How can I better constrain distributions with extremely long tails?

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CamillaNegri1
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Joined: Tue Mar 03, 2020 12:06 pm

How can I better constrain distributions with extremely long tails?

Post by CamillaNegri1 »

I have a few nodes with extremely long tails, which (I am guessing) leads to getting the errors "Discretization problem" etc, which means I have lots of overflow samples. I understand that a potential solution could be to reject the invalid samples, However, what if I want to have a more "permanent" solution? I still want to keep my upper boundary because it's physically logical.
marek [BayesFusion]
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Joined: Tue Dec 11, 2007 4:24 pm

Re: How can I better constrain distributions with extremely long tails?

Post by marek [BayesFusion] »

Hi Camilla,

I wish I had an answer for you but I'm afraid that there is really not a good way of dealing with this. It is really a question from outside of Bayesian network models, by the way. I would definitely keep the domains as they are, i.e., specify what ranges of values are legal for each of your variables. Rejecting invalid samples seems to me the way to go. Will you be losing anything if you do that? If you lose possible values, then perhaps you should extend the ranges of your variables?

I'm sorry I don't have a good answer for you. If I misunderstood your question, please describe the problem in more detail.
Cheers,

Marek
CamillaNegri1
Posts: 14
Joined: Tue Mar 03, 2020 12:06 pm

Re: How can I better constrain distributions with extremely long tails?

Post by CamillaNegri1 »

Dear Marek,

you're understanding my question completely, and I have also discussed with colleagues rejecting invalid samples as a solution. But what if I move my network to another tool (not Genie) and I cannot reject my samples? Also, I struggle to determine whether I'd loose information that way. Meanwhile, my problem with extending the ranges is that I am afraid they won't be physically logical.

I realize this is a vast subject that goes beyond BBNs, do you have any literature to recommend on this topic?

Thanks for your time and efforts!

Camilla
marek [BayesFusion]
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Posts: 430
Joined: Tue Dec 11, 2007 4:24 pm

Re: How can I better constrain distributions with extremely long tails?

Post by marek [BayesFusion] »

Hi Camilla,

I have always thought about this (i.e., modeling) as common sense, so nothing comes to mind in terms of the literature. As far as behavior of distributions with long tails goes, there is plenty of literature, including books -- a Google search will get you better results than what I can find for you. I am far from being an expert in this area.

My feeling is still that keeping the ranges consistent with physical constraints (e.g., length being not negative, height of a human being between zero and say 250cm, etc.) is the right thing to do. If you are missing any samples that you would not like to miss, it probably means that some of your equations or distributions were not right.
Good luck!

Marek
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