RUU #19: Inference on the free binomial model について・・・
In this clip, I study inference on the free binomial model. Recall that the binomial distribution gives the probability for a given number of successes,k, for a given number, n, of repeatable independent trials. A fixed success probability, p, is assumed (hence repeatable trials). The object is to gather info on the value of p, and handle that info using Bayes formula, since it will typically be a' priori uncertain.
The example is from a game called Age of Wonders (Shadow Magic), which I warmly recommend, by the way. (It's an excellent time waster :) I'm studying the probability for a knight winning over a dragon, by doing 100 separate «battles». The result is 9 surviving knights. I then study that data using probabilistic theory. The results include the posterior probability of p (the probability of p given the data), estimates of p, the standard deviation of p, a 90% credibility interval for p (an interval of p where more than 90% of the probability is situated) and predictions of future events based on the posterior distribution.
The slides can be found here:
http://folk.uio.no/trondr/uncert19.pdf
R code for doing the inference can be found here:
http://folk.uio.no/trondr/uncert19.R
The statistical programming tool R can be downloaded freely, here:
http://www.r-project.org/
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