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fixed markdown usage
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lnauta committed Jan 13, 2017
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11 changes: 5 additions & 6 deletions Chapter6_Priorities/Ch6_Priors_PyMC2.ipynb
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"cell_type": "markdown",
"metadata": {},
"source": [
"#####Example: Bayesian Multi-Armed Bandits\n",
"##### Example: Bayesian Multi-Armed Bandits\n",
"*Adapted from an example by Ted Dunning of MapR Technologies*\n",
"\n",
"> Suppose you are faced with $N$ slot machines (colourfully called multi-armed bandits). Each bandit has an unknown probability of distributing a prize (assume for now the prizes are the same for each bandit, only the probabilities differ). Some bandits are very generous, others not so much. Of course, you don't know what these probabilities are. By only choosing one bandit per round, our task is devise a strategy to maximize our winnings.\n",
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"cell_type": "markdown",
"metadata": {},
"source": [
"##Effect of the prior as $N$ increases\n",
"## Effect of the prior as $N$ increases\n",
"\n",
"In the first chapter, I proposed that as the amount of observations, or data, that we posses, the less the prior matters. This is intuitive. After all, our prior is based on previous information, and eventually enough new information will shadow our previous information's value. The smothering of the prior by enough data is also helpful: if our prior is significantly wrong, then the self-correcting nature of the data will present to us a *less wrong*, and eventually *correct*, posterior. \n",
"\n",
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"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"#Bayesian Rugby#\n",
"# Bayesian Rugby\n",
"Note: This submission comes from Peadar Coyle and is our first 'guest' example. \n",
"Peadar is known as @springcoil on Twitter and is an Irish Data Scientist with a Mathematical focus, he is currently based in Luxembourg. \n",
"I came across the following blog post on http://danielweitzenfeld.github.io/passtheroc/blog/2014/10/28/bayes-premier-league/ \n",
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"\n",
"Since I am a rugby fan I decide to apply the results of the paper [Bayesian Football](http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0CC8QFjAC&url=http%3A%2F%2Fwww.statistica.it%2Fgianluca%2FResearch%2FBaioBlangiardo.pdf&ei=0m3aVKK2KMm6UarSgYgM&usg=AFQjCNGiEg26H58zDiEIx3C7diUzfq3bJQ&sig2=yICsOBSJBniJNzlLW-H86g&bvm=bv.85464276,d.d24) to the Six Nations.\n",
"\n",
"##Acquiring the data##\n",
"## Acquiring the data\n",
"The first step was to acquire the data - which I created in a csv file from data I got on wikipedia and sports websites. To be honest a lot of this turned out to be manual entry. But this is fine for T=6 teams :) \n",
"\n",
"We largely follow the code of the website cited above, with only a few small changes. We do less wrangling because I personally curated the data. \n",
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"cell_type": "markdown",
"metadata": {},
"source": [
"#The model. #\n",
"# The model\n",
"The league is made up by a total of T= 6 teams, playing each other once \n",
"in a season. We indicate the number of points scored by the home and the away team in the g-th game of the season (15 games) as $y_{g1}$ and $y_{g2}$ respectively. \n",
"\n",
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