February 2010

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Bayes' theorem



Philosophical foundations

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A law of probability that describes the proper way to incorporate new evidence into prior probabilities to form an updated probability estimate. Bayesian rationality takes its name from this theorem, as it is regarded as the foundation of consistent rational reasoning under uncertainty. A.k.a. “Bayes’s Theorem” or “Bayes’s Rule”.

Eliezer Yudkowsky is on bloggingheads.tv with the statistician Andrew Gelman.

Several different points of fascination about Bayes…

When looking further, there is however a whole crowd on the blogs that seems to see more in Bayes’s theorem than a mere probability inversion…

Bayesian statistics is a system for describing epistemological uncertainty using the mathematical language of probability.
Bayesian probability is one of the most popular interpretations of the concept of probability.

Edwin T. Jaynes was one of the first people to realize that probability theory, as originated by Laplace, is a generalization of Aristotelian logic that reduces to deductive logic in the special case that our hypotheses are either true or false. This web site has been established to help promote this interpretation of probability theory by distributing articles, books and related material. As Ed Jaynes originated this interpretation of probability theory we have a large selection of his articles, as well as articles by a number of other people who use probability theory in this way…

Bayesian statistics is so closely linked with induction that one often hears it called “Bayesian induction.” What could be more inductive than taking a prior, gathering data, updating the prior with Bayes Law, and limiting to the true distribution of some parameter?

Gelman (of the popular statistics blog) and Shalizi point that, in practice, Bayesian statistics should actually be seen as Popper-style hypothesis-based deduction. The problem is intricately linked to the “taking a prior” above.

Or, how to recognize Bayes’ theorem when you meet one making small talk at a cocktail party.

Still, I’m sure Blogger won’t mind me using their resources instead. The basic idea is that there’s a distinction between true values x and measured values y. You start off with a prior probability distribution over the true values. You then have a likelihood function, which gives you the probability P(y|x) of measuring any value y given a hypothetical true value x.

In other words, What is so special about starting with a human-generated hypothesis? Bayesian methods suggest what I think is the right answer: To get from probabilistic evidence to the probability of something requires combining the evidence with a prior expectation, a “prior probability”, and human hypothesis generation enables this requirement to be ignored with considerable practical success.

Andrew Gelman recently responded to a commenter on the Yudkowsky/Gelman diavlog; the commenter complained that Bayesian statistics were too subjective and lacked rigor.  I shall explain why this is unbelievably ironic…

Maybe this kind of Bayesian method for “proving the null” could be used to achieve a better balance.

Bayesian brain is a term that is used to refer to the ability of the nervous system to operate in situations of uncertainty in a fashion that is close to the optimal prescribed by Bayesian statistics.



Expect this link collection to be permanently updated.

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via acceleratingfuture.com/michael/blog/

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This video describes rewarding brain stimulation.
For references and more information visit iplant.eu/rbs.html

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Ben Goldacre, doctor and author of Bad Science, explains what the placebo effect is and describes its role in medical research and in the pharmaceutical industry.

via shockmd.com/the-placebo-effect-explained-in-a-video/

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I’ve been to Essen lately. Although I had little time for leisure, of course I took a few photos anyway.

More here.

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Science is the only news. When you scan through a newspaper or magazine, all the human interest stuff is the same old he-said-she-said, the politics and economics the same sorry cyclic dramas, the fashions a pathetic illusion of newness, and even the technology is predictable if you know the science. Human nature doesn’t change much; science does, and the change accrues, altering the world irreversibly.

— Stewart Brand, Whole Earth Discipline (2009), p. 216

via michaelgr.com/science-is-the-only-news/


Here is a, in retrospect, hilarious article from the Newsweek magazine issue dated Feb 27, 1995.

After two decades online, I’m perplexed. It’s not that I haven’t had a gas of a good time on the Internet. I’ve met great people and even caught a hacker or two. But today, I’m uneasy about this most trendy and oversold community. Visionaries see a future of telecommuting workers, interactive libraries and multimedia classrooms. They speak of electronic town meetings and virtual communities. Commerce and business will shift from offices and malls to networks and modems. And the freedom of digital networks will make government more democratic.

Baloney. Do our computer pundits lack all common sense? The truth in no online database will replace your daily newspaper, no CD-ROM can take the place of a competent teacher and no computer network will change the way government works.

How about electronic publishing? Try reading a book on disc. At best, it’s an unpleasant chore: the myopic glow of a clunky computer replaces the friendly pages of a book. And you can’t tote that laptop to the beach. Yet Nicholas Negroponte, director of the MIT Media Lab, predicts that we’ll soon buy books and newspapers straight over the Intenet. Uh, sure.

Logged onto the World Wide Web, I hunt for the date of the Battle of Trafalgar. Hundreds of files show up, and it takes 15 minutes to unravel them–one’s a biography written by an eighth grader, the second is a computer game that doesn’t work and the third is an image of a London monument. None answers my question, and my search is periodically interrupted by messages like, “Too many connectios, try again later.”

Then there are those pushing computers into schools(…)–but think of your own experience: can you recall even one educational filmstrip of decades past?

Then there’s cyberbusiness. We’re promised instant catalog shopping–just point and click for great deals. We’ll order airline tickets over the network, make restaurant reservations and negotiate sales contracts. Stores will become obselete. So how come my local mall does more business in an afternoon than the entire Internet handles in a month?

And who’d prefer cybersex to the real thing?

Read the whole piece, many more precious insights can be found in it:

via @KnightMare

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The Singularity: An Appraisal from Michael Johnson on Vimeo.

This panel was held at Boskone 47 in Boston, MA on February 12th, 2010. Moderating was the Guest of Honor, Alastair Reynolds. Other panel participants included several time Hugo Award winner Vernor Vinge, Locus Award winner Charles Stross, and Karl Schroeder.

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via robertwiblin.wordpress.com

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More: The Ultimate Collection of Scaling Visualisations

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