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A better approch?

Posted By: Timothy Chow
Date: Thursday, 5 November 2009, at 3:37 p.m.

In Response To: A better approch? (Maik Stiebler)

Maik Stiebler wrote:

Uniform is Gaussian with s->infinity. Change the "uniform" in my previous post to "normal with a very large variance, if you're more comfortable with that, it does not change the essence of my message.

I accept the main point of your post, that it's reasonable to use a normal approximation here. So we're basically in agreement here.

However, I still don't get this technical point. I don't understand what you mean by "uniform is Gaussian with s -> infinity." Let's be more explicit here about what "uniform" means. There is no uniform distribution on the whole real line. I was taking it for granted that we were talking about a uniform distribution on a finite interval. This is certainly true at DMP. For money play, things are a little messy, because in principle the equity could be unbounded. I think one would then have to either give up on the idea of a "uniform" prior, or enforce some arbitrary upper bound. In any case, by "uniform" one can only mean uniform on a finite, bounded interval. This is not a Gaussian distribution in any sense, whether s -> infinity or not.

I believe that the posterior converges to a Gaussian but I don't understand what you're saying when you insist that it is a Gaussian.

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