Discrete choice models allow for the analysis and prediction of individuals' choice behavior. The objective of the course is to introduce both methodological and applied aspects, in the field of marketing, transportation, and finance.

Official source

https://edu.epfl.ch/coursebook/en/mathematical-modelling-of-behavior-MATH-463

Moodle Page

http://go.epfl.ch/MATH-463

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Michel Bierlaire

Born in 1967, Michel Bierlaire holds a PhD in Mathematical Sciences from the Facultés Universitaires Notre-Dame de la Paix, Namur, Belgium (University of Namur). Between 1995 and 1998, he was research associate and project manager at the Intelligent Transportation Systems Program of the Massachusetts Institute of Technology (Cambridge, Ma, USA). Between 1998 and 2006, he was a junior faculty in the Operations Research group ROSO within the Institute of Mathematics at EPFL. In 2006, he was appointed associate professor in the School of Architecture, Civil and Environmental Engineering at EPFL, where he became the director of the Transport and Mobility laboratory. Since 2009, he is the director of TraCE, the Transportation Center. From 2009 to 2017, he was the director of Doctoral Program in Civil and Environmental Engineering at EPFL. In 2012, he was appointed full professor at EPFL. Since September 2017, he is the head of the Civil Engineering Institute at EPFL. His main expertise is in the design, development and applications of models and algorithms for the design, analysis and management of transportation systems. Namely, he has been active in demand modeling (discrete choice models, estimation of origin-destination matrices), operations research (scheduling, assignment, etc.) and Dynamic Traffic Management Systems. As of August 2021, he has published 136 papers in international journals, 4 books, 41 book chapters, 193 articles in conference proceedings, 182 technical reports, and has given 195 scientific seminars. His Google Scholar h-index is 68. He is the founder, organizer and lecturer of the EPFL Advanced Continuing Education Course "Discrete Choice Analysis: Predicting Demand and Market Shares". He is the founder of hEART: the European Association for Research in Transportation. He was the founding Editor-in-Chief of the EURO Journal on Transportation and Logistics, from 2011 to 2019. He is an Associate Editor of Operations Research. He is the editor of two special issues for the journal Transportation Research Part C. He has been member of the Editorial Advisory Board (EAB) of Transportation Research Part B since 1995, of Transportation Research Part C since January 1, 2006.

Mathematical model

A mathematical model is an abstract description of a concrete system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science).

Discrete choice

In economics, discrete choice models, or qualitative choice models, describe, explain, and predict choices between two or more discrete alternatives, such as entering or not entering the labor market, or choosing between modes of transport. Such choices contrast with standard consumption models in which the quantity of each good consumed is assumed to be a continuous variable. In the continuous case, calculus methods (e.g. first-order conditions) can be used to determine the optimum amount chosen, and demand can be modeled empirically using regression analysis.

Rational choice theory

Rational choice theory refers to a set of guidelines that help understand economic and social behaviour. The theory originated in the eighteenth century and can be traced back to political economist and philosopher, Adam Smith. The theory postulates that an individual will perform a cost-benefit analysis to determine whether an option is right for them. It also suggests that an individual's self-driven rational actions will help better the overall economy. Rational choice theory looks at three concepts: rational actors, self interest and the invisible hand.

Mixed model

A mixed model, mixed-effects model or mixed error-component model is a statistical model containing both fixed effects and random effects. These models are useful in a wide variety of disciplines in the physical, biological and social sciences. They are particularly useful in settings where repeated measurements are made on the same statistical units (longitudinal study), or where measurements are made on clusters of related statistical units.

Multinomial logistic regression

In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.).