The hidden side of probabilities and statistics
Students know this well: understanding probabilities and statistics often requires an adaptation period. Who has never confused correlation and causation? Chance being by nature unpredictable, how can we hope to build certainties on it? Even more surprising: how to create models on unpredictable phenomena? Our intuition being severely tested, paradoxes follow one after another, which the entertainment world (casinos, board games, media, card games or games of chance...) has known how to take advantage of. But taming chance even just a little brings powerful tools in a world where everything is connected: internet users' choices, online reservations, detection of unsolicited electronic mail rely on a theorem discovered three hundred years ago by an English theologian named Thomas Bayes.
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The Monty Hall paradox
Who has never dreamed of hitting the jackpot, of beating the odds? Games of chance such as roulette and Loto leave considerable uncertainty over whether you will win. Probability helps us understand these games and make the best decision as they unfold.
Correlation gone too far
The thermometer does not cause the temperature! Obvious, isn't it? And yet, how many people still confuse correlation with causation, or interpret two events coinciding as one causing the other... Let's unpack these mechanisms.
Joseph Bertrand's probability paradoxes
Joseph Louis François Bertrand (1822–1900) is known for his research in analysis. Less well known is the remarkable book on probability that he published in 1889 (see
Statistical fluctuations: beware small samples
Extracting knowledge from a mass of homogeneous data is the province of statistics. Yet it is quite an art: the conclusions must be treated with care! Small fluctuations around the mean can invalidate an entire line of reasoning. Let us learn how to spot them.
The very delicate principle of indifference
The principle of indifference invites us to reflect on the subtle blend of knowledge and ignorance. The probabilities it generates are sometimes surprising, but always consistent. By analyzing a problem's data, it dictates the probabilities that should rationally be assigned.
Bayes' theorem: the star of web algorithms
If the Internet can now suggest books or holiday plans to you with remarkable accuracy, it is thanks to yesterday's researchers, who envisioned computing when computers barely existed. One remarkable figure stood out, though he remains far too little known: Thomas Bayes.
Expected value and its surprising paradoxes
Expected payoff is essential to rational decision-making, but tricky to use. Many paradoxes arise from misinterpreting what it represents. Casinos—and the unscrupulous people who encourage you to wager your money—understand this only too well...