# Blog Archives

## Statistical Interests in Large Cities

January 10, 2014
By

I always thought that there were some kind of schools in statistics, areas (not to say universities or laboratories) where people had common interest in term of statistical methodology. Like people with strong interest in extreme values, or in Lévy Processes. I wanted to check this point so I did extract information about articles puslished in about 35 journals...

## Sequences defined using a Linear Recurrence

January 6, 2014
By
$u_n=a+b u_{n-1}$

In the introduction to the time series course (MAT8181) this morning, we did spend some time on the expression of (deterministic) sequences defined using a linear recurence (we will need that later on, so I wanted to make sure that those results were familiar to everyone). First order recurence The most simple case is the first order recurence, where...

## Random points on some hemisphere

December 18, 2013
By
$n$

In my previous post, I tried to answer the following question Consider  points uniformly distributed on a sphere. What is the probability that the  points lie on a same hemisphere, for some hemisphere (there is no south or north here) ? If I have been able to use Monte Carlo simulations in dimension 2 (on a circle, not on a sphere), I could...

## Conditional dependence measures

December 17, 2013
By
$(Y_1,Y_2)$

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...

## On Wigner’s law (and the semi-circle)

December 16, 2013
By
$n\times n$

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...

## Random points on the Earth

December 7, 2013
By
$n$

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...

## Conditional densities, on one single graph

December 5, 2013
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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...

## Binomial regression model

November 18, 2013
By
$Y_i\sim\mathcal{B}(p(\boldsymbol{X_i}))$

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...

## Maximum Likelihood versus Goodness of Fit

November 8, 2013
By
$\{X_1,\cdots,X_n\}$

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...

## Generating functions

November 8, 2013
By
$F(x)=1-e^{-x}/3$

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...