Archive for the ‘Statistics’ Category

Visiting UCLA

28/02/2013

I shall be spending next week (4th-9th March) at the UCLA Department of Linguistics, where I shall give five hours of talks on Statistics for Historical Linguistics: a two-hour review of the field (Thursday morning), a two-hour presentation of my own DPhil work (pdf) (Friday afternoon), and a one-hour tutorial on TraitLab (Friday afternoon?). Abstracts:

1. Statistical methods in Historical Linguistics (Thursday morning)
Recent advances in our understanding of language change, in statistical methodology, and in computational power, along with an increasing wealth of available data, have allowed significant progress in statistical modelling of language change, and quantitative methods are gaining traction in Historical Linguistics. Models have been developed for the change through time of vocabulary, morpho-syntactic and phonetic traits. I shall present a review of these models (from a statistician’s point of view), starting with Morris Swadesh’s failed attempts at glottochronology, then looking at some models developed in the last decade. In parallel, I shall provide brief insights into statistical tools such as Bayesian statistics and Markov Chain Monte Carlo, in order to show how to use these effectively for linguistic applications.
2. A phylogenetic model of language diversification (Friday afternoon)
Language diversification is a random process similar in many ways to biological evolution. We model the diversification of so-called “core” lexical data by a stochastic process on a phylogenetic tree. We initially focus on the Indo-European language family. The age of the most recent common ancestor of these languages is of particular interest and issues of dating ancient languages have been subject to controversy. We use Markov Chain Monte Carlo to estimate the tree topology, internal node ages and model parameters. Our model includes several aspects specific to language diversification, such as rate heterogeneity and the data registration process, and we show that lexical borrowing does not bias our estimates. We show the robustness of our model through extensive validation and analyse two independent data sets to estimates the age of Proto-Indo-European. We then analyse a data set of Semitic languages, and show an extension of our model to explore whether languages evolve in “punctuational bursts”. Finally, we revisit an analysis of several small data sets by Bergsland & Vogt (1962).
Joint work with Geoff Nicholls

3. Tutorial and practical: TraitLab, a package for phylogenies of linguistic and cultural traits
In this tutorial, I shall present how to use the TraitLab package, which was initially developed specifically for the modelling of core vocabulary change through time, and guide interested attendants through an analysis of a simple data set. TraitLab is a software package for simulating, fitting and analysing tree-like binary data under a stochastic Dollo model of evolution. It handles “catastrophic” rate heterogeneity and missing data. The core of the package is a Markov chain Monte Carlo (MCMC) sampling algorithm that enables the user to sample from the Bayesian joint posterior distributions for tree topologies, clade and root ages, and the trait loss and catastrophe rates for a given data set. Data can be simulated according to the fitted Dollo model or according to a number of generalized models that allow for borrowing (horizontal transfer) of traits, heterogeneity in the trait loss rate and biases in the data collection  process. Both the raw data and the output of MCMC runs can be inspected using a number of useful graphical and analytical tools  provided within the package. TraitLab is freely available and runs within the Matlab computing environment.

Attendants who wish to use TraitLab during the practical should have a computer with Matlab installed.

TraitLab was developed jointly with Geoff Nicholls and David Welch.

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Accepted: Wang-Landau Flat Histogram

14/12/2012

Excellent news to start the week-end: our paper with Pierre Jacob The Wang-Landau Algorithm Reaches the Flat Histogram in Finite Time has been accepted for publication in Annals of Applied Probability.

For details, see this blog post or read the paper on arXiv.

Contigency exigency

14/12/2012

The SIGecom Exchanges, an engineering and economics journal on e-commerce, run a puzzle in each issue, written by Daniel Reeves (more on Dan’s awesomeness soon). The December 2011 puzzle asked to find a scheme to pay a lawyer when there is uncertainty in the fruits of their labour, while still taking into account the amount of labour (see here for the complete puzzle).

After 6 months without a solution, Dan offered a bounty for this puzzle, where the award would be a realization of a uniform draw between 0 and 500 dollars (realization given by geohashing). After some extra nerdery to choose the winner of the bounty between Arthur Breitman and myself, I ended up winning $65.14, and my solution appears in the latest issue of the SIGecom Exchanges.

This was great fun; other journals should pick up the idea!

A Million Random Digits with 100,000 Normal Deviates

20/01/2011

Random digitsI had heard before of the 1955 book A Million Random Digits with 100,000 Normal Deviates (which is exactly what you think it is), but until Greg Ross pointed them out, I had never looked at the comments on Amazon.  They are hilarious. A short selection:

  • “Such a terrific reference work! But with so many terrific random digits, it’s a shame they didn’t sort them, to make it easier to find the one you’re looking for.”
  • “If you like this book, I highly recommend that you read it in the original binary.”
  • “While the printed version is good, I would have expected the publisher to have an audiobook version as well.”
  • “Once you get about halfway in, the rest of the story is pretty predictable.”
  • “What other author could give us such a masterpiece? Infinite monkeys typing on infinite typewriters might be able to produce Shakespeare, but they could never produce something like this!”
  • “My only regret is that there isn’t a sequel, because the author left it at a cliffhanger. ”
  • “It starts with an innocent 10097, rapidly succeded by 32533. The reader has no idea if 10097 will ever appear again, and that’s the thrilling part. I won’t spoil the story, so if you want to know whether 10097 is repeated, buy the book.”

(David Pogue has a list of other Amazon products which attract funny “reviews”.)

A Million Random Digits with 100,000 Normal DeviatesA

Ngrams: when Statistics overtook Mathematics

20/12/2010

The Internet is abuzz (1 2 3)with Google’s Ngrams Viewer which allows to track frequency of usage of words and short phrases in “lots of books” from 1500 to 2008, in six languages.

It would be easy to spend hours playing at these data. Here is a quick look at when Statistics (rightfully) overtook Mathematics, in English and in French books:

Statistics overtook Mathematics half-a-century earlier in English than it did in French. I wonder what caused the bump in French around 1960.

Data on shared bicycles in Lyon

14/12/2010

Pablo Jensen et al. recently posted on arXiv a short analysis of a fantastic data set: 11 million trips made with the shared bicycles Vélo’v in Lyon. For every trip, the start station, final station, and trip time, duration and distance are available.

Among other things, they show that the average Vélo’v is faster than the average car at peak time, that cyclists are faster on Wednesdays and slower during the week-ends, and that winter speeds are higher (presumably because casual – hence slower – cyclists only cycle during the summer). My guess would be that cyclists who ride their own bikes, rather than use Vélo’v, are even faster, since they are probably more used to cycling and definitely have better and lighter bikes.

Given the start and final point of a trip, they can also calculate the length of the shortest path which obeys all one-way streets, and they show that a whopping 61% of cyclists take a shortcut, which must involve cycling the wrong way or on pavements. (It goes without saying that Parisian cyclists would never do such a thing.)

This is a fantastic data set, and I cannot wait to see more analyses, or some visualizations à la Pedro M. Cruz.

Easter eggs

13/09/2010

In a comment to his post on Algerians’ disinterest for sex during the Ramadan, Arthur Charpentier shows a graph supporting the claim that around Easter, the French care more and more about eggs and less about Easter itself:

Google Trends : Pâques, oeuf

Assuming Google Trends can be trusted so far back in time, the true story is actually different: the French don’t care less about Easter, they just care less about spelling. If you remove the circumflex from Pâques and search for Paques instead, you will see that the interest in Easter remains roughly constant.

Google Trends: Paques, Oeuf, Pâques

(Note that the correct spelling of oeuf is actually œuf with a ligature, but that is not easily accessible on a French keyboard, nor is it supported by Google Trends.)

The same thing happens at Christmas. It might seem that the French prefer presents to Christmas (Noël vs cadeau)

Google Trends: Noël, cadeau

but they simply ignore the umlaut more and more:

Google Trends: Noël, cadeau, Noel