Statisfaction

A good tool for researchers ?

Posted in Geek by JB Salomond on 17 January 2013

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Hi there !

Like Pierre a while ago, I got fed up with printing articles, annotating them, losing them, re-printing them, and so on. Moreover, I also wanted to be able to carry more than one or two books in my bag without ruining my back. E-Ink readers seemed good but at some point I changed my mind

After the ISBA conference in Kyoto, where I saw bazillions of IPads, I thought that tablets really worth the shot. I am cool with reading on a LCD screen, I probably won’t read scientific articles/books outside in the sun, and I like the idea of a light device that can replace my laptop in conferences. Furthermore, there is now a large choice of apps to annotate pdf which is crucial for me.

The device I chose run on Android (mainly because there is no memory extension on Apple devices), combined with a good capacitive pen, an annotation app such as eZreader that get your pdf directly from Dropbox (which is simply awesome). You can even use LaTeX (without fancy packages…) which may become handy.

I hope that I will not experience the same disappointment as Pierre did with his reader, but for the moment a tablet seems just what I needed !

A glimps of Inverse Problems

Posted in General, Seminar/Conference, Statistics by JB Salomond on 15 November 2012

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Hi folks !

Last Tuesday a seminar on Bayesian procedure for inverse problems took place at CREST. We had time for two presentations of young researchers Bartek Knapik and Kolyan Ray. Both presentations deal with the problem of observing a noisy version of a linear transform of the parameter of interest

Y_i = K\mu + \frac{1}{\sqrt{n}} Z
where K is a linear operator and Z a Gaussian white noise.  Both presentations considered asymptotic properties of the posterior distribution (Their papers can be found on arxiv, here for Bartek’s, and here for Kolyan’s). There is a wide literature on asymptotic properties of the posterior distribution in direc models. When looking at the concentration of f toward a true distribution f_0  given the data, with respect to some distance d(.,.),  well known problem is to derive concentration rates, that is the rate \epsilon_n such that

\pi(d(f,f_0) > \epsilon_n | X^n) \to 0.

For inverse problems, the usual methods as introduced by Ghosal, Ghosh and van der Vaart (2000) usually fails, and thus results in this settings are in general difficult to obtain.

Bartek presented some very refined results in the conjugate case. He manages to get some results on the concentration rates of the posterior distribution, on Bayesian Credible Sets and Bernstein – Von Mises theorems – that states that the posterior is asymptotically Gaussian – when estimating a linear functional of the parameter of interest. Kolyan got some general conditions on the prior to achieve concentration rate, and prove that these techniques leads to optimal concentration rates for classical models.

I only knew little about inverse problems but both talks were very accessible and I will surely get more involved in this field !

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