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What are the practical applications of non discrete probabilty spaces?

Anonymous Wed 11 Dec 04:25:04 2019 No.11216550 View Reply Original Report

Quoted By: >>11216586 >>11217187 >>11217315 >>11217850

What are the real life applications of doing this?
Specifically related to practical things like economics or data analysis.
Serious question don't want to be polemic.
This is from Billingsley.

Anonymous

Anonymous Wed 11 Dec 2019 04:42:47 No.11216586 Report

Quoted By: >>11216624

>>11216550
Open ANY decent book on probability theory, there will be plenty of examples.
Prices, income, consumer preferences, everything is modeled as a continuous process.
In fact, it us much, much less likely that you encounter discrete distribution when doing research in sciences than a continuous one (or even singular! Imagine that).

Normal distribution alone models so much. Weibull distribution is used for failure rates, exponential/Poisson for arrival rates, etc.

And if that's not enough, central to inferential statistics are statistical tests and all of them use, surprise, continuous distributions - chi-square, normal, Student, F-distribution, Kolmogorov-Smirnov has its own distribution, Dickey-Fuller has its own distribution, Durbin-Watson has its own distribution.

Just open *something*. A book, a wiki page, anything.

Anonymous

Anonymous Wed 11 Dec 2019 05:01:02 No.11216624 Report

Quoted By: >>11216675

>>11216586
Thanks a bunch.
I saw Billingsley as recommended reference book but I didn't know whether it was worth reading it.

How about Lebesgue specifically?
Can we assume that the Riemann–Stieltjes is enough for any real life purpose?

Anonymous

Anonymous Wed 11 Dec 2019 05:36:06 No.11216675 Report

Quoted By: >>11216724

>>11216624
If you are just interested in applications, sure.
The strength of the Lesbesgue integral is that it is more powerful when proving things involving limits (theorems like monotone/dominant convergence).
Also it allows to consider things like the limit of a sum of discrete random variables - this could have a cumulative probability distribution but no associated probability density (singular measure).

But you can read about applications of continuous random variables (which, to reiterate, is the main point of probability and statistics and is used everywhere) with the knowledge of Riemann integration only.

If you intend to delve deeper into theoretical economics, you may need Lesbesgue integration though.

Anonymous

Anonymous Wed 11 Dec 2019 06:10:50 No.11216724 Report

Quoted By: >>11217082

>>11216675
Very informative, thanks.
Any specific books you can recommend on the subject or that you have used?

Anonymous

Anonymous Wed 11 Dec 2019 11:14:39 No.11217081 Report

Quoted By: >>11217096 >>11217155 >>11217187

Are you a fucking idiot? Since when are prices of things discrete? Discrete probability spaces are a minority.

Anonymous

Anonymous Wed 11 Dec 2019 11:16:02 No.11217082 Report

Quoted By:

>>11216724
Not that guy, but just study any intro to probability book. The Lebesgue integration is already included, but you don't need to formalize that stuff, you'll just see shit as continuing weighting or convolution.

Anonymous

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Anonymous Wed 11 Dec 2019 11:32:59 No.11217096 Report

Quoted By: >>11217187

>>11217081
>Are you a fucking idiot? Since when are prices of things discrete? Discrete probability spaces are a minority.

Anonymous

Anonymous Wed 11 Dec 2019 12:41:55 No.11217155 Report

Quoted By: >>11217161 >>11217187

>>11217081
>Since when are prices of things discrete?
Since forever.
Every price has a finite decimal expansion.
Meaning it has the form $\displaystyle \frac{n}{10^{k}}$ for $n$ integer and $k$ non negative.
Have you ever spent $1/3$ of some currency.

Anonymous

Anonymous Wed 11 Dec 2019 12:45:57 No.11217161 Report

Quoted By:

>>11217155
Yes, I have.

Anonymous

Anonymous Wed 11 Dec 2019 13:05:06 No.11217187 Report

Quoted By:

>>11216550
>>11217096
>>11217081
>>11217155
as an example, why bother with modelling prices discretely? The finite decimal expansion is a nuanced technicality. Approximate with a continuous probability space, then take the floor/ceiling/round at the end. You can't buy anything with 1 penny, so who really cares if you are off by 1 penny?

Anonymous

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Anonymous Wed 11 Dec 2019 14:08:26 No.11217277 Report

Quoted By:

Is this better than Billingsley?
Billingsley is a meme who the fuck reads that.

Anonymous

Anonymous Wed 11 Dec 2019 14:48:16 No.11217315 Report

Quoted By:

>>11216550
>non-discrete probability
almost everything?

Anonymous

Anonymous Wed 11 Dec 2019 19:05:20 No.11217850 Report

Quoted By:

>>11216550
protip: none

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