0471920835
2009-11-01 - extension: pdf - size: 2 MB
0471920835
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BR-0427-BMF
2009-10-30 - extension: rar - size: 7 MB
BR-0427-BMF
Hosted on: rapidshare.com
Video results for: bayesian methodsMore results from video
Fermat number inference - 2/2 Re:Stanford Challenge In this two-part set of clips, I take a look at a particular inference on the so-called Fermat (More) In this two-part set of clips, I take a look at a particular inference on the so-called Fermat numbers. These numbers were inferred to be only prime numbers, but that later turned out to be false. I show how to tackle this problem using statistical tools, in order to see exactly how much you would trust the inference in this case. I do not elaborate too much on the statistical methods, so this can be seen more as a demo than anything else.
In this second clip, I study the Bayesian approach. I start off with a numeric experiment to determine the a' priori' probability that an arbitrary sequence produces only prime numbers. I use conservative estimate of 10% which produces an a' posteriori (after data) probability of 94%, with a 6% chance of being wrong. I then try a more sophisticated method, using a probability distribution for the prior probability, yielding a mean posterior probability of 19% for being wrong in the inference. Thus, the analysis shows that even though the data indicates that the sequence contains only prime numbers, we can not put a lot of trust in that assumption. When the next part of the sequence arrives, the probability for the sequence being only prime collapses to zero.
Some useful wikipedia links:
http://en.wikipedia.org/wiki/Bayes_theorem
(Tells how to deduce Bayes theorem from
the rules of probability)
http://en.wikipedia.org/wiki/Bayesian_probability
(Contains a description of probability distributions on probabilities!)
Intro to Bayesian statistics with comparisons between Bayesian and frequentist statistics (somewhat biased, perhaps):
http://www.cs.ubc.ca/~hutter/earg/presentations/whyBayes.ppt
The number of primes below specified thresholds can be found here:
http://primes.utm.edu/howmany.shtml
One very useful book:
E.T. Jaynes
Probability theory - the logic of science (Less)
Fermat number inference - 1/2 Re:Stanford Challenge websnarf In this two-part set of clips, I take a look at a particular inference on the so-called Fermat (More) In this two-part set of clips, I take a look at a particular inference on the so-called Fermat numbers. These numbers were inferred to be only prime numbers, but that later turned out to be false. I show how to tackle this problem using statistical tools, in order to see exactly how much you would trust the inference in this case. I do not elaborate too much on the statistical methods, so this can be seen more as a demo than anything else.
In the first clip, I do a little intro and then start off with frequentist hypothesis-testing. That goes a bit awry, which is precisely what I want to demonstrate here, though a more thorough treatment may yield better results. If this is a little un-satisfying, you can fast-forward to the end, where I introduce Bayesian statistics.
The number of primes below specified thresholds can be found here:
http://primes.utm.edu/howmany.shtml
For more on p-values, see
http://en.wikipedia.org/wiki/P-value (Less)
Bayesian Methods for Ecology 2007 PDF
2009-05-15 - extension: pdf - size: 2 MB
Bayesian Methods for Ecology 2007 PDF
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BaMethFin
2009-06-17 - extension: rar - size: 2 MB
BaMethFin
Hosted on: megaupload.com
BaMethFin
2009-06-17 - extension: rar - size: 2 MB
BaMethFin
Hosted on: depositfiles.com