Physicists Find Users Uninterested After 36 Hours 141
SuperGrads writes "Statistical physicists working in the US and Hungary have found that the number of people reading a particular news story on the web decreases with time by a power law rather than exponentially as was previously thought. The finding has implications for the study of information flow in social networks, marketing and web design."
Re:maybe because it's not "news" anymore? (Score:5, Informative)
Furthermore, the study was not done by taking people and finding out how quickly they became disinterested in one story or another. A quick glance at the summary informs us that the subject of the study was the number of people reading a news story (more likely downloading the story) at a given time. That this number decreases with time is obvious. However, it was expected that the decrease would follow an exponential curve, whereas the experiment showed a power law curve instead.
Re:maybe because it's not "news" anymore? (Score:3, Informative)
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Science & Technology / Psychology [economist.com]
Bayes rules
Jan 5th 2006
From The Economist print edition
A once-neglected statistical technique may help to explain how the mind works
IMAGE [economist.com]
SCIENCE, being a human activity, is not immune to fashion. For example, one of the first mathematicians to study the subject of probability theory was an English clergyman called Thomas Bayes, who was born in 1702 and died in 1761. His ideas about the prediction of future events from one or two examples were popular for a while, and have never been fundamentally challenged. But they were eventually overwhelmed by those of the “frequentist” school, which developed the methods based on sampling from a large population that now dominate the field and are used to predict things as diverse as the outcomes of elections and preferences for chocolate bars.
Recently, however, Bayes’s ideas have made a comeback among computer scientists trying to design software with human-like intelligence. Bayesian reasoning now lies at the heart of leading internet search engines and automated “help wizards”. That has prompted some psychologists to ask if the human brain itself might be a Bayesian-reasoning machine. They suggest that the Bayesian capacity to draw strong inferences from sparse data could be crucial to the way the mind perceives the world, plans actions, comprehends and learns language, reasons from correlation to causation, and even understands the goals and beliefs of other minds.
These researchers have conducted laboratory experiments that convince them they are on the right track, but only recently have they begun to look at whether the brain copes with everyday judgments in the real world in a Bayesian manner. In research to be published later this year in Psychological Science, Thomas Griffiths of Brown University in Rhode Island and Joshua Tenenbaum of the Massachusetts Institute of Technology put the idea of a Bayesian brain to a quotidian test. They found that it passes with flying colours.
Prior assumptions
The key to successful Bayesian reasoning is not in having an extensive, unbiased sample, which is the eternal worry of frequentists, but rather in having an appropriate “prior”, as it is known to the cognoscenti. This prior is an assumption about the way the world works—in essence, a hypothesis about reality—that can be expressed as a mathematical probability distribution of the frequency with which events of a particular magnitude happen.
The best known of these probability distributions is the “normal”, or Gaussian distribution. This has a curve similar to the cross-section of a bell, with events of middling magnitude being common, and those of small and large magnitude rare, so it is sometimes known by a third name, the bell-curve distribution. But there are also the Poisson distribution, the Erlang distribution, the power-law distribution and many even weirder ones that are not the consequence of simple mathematical equations (or, at least, of equations that mathematicians regard as simple).
With the correct prior, even a single piece of data can be used to make meaningful Bayesian predictions. By contrast frequentists, though they deal with the same probability distributions as Bayesians, make fewer prior assumptions about the distribution that applies in any particular situation. Frequentism is thus a more robust approach, but one that is not well suited to
Half Life = Exponential! (Score:2, Informative)
A power law relationship is something of the form y = A*t^k, which cannot be used to model a rate with a half life, since the time to reduce the rate by half depends on where you start, and increases as time increases.
Also any exponential function (with negative k) eventually decays faster than any power law function. The power law can start decaying faster, but since the half life will increase with time, the exponential function with a constant half-life will always eventually get under it. (L'Hospital's rule is your friend.)
So to say that something that can be described with a half life follows a power law rather than a exponential function, and decays faster than an exponential function, indicates a complete ignorance of the methematical terms. This also calls into question the validity of everything else the article says.
Re:Exponent? Power? (Score:5, Informative)