Archive for probability theory

Bayes on the radio (regrets)

Posted in Books, Kids, Running, Statistics with tags , , , , , on November 13, 2012 by xi'an

While running this morning I was reconsidering (over and over) my discussion of Bayes’ formula on the radio and thought I should have turned the presentation of Bayes’ theorem differently. I spent much too much time on the math side of Bayes’ formula and not enough on the stat side. The math aspect is not of real importance as it is a mere reformulation of conditional probabilities. The stat side is what matters as introducing a (prior) distribution on the parameter (space) is the #1 specificity of Bayesian statistics…. And the focus point of most criticisms, as expressed later by the physicist working on the Higgs boson, Dirk Zerwas.

I also regret not mentioning that Bayes’ formula was taught in French high schools, as illustrated by the anecdote of Bayes at the bac. And not reacting at the question about Bayes in the courtroom with yet another anecdote of Bayes’ formula been thrown out of the accepted tools by an English court of appeal about a year ago. Oh well, another argument for sticking to the written world.

Computational Challenges in Probability [ICERM, Sept. 5 - Dec. 7]

Posted in Statistics, Travel, University life with tags , , , , , , , , , on May 18, 2012 by xi'an

I have just received an invitation to take part in the program “Computational Challenges in Probability” organised by ICERM (Institute for Computational and Experimental Research in Mathematics, located in what sounds like a terrific building!) next semester. Here is the purpose statement:

The Fall 2012 Semester on “Computational Challenges in Probability” aims to bring together leading experts and young researchers who are advancing the use of probabilistic and computational methods to study complex models in a variety of fields. The goal is to identify common challenges, exchange existing tools, reveal new application areas and forge new collaborative efforts. The semester includes four workshops – Bayesian Nonparametrics, Uncertainty Quantification, Monte Carlo Methods in the Physical and Biological Sciences and Performance Analysis of Monte Carlo Methods. In addition, synergistic activities will be planned throughout the duration of the semester. In particular, there will be several short courses and plenary invited talks by experts on related topics such as graphical models, randomized algorithms and stochastic networks, regular weekly seminars and relevant film screenings.

There are thus four workshops organised over the period and an impressive collection of long-term participants. I will most likely take part in the last workshop, “Performance Analysis of Monte Carlo Methods”, although I would like to attend all of them! (Interesting side remark: while looking at the ICERM website, I found that May 18th is the Day of Data! Great, except that neither the word statistitics nor the word statistician appear on the page…)

Jaynes’ marginalisation paradox

Posted in Books, Statistics, University life with tags , , on June 13, 2011 by xi'an

After delivering my one-day lecture on Jaynes’ Probability Theory, I gave as assignment to the students that they wrote their own analysis of Chapter 15 (Paradoxes of probability theory), given its extensive and exciting coverage of the marginalisation paradoxes and my omission of it in the lecture notes… Up to now, only Jean-Bernard Salomon has returned a (good albeit short) synthesis of the chapter, seemingly siding with Jaynes’ analysis that a “good” noninformative prior should avoid the paradox. (In short, my own view of the problem is to side with Dawid, Stone, and Zidek, in that the paradox is only a paradox when interpreting marginals of infinite measures as if they were probability marginals…) This made me wonder if there could be a squared marginalisation paradox: find a statistical model parameterised by θ with a nuisance parameter η=η(θ) such that when the parameter of interest is ξ=ξ(θ) the prior on η solving the marginalisation paradox is not the same as when the parameter of interest is ζ=ζ(θ) [I have not given the problem more than a few seconds thought so this may prove a logical impossibility!]

Frequency vs. probability

Posted in Statistics with tags , , , , , , , on May 6, 2011 by xi'an

Probabilities obtained by maximum entropy cannot be relevant to physical predictions because they have nothing to do with frequencies.” E.T. Jaynes, PT, p.366

A frequency is a factual property of the real world that we measure or estimate. The phrase `estimating a probability’ is just as much an incongruity as `assigning a frequency’. The fundamental, inescapable distinction between probability and frequency lies in this relativity principle: probabilities change when we change our state of knowledge, frequencies do not.” E.T. Jaynes, PT, p.292

A few days ago, I got the following email exchange with Jelle Wybe de Jong from The Netherlands:

Q. I have a question regarding your slides of your presentation of Jaynes’ Probability Theory. You used the [above second] quote: Do you agree with this statement? It seems to me that a lot of  ‘Bayesians’ still refer to ‘estimating’ probabilities. Does it make sense for example for a bank to estimate a probability of default for their loan portfolio? Or does it only make sense to estimate a default frequency and summarize the uncertainty (state of knowledge) through the posterior? Continue reading

Jaynes’ back on track!

Posted in Books, Statistics, University life with tags , , on March 30, 2011 by xi'an

Following the cancellation of my reading seminar on Jaynes’ Probability Theory, and requests from several would-be-attendees, I am giving a one-day [crash] course on the book on April 11. It will be at ENSAE, salle 11, from 9:30 till 4:00pm [or earlier if I exhaust the slides, the material or the audience], with a break at noon. Once again, it is open to everyone, but attendants must register with Nadine Guedj [at ensae.fr]. Several copies of Probability Theory are available  in the library. The slides are available as earlier as

Obviously, this is a last call!

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