Polya Urn Simulation
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Polya Urn Simulation
1–10 of 21 posts
Re: Polya Urn Simulation
#2I must admit: this went against my intuition. My first guess was that you would end up with an urn full of either red or blue balls.
Re: Polya Urn Simulation
#3I must admit: this went against my intuition. My first guess was that you would end up with an urn full of either red or blue balls.
Me too, but only because I was expecting something interesting to happen since it was on HN!
Re: Polya Urn Simulation
#4I must admit: this went against my intuition. My first guess was that you would end up with an urn full of either red or blue balls.
Yeah, I don't know what my intuition was.
But the problem is symmetric, and even if pick a red, you end up with two reds and one blue, so not so much imbalanced.
And even if the mix becomes really imbalanced, say 7 red and one blue, picking the rarest color will have more effect than picking the most common one. So you could consider that the system tries to balance itself naturally, hence avoiding huge swings in some direction or the other.
Re: Polya Urn Simulation
#5> After a large number of picks, what is the behavior of the proportion of red balls in the urn
Isn’t the more enticing question how strong the bias towards the first picked Color is?
Re: Polya Urn Simulation
#6Pretty sure the variables the author picked are not the most interesting ones.
Urn models are engineered to have a rich get richer bias which is best seen by varying the initial populations.
Instead of offering trial count and pick counts which are (invariates in the actual model) he could have picked initial ball count and initial white/red ratio.
Re: Polya Urn Simulation
#7I must admit: this went against my intuition. My first guess was that you would end up with an urn full of either red or blue balls.
Me too, but only because I was expecting something interesting to happen since it was on HN!
The uniform distribution result is not interesting enough for you?
Re: Polya Urn Simulation
#8I must admit: this went against my intuition. My first guess was that you would end up with an urn full of either red or blue balls.
Bear in mind the default behaviour if there were just two balls and you never added any more. Then the proportion of red picks vs blue picks would tend to 1/2. So there's naturally a tendency for the proportion to concentrate in the middle.
As you say, the way in which new balls are added tends to push the proportion towards the extremes.
The uniform distribution is the result of these two tendencies exactly cancelling out.
Re: Polya Urn Simulation
#9> After a large number of picks, what is the behavior of the proportion of red balls in the urn Isn’t the more enticing question how strong the bias towards the first picked Color is?
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Re: Polya Urn Simulation
#10> After a large number of picks, what is the behavior of the proportion of red balls in the urn Isn’t the more enticing question how strong the bias towards the first picked Color is?
The expected terminal fraction is always equal to the current fraction. (Or is it?)