Blog Archives

Conditional dependence measures

December 17, 2013
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Conditional dependence measures

This week, I spend some time at the Workshop on Nonparametric Curve Smoothing conference at Concordia. Yesterday afternoon, Noël Veraverbeke show an interesting graph, to illustrate conditional copulas (and the derivation of conditional dependence measures, such as Kendall’s tau, or Spearman’s rho). A long time ago, in my PhD thesis (mainly on conditional copulas) I did try to derive conditional...

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On Wigner’s law (and the semi-circle)

December 16, 2013
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On Wigner’s law (and the semi-circle)

There is something that I love about mathematics: sometimes, you discover – by chance – a law. It has always been there, it might have been well known by some people (specialized in some given field), but you did not know it. And then, you discover it, and you start wondering how comes you never heard about it before… I...

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Random points on the Earth

December 7, 2013
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Random points on the Earth

The problem with puzzles is that you keep it in your head for days, until you find an answer. Or at least some ideas about a possible answer. This is what happened to me a few weeks ago, when a colleague of mine asked me the following question : Consider points uniformly distributed on a sphere. What is the...

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Conditional densities, on one single graph

December 5, 2013
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Conditional densities, on one single graph

With Stéphane Tufféry we’ve been working on credit scoring1 and we’ve been using the popular german credit dataset, > myVariableNames <- c("checking_status","duration","credit_history", + "purpose","credit_amount","savings","employment","installment_rate", + "personal_status","other_parties","residence_since","property_magnitude", + "age","other_payment_plans","housing","existing_credits","job", + "num_dependents","telephone","foreign_worker","class") > credit = read.table( + "http://archive.ics.uci.edu/ml/machine-learning-databases/statlog/german/german.data", + header=FALSE,col.names=myVariableNames) > credit$class <- credit$class-1 We wanted to get a nice code to produce a graph like the one below, Yesterday, Stéphane...

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Binomial regression model

November 18, 2013
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Binomial regression model

Most of the time, when we introduce binomial models, such as the logistic or probit models, we discuss only Bernoulli variables, . This year (actually also the year before), I discuss extensions to multinomial regressions, where  is a function on some simplex. The multinomial logistic model was mention here. The idea is to consider, for instance with three possible classes the following...

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Maximum Likelihood versus Goodness of Fit

November 8, 2013
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Maximum Likelihood versus Goodness of Fit

Thursday, I got an interesting question from a colleague of mine (JP). I mean, the way I understood the question turned out to be a nice puzzle (but I have to confess I might have misunderstood). The question is the following : consider a i.i.d. sample of continuous variables. We would like to choose between two (parametric) families for...

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Generating functions

November 8, 2013
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Generating functions

Today, I wanted to publish a post on generating functions, based on discussions I had with Jean-Francois while having our coffee after lunch a couple of times already. The other reason is that I publish my post while my student just finished their Probability exam (and there were a few questions on generating functions). A short introduction (back on...

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Smoothing mortality rates

November 4, 2013
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Smoothing mortality rates

This morning, I was working with Julie, a student of mine, coming from Rennes, on mortality tables. Actually, we work on genealogical datasets from a small region in Québec, and we can observe a lot of volatiliy. If I borrow one of her graph, we get something like Since we have some missing data, we wanted to use some...

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Halloween and candies (a ballot problem)

October 30, 2013
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Halloween and candies (a ballot problem)

This year, for Halloween, a post on candies (I promise, next year I will write another post on zombies). But I don’t want to focus on the kids problems (last year, we tried to minimize their walking distance to collect as much candies as possible, with part 1 and part 2), I want to discuss my own problems. Because usually, the kids wear...

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More significant? so what…

October 30, 2013
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More significant? so what…

Following my non-life insurance class, this morning, I had an interesting question from a student, that I will try to illustrate, and reformulate as accurately as possible. Consider a simple regression model, with one variable of interest, and one possible explanatory variable. Assume that we have two possible models, with the following output (yes, I do hide interesting parts...

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