Articles by arthur charpentier

Lilliefors, Kolmogorov-Smirnov and cross-validation

January 5, 2021 | arthur charpentier

In statistics, Kolmogorov–Smirnov test is a popular procedure to test, from a sample is drawn from a distribution , or usually , where is some parametric distribution. For instance, we can test (where ) using that test. More specifically, I wanted to discuss today -values. Given let us draw samples of size , ...
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Insurance Pricing Game

December 18, 2020 | arthur charpentier

Would you like to put your data science skills to the test? Imperial College London, Universite du Quebec à Montreal (UQAM), and actuarial institutes in Singapore, the UK, including the IFoA, and Australia, ASTIN, the Casualty Actuarial Society are co-organising a global data science competition. Would you like to accurately predict ...
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Trees and forests

November 30, 2020 | arthur charpentier

For my ACT6100 weekly quiz, I usually generate some datasets, and then ask students to compare various predictive algorithms. Last week, it was about classification trees and random forests. And students were surprised to have such differences (they had to estimate the probability to have a specific label, for the ...
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Testing for Covid-19 in the U.S.

April 28, 2020 | arthur charpentier

For almost a month, on a daily basis, we are working with colleagues (Romuald, Chi and Mathieu) on modeling the dynamics of the recent pandemic. I learn of lot of things discussing with them, but we keep struggling with the tests. Paul, in Montréal, helped me a little bit, ...
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Modeling Pandemics (3)

March 20, 2020 | arthur charpentier

In Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention, a more complex model than the one we’ve seen yesterday was considered (and is called the SEIR model). Consider a population of size , and assume that is the number of susceptible, the number of exposed, the number ...
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Modeling pandemics (2)

March 20, 2020 | arthur charpentier

When introducing the SIR model, in our initial post, we got an ordinary differential equation, but we did not really discuss stability, and periodicity. It has to do with the Jacobian matrix of the system. But first of all, we had three equations for three function, but actuallyso it means ...
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Modeling pandemics (1)

March 19, 2020 | arthur charpentier

The most popular model to model epidemics is the so-called SIR model – or Kermack-McKendrick. Consider a population of size , and assume that is the number of susceptible, the number of infectious, and for the number recovered (or immune) individuals, so that which implies that . In order to be more realistic, ...
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Function basis and regression

March 1, 2020 | arthur charpentier

In the first part of the course on linear models, we’ve seen how to construct a linear model when the vector of covariates is given, so that is either simply (for standard linear models) or a functional of (in GLMs). But more generally, we can consider transformations of the ...
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Lasso Regression (home made)

February 17, 2020 | arthur charpentier

To compute Lasso regression, define the soft-thresholding functionThe R function would be soft_thresholding = function(x,a){ sign(x) * pmax(abs(x)-a,0) } To solve our optimization problem, set so that the optimization problem can be written, equivalently hence and one gets or, if we develop Again, if there are ...
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Quantile Regression (home made, part 2)

February 17, 2020 | arthur charpentier

A few months ago, I posted a note with some home made codes for quantile regression… there was something odd on the output, but it was because there was a (small) mathematical problem in my equation. So since I should teach those tomorrow, let me fix them. Median Consider a ...
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On Cochran Theorem (and Orthogonal Projections)

January 15, 2020 | arthur charpentier

Cochran Theorem – from The distribution of quadratic forms in a normal system, with applications to the analysis of covariance published in 1934 – is probably the most import one in a regression course. It is an application of a nice result on quadratic forms of Gaussian vectors. More precisely, we can prove ...
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On the conjugate function

January 13, 2020 | arthur charpentier

In the MAT7381 course (graduate course on regression models), we will talk about optimization, and a classical tool is the so-called conjugate. Given a function its conjugate is function such that so, long story short, is the maximum gap between the linear function and . Just to visualize, consider a simple ...
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