#arcsin law #brownian motion #paradox #stochastic

The probability of going through a bad patch

We’ve heard it: people that invest on the stock market or that gamble in lotteries, casinos, etc usually say “I’m going through a bad patch” (or bad spell). That is, they have been losing money for a while, but hey! better times are ahead and there’s no reason to quit. Are they sure? Are better times ahead? How close is “ahead” to today? Let’s work through a specific example to see how far is “ahead”. Suppose we play a fair game: we toss a coin and with probability 1/2 we get $1 (heads) and with probability 1/2 we lose $1 (tails). We play the game \(n\) times and compute our capital \(C(n)\) up to time \(n\). If our initial capital is zero, then we expect that our capital fluctuate around zero as the coin-tossing game goes on. Sometimes we will be in the “winning area”, where our capital is positive \(C(n)\) > 0. However, we can also be in the “losing area” in which our capital is negative \(C(n)\) < 0. If we are going through a bad patch (being in the losing area) we expect that waiting long enough we will recover and come back to the winning area. ...

#journal #papers #self-advertising

Being part of "best of 2008"

I got wonderful news today. Our paper “Specialization and herding behavior of trading firms in a financial market” (pdf) has been selected by the Editorial Board of New Journal of Physics as part of the Journal’s Best of 2008. According to their site, “Best of 2008” is a compilation of articles selected by the Editorial Board and staff team on the basis of criteria including referee endorsements, readership and citation levels and simple broad appeal. All articles are permanently free to read. ...

The use of statistics

Mark Twain (1924) probably had politicians in mind when he reiterated Disraeli’s famous remark ("There are three kinds of lies: lies, damned lies and statistics"). Scientists, we hope, would never use data in such a selective manner to suit their own ends. But, alas, the analysis of data is often the source of some exasperation even in an academic context. On hearing comments like ‘the result of this experiment was inconclusive, so we had to use statistics’, we are frequently left wondering as to what strange tricks have been played on the data. D. S. Sivia in Data Analysis: A bayesian Tutorial ...

#Fokker-Planck #Ito #Stochastic Differential Equations

Itô calculus for the rest of us

One of the areas of my research is stochastic differential equations (SDE). I posted about it several times before. One of the things students and collaborators keep asking me about SDEs is the weird stochastic Itô Calculus. Itô Calculus is different from what you learn in 101 calculus. In particular, the chain rule is not longer valid. Let me explain it with an example. Suppose you have the following equation ...

#Paradox #Queueing theory #Stochastic

Waiting for the bus

Although the public transportation system in Madrid is very good, I don’t usually take the bus or the train to move around. But sometimes my car decides I should take public transportation (bus or train). One of things I always found intriguing is that I always wait way more for the bus than what is expected according to the frequency quoted by the transportation companies at the bus or train stop. For example: if the frequency of the buses is 4 per hour, you should expect a bus each 15 minutes on average, although fluctuations around this value may occur due to traffic conditions. Thus, arriving at the bus stop at random will get you an average of 15/2 = 7.5 minutes of wait. I have the impression I always wait 15 minutes instead. How can this be? Is it that I am so unlucky I always arrive at the bus stop when the previous bus has just left? ...

#Add new tag #impact factor #long tail #social networks

Publish and... perish

In the old days, research quality was measured by the number of papers you published. Publishing was a hard process and only few scientists were able to publish several papers per year. However, with the bloom of new journals, the appearance of electronic editorial process, and the specialization of research fields, the number of publications per year has grow exponentially during the last decades. Thus publishing is not longer a good measure of the quality of research. As an example if this I recently attended a talk by Sid Redner in which he showed the following data extracted from the Physical Review citation data of 353000 papers: ...