1) Turning Data into knowledge : the unexpected power of the Bayesian statistics
http://www.nytimes.com/2014/09/30/science/the-odds-continually-updated.html
Indubitably, one of the most glorious moment of the Bayesian statistics occurred in January when it enabled the rescuers to find a fisherman lost at sea 12 hours earlier. The model based on Bayesian calculations narrowed down the places where to search until the man was rescued. A particular characteristic of this statistic method is that the odds are continually updated as all new relevant information that may emerge is included in the model. This feature may help to solve some counterintuitive problems as the F. D. Flam’s article discusses concerning the Monty Hall paradox. In this TV game show, a contestant has to pick one of three doors: a car is hidden behind one, a goat behind the other two. After the contestant makes his choice, the host reveals a door behind which a goat lies. The contestant can then stick with his choice or switch to the other door. The Bayesian calculation shows that the contestant should switch because he receives an “update of knowledge”. While the odd of him guessing right remains unaffected (1/3) the odds of him guessing wrong are now 2/3. A Bayesian evaluation of the problem leads in this case to a total change of perspective.
As F.D. Flam notes, “Bayesian calculations go indeed straight for the probability of the hypothesis, factoring in not just the data but any other relevant information”. This method is frequently opposed to a more classical approach known as frequentist statistics. This traditional method essentially applies probability to data in order to determine whether the later are coherent or not. Frequentist probability does not take into consideration all the relevant factors that could affect the results, including our own prejudices. In the Bayesian statistics model probabilities are interpreted as a degree of belief based on empirical observations and not as the solely frequency of a phenomenon. Proponents of this method argue that its generalization will help solve increasingly complex problems as well as contribute to improving the reliability of research. According to Andrew Gelman, a statistics professor at Columbia, probably more than 20 % of the studies published in “prominent journals” rely on wrong results, especially because editors tend to put forward counterintuitive results. Bayes’s Rule could be used to cross-check those suspicious findings and could act in a complementary way with the frequentist statistics.
The debate about which statistical model should be adopted to turn data into predictions remains lively. Reality is too complex to be contained in a single model and that is why thinking about statistics involves thinking about the nature of reality itself. There is no good answer to these questions but it can be argued that Bayesian statistics help to “flag spurious results”.