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We want to predict how many points per game LeBron James is going to get per game. Assume there is some underlying theta that does not change game to game, that predicts how many points he will get. For previous information, we have NBA league averages, and we have Lebron James points per game for previous years and games.

How do you choose a prior here?

It would be easy to get say a league average of points per game on all starters who play roughly the same minutes as Lebron. And it is easy to get Lebron's point per games for previous games. The main question is, if I am using a beta distribution to describe the prior, how do I decide what level of sureness to assign the prior? How do we combine Lebron's previous years of points, the league average, and a beta distribution into an accurate description of a prior for Lebron and how sure we are of it (without making arbitrary decisions). Thanks for any thoughts!!

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  • $\begingroup$ Let's say I was gonna do a beta distribution of whether lebron gets above 20 points a game and base it on a prior of league average for players who play a similar number of minutes. Then the beta could be something like B(20,000, 18,000) which obviously will dominate any Lebron James specific information we add in. $\endgroup$
    – appleLover
    Jul 20 '13 at 19:29
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    $\begingroup$ The prior distribution is a specification for the parameter(s) of the model for the data. To specify a prior one needs to know what model you use for the data. So, what is it? $\endgroup$
    – QuantIbex
    Jul 20 '13 at 20:53
  • $\begingroup$ quantlbex, to start off I am going to do a really simple model, I will say that for each player, for each season, there is some underlying theta which predicts how many points they score in a game. Let me know if you need more info... $\endgroup$
    – appleLover
    Jul 21 '13 at 0:34
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    $\begingroup$ What is this "really simple model"? How does the $\theta$ result in a the number of points for the player of interest? $\endgroup$
    – QuantIbex
    Jul 21 '13 at 0:50
  • $\begingroup$ @Quantlbex makes good points. Your first comment above suggests you are actually thinking of modelling the binary outcome of whether he gets above 20 points in an individual game, not the actual points he gets (I don't know what sport we're talking about here or how the points work, but would think something like a Poisson or negative binomial distribution might be ok for the basis of the number of points). Once you've resolved some of these basic questions we could focus on the point of philosophical interest ie what "prior information" do we hold. $\endgroup$ Jul 21 '13 at 1:08

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