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Topic: Non standard probability theory
Replies: 12   Last Post: Dec 19, 2013 8:03 PM

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Scott Berg

Posts: 2,111
Registered: 12/12/04
Re: Non standard probability theory
Posted: Nov 12, 2012 12:40 PM
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"kir" <> wrote in message
On Sunday, November 11, 2012 4:18:15 PM UTC-5, Ray Vickson wrote:
> On Sunday, November 11, 2012 7:38:09 AM UTC-8, kir wrote:

>>> > What kind of work is being done in probability theory beyond the
>>> > standard normally used? I know that negative >>>probabilities have
>>> > been discussed. Is there anything else?


>> I'm not sure this is what you want, but there has been work in
>> Probability theory using "non-standard analysis", so >one can talk about
>> actual infinitesimals, etc. Perhaps the most accessible introduction to
>> this is the old but still >good >little book by Edward Nelson ("Radically
>> Elementary Probability", Princeton U. Press). You can download a >free
>> pdf >version from Edward Nelson's home page: just go to his publications
>> list and click on the book title.


>> RGV

>Primarily dealing with nonstandard analysis. I suppose I really need to
>study measure theory before I can dive in too >deep. Dealing with
>infinitesimals is a great extension in my opinion. It always bothered me
>that we often define >something with probability zero to mean it can't
>occur, yet even though in the case of an infinite probability >distribution

> >X P(X=x) = 0 for all x values. One x value DOES occur.

>What's really true is that it occurs with infinitesimal probability.

better yet, look for error ball of radius approaching zero.

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