# Author: Arthur Charpentier

This is the second part of a series on sports betting… Sports betting has long fascinated economists and statisticians. Griffith (1949) showed early on that horse race bettors put too much money on horses that have little chance of winning, and too little on those that have the best chance…

## A brief history of sports betting

this article was originaly published – in French – in variance.eu A report by the American Gaming Association (May 2017) estimated that between $100 billion and $400 billion was bet each year on an estimated gross income of between $5 billion and $20 billion, just for sports betting. We will…

## What it the interpretation of the diagonal for a ROC curve

Last Friday, we discussed the use of ROC curves to describe the goodness of a classifier. I did say that I will post a brief paragraph on the interpretation of the diagonal. If you look around some say that it describes the “strategy of randomly guessing a class“, that it…

## On the poor performance of classifiers in insurance models

Each time we have a case study in my actuarial courses (with real data), students are surprised to have hard time getting a “good” model, and they are always surprised to have a low AUC, when trying to model the probability to claim a loss, to die, to fraud, etc.…

## Variance decomposition and price segmentation in Insurance

Today, I was giving a talk at the Economics department, and I got a very interesting question about some tables I keep showing to explain why insurance companies like segmentation. The tables illustrate three different case. Here, S stands for the individual (random) loss. the first one is the case…

## Random thoughts on econometric models with (pure) random features

For my lectures on applied linear models, I wanted to illustrate the fact that the R^2 is never a good measure of the goodness of the model, since it’s quite easy to improve it. Consider the following dataset n=100 df=data.frame(matrix(rnorm(n*n),n,n)) names(df)=c("Y",paste("X",1:99,sep="")) with one variable of interest y, and 99 features…

## Do risk classes go beyond stereotypes?

Generalization, stereotypes and clichés In Thinking, Fast and Slow, Daniel Kahneman discusses at length the importance of stereotypes in understanding many decision-making processes. A so-called System 1 is used for quick decision-making: it allows us to recognize people and objects, helps us focus our attention, and encourages us to fear…

## Fondations of Machine Learning, part 5

This post is the nineth (and probably last) one of our series on the history and foundations of econometric and machine learning models. The first fours were on econometrics techniques. Part 8 is online here. Optimization and algorithmic aspects In econometrics, (numerical) optimization became omnipresent as soon as we left…

## Fondations of Machine Learning, part 4

This post is the eighth one of our series on the history and foundations of econometric and machine learning models. The first fours were on econometrics techniques. Part 7 is online here. Penalization and variables selection One important concept in econometrics is Ockham’s razor – also known as the law…

## Fondations of Machine Learning, part 2

This post is the sixth one of our series on the history and foundations of econometric and machine learning models. The first fours were on econometrics techniques. Part 5 is online here. The probabilistic formalism in the 80’s We have a training sample, with observations (\mathbf{x}_i,y_i) where the variables y…

## Fondations of Machine Learning, part 1

This post is the fifth one of our series on the history and foundations of econometric and machine learning models. The first fours were on econometrics techniques. Part 4 is online here. In parallel with these tools developed by, and for economists, a whole literature has been developed on similar…

## Probabilistic Fondations of Econometrics, part 4

This post is the fourth one of our series on the history and foundations of econometric and machine learning models. Part 3 is online here. Goodness of Fit, and Model In the Gaussian linear model, the determination coefficient – noted R^2 – is often used as a measure of fit…

## Probabilistic Fondations of Econometrics, part 3

This post is the third one of our series on the history and foundations of econometric and machine learning models. Part 2 is online here. Exponential family and linear models The Gaussian linear model is a special case of a large family of linear models, obtained when the conditional distribution…

## Probabilistic Fondations of Econometrics, part 2

This post is the second one of our series on the history and foundations of econometric and machine learning models. Part 1 is online here. Geometric Properties of this Linear Model Let’s define the scalar product in \mathbb{R}^n, ⟨\mathbf{a},\mathbf{b}⟩=\mathbf{a}^T\mathbf{b}, and let’s note \|\cdot\| the associated Euclidean standard, \|\mathbf{a}\|=\sqrt{\mathbf{a}^T\mathbf{a}} (denoted \|\cdot\|_{\ell_2}…

## Probabilistic Fondations of Econometrics, part 1

In a series of posts, I wanted to get into details of the history and foundations of econometric and machine learning models. I will be some sort of online version of our joint paper with Emmanuel Flachaire and Antoine Ly, Econometrics and Machine Learning (initially writen in French), that will…

## Networks to reinvent insurance?

The theory of networks, or graphs, was born in 1735, following the work of Leonard Euler, who tried to find a walk – starting from a given point – that would bring us back to that point by passing once and only once through each of the seven bridges in…