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outrun
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Re: negative transition probability

November 9th, 2016, 11:51 am

Negative weights in the trinomial tree mean that you are trying to model a certain yield/volatility configuration which it can't handle. Indeed not up for it.

And stop calling it negative probabilities, pseudoscience has its own vocabulary, it's called pseudoprobability because it's not a probability. This is definition abuse I have seen since dunrepp
 
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Cuchulainn
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Re: negative transition probability

November 9th, 2016, 12:07 pm

Negative weights in the trinomial tree mean that you are trying to model a certain yield/volatility configuration which it can't handle. Indeed not up for it.

And stop calling it negative probabilities, pseudoscience has its own vocabulary, it's called pseudoprobability because it's not a probability. This is definition abuse I have seen since dunrepp
+1
 
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Collector
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Re: negative transition probability

November 9th, 2016, 2:08 pm

And stop calling it negative probabilities, pseudoscience has its own vocabulary, it's called pseudoprobability because it's not a probability. This is definition abuse I have seen since dunrepp
Will the Professor take notice ? R.F.
 
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outrun
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Re: negative transition probability

November 9th, 2016, 2:49 pm

And stop calling it negative probabilities, pseudoscience has its own vocabulary, it's called pseudoprobability because it's not a probability. This is definition abuse I have seen since dunrepp
Will the Professor take notice ? R.F.
"we must say it this way if we wish that our way of thought and language be precisely the same whether the quantities are either positive or negative"

No, I don't wish for that, it (note: "quantities") has nothing to do with probabilities. Maybe with conditional probabilities or just operators..

Always good to read RF though, thanks
 
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outrun
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Re: negative transition probability

November 9th, 2016, 3:16 pm

I was just in the supermarket, trying to get my hands on the last batch of cans, and then I got this great idea. I'm pretty sure I've proven the Riemann conjecture *but* under the condition of validity of negative probabilities. So I propose a bet! 

1) I provide a proof of the Riemann conjecture starting out with a validity of negative probabilities axioma. It will be easy to follow for you to accept this bet. I've done this twice before here on this forum. It was so awesome that someones head exploded.
2) I submit the proof to some journal, collect the $1mln millennium prize money, and give you half!
3) In case they don't accept my paper (and deny me the $1mln prize) because of that axioma, you give me $50k to compensate me for wasting my time. This is just 10% of your upside.
 
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Traden4Alpha
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Re: negative transition probability

November 9th, 2016, 3:27 pm

Given N axioms there are O(3^N) possible mathematical systems based on whether we assert each axiom to be strictly true, strictly false, or not asserted. Obviously, most of these systems are nonsensical but there's still a rather large set of potentially meaningful systems. And if the average sensible system contains M axiomatic assertions, then there's another O(2^M) sensible systems based on relaxation of some of those assertions (e.g., geometry where Euclid's 5th is not asserted).

The point is that there are a very large number variant systems of which mainstream math only focuses on the tiniest percentage of them. But there's a limited vocabulary of common mathematical terms (e.g., probability, function, or exponential) when we communicate. Although signaling the non-standard variant of a term is crucial, I'm not sure that appending pseudo is the best strategy. Do we really want to have pseudoprobabilities (e.g., probabilities that can be negative), pseudofunctions (functions that output a set instead of a scalar), or pseudoexponentials (e.g., exp() that operates element-by-element on an array) to denote alternative mathematical systems?
 
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outrun
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Re: negative transition probability

November 9th, 2016, 3:43 pm

This is worse, probability had a precise meaning, and this new definition conflicts.

Matrix exponential is named matrix exponential and not exponential. Also: passing a matrix to exp and getting new behaviors does not *invalidate* the more common usage of passing numbers. It's type specific parallel non-conflicting behavior. So that not a good analogy.
 
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outrun
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Re: negative transition probability

November 9th, 2016, 3:52 pm

It's no different from claiming that 1.5 is an integer.
 
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Collector
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Re: negative transition probability

November 9th, 2016, 3:54 pm

This is worse, probability had a precise meaning, and this new definition conflicts.

Matrix exponential is named matrix exponential and not exponential. Also: passing a matrix to exp and getting new behaviors does not *invalidate* the more common usage of passing numbers. It's type specific parallel non-conflicting behavior. So that not a good analogy.
and when we talk about an atom we naturally always use its precise original meaning: uncuttable, indivisible particle? It was the main point of the atom was it not...until the word was totally polluted (by great scientists.)

welcome to the real word where language and words changes their meaning over time, and even have different meaning among different gropes of people, it is possibly outside the Gaussian way of thinking  ;-)

So who should we blame this time for polluting the precise (?) meaning of probability: Feyman, Dirac? 

"and this new definition conflicts. " define "new" ? ;-) a little bit of precision is expected. Is Feyman not quite old ;-) Well quite new compared to the indivisible atom!

What we need is possibly Imprecise probability
 
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Cuchulainn
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Re: negative transition probability

November 9th, 2016, 4:16 pm

It's fun listening to non-mathematicians talking about mathematics. It's all over the place.
 
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Collector
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Re: negative transition probability

November 9th, 2016, 4:28 pm

It's fun listening to non-mathematicians talking about mathematics. It's all over the place.
I thought mathematicians derive equations ;-) and not talk so much about wording and framing. If not can express it with math, then express it with probability ;-) I am talking about negative probabilities of course, sorry I mean negative pseudo probabilities to be precise-im!!   
 
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Traden4Alpha
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Re: negative transition probability

November 9th, 2016, 4:36 pm

This is worse, probability had a precise meaning, and this new definition conflicts.

Matrix exponential is named matrix exponential and not exponential. Also: passing a matrix to exp and getting new behaviors does not *invalidate* the more common usage of passing numbers. It's type specific parallel non-conflicting behavior. So that not a good analogy.
Many things have a precise meaning under the most common variants of math that are horribly violated under other variants of math.

A "line" is certainly very well defined. Yet the common definition is violated by non-Euclidean geometry and our actual universe.

As for 1.5 being an integer, it certainly has integer-like properties when encoded as a fixed-point integer data format.

At some level it's not unlike the namespace concept in software or computer networks. As long as we are careful to signal the scope of the name, things work out. Maybe math needs to avoid the equivalent of global variables and not assert that "probability" has only one possible definition that must be true in all contexts and scopes. Global names assume that the usage patterns of math are fixed for all time which does not seem like a robust assumption.
 
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outrun
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Re: negative transition probability

November 9th, 2016, 4:50 pm

The Indian PI bill that tried to redefine PI to 3.2 by law

http://m.mentalfloss.com/article.php?id=30214


Wouldn't it be easy if we could prove a bunch of conjecture by redefining the objects they conjur about?
 
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Traden4Alpha
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Re: negative transition probability

November 9th, 2016, 5:57 pm

The Indian PI bill that tried to redefine PI to 3.2 by law

http://m.mentalfloss.com/article.php?id=30214


Wouldn't it be easy if we could prove a bunch of conjecture by redefining the objects they conjur about?
Actually, Pi = 4:

Image

I do agree with your point. A conjecture has a associated context of defined elements and if one changes the definitions, one changes the meaning of the conjecture. A proven conjecture about a Euclidean line may not be a proven conjecture about a non-Euclidean line and vice versa. It's then a matter of who defines the "normal" set of definitions and terms and whether those mainstream terms change over time.

Change the definition of "distance" and one changes many other things. In L-2 space, Pi = 3.14159.... but in L-1 space it is 4.
 
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Collector
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Re: negative transition probability

November 9th, 2016, 9:39 pm

October 2016: ,Negative Probabilities and contextually Journal of Mathematical Psychology, Foundations of Probability Theory in Psychology and Beyond (mostly beyond I think :-)

I can't see the abstract, I suspect it is a probability treatment for people denying Negative Probabilities? or possibly a probability treatment for people abusing this term  ;-O

Psychologists hay jacking negative probabilities, what? This is getting very very dangerous!   (Physics and finance okay, negative probabilities + Psychology is just beyond my probability model )


Outrun on his first appointment with the Mathematical Psychologists
 
And stop calling it negative probabilities, pseudoscience has its own vocabulary
Mathematical Psychologist: Do you want the blue or the purple pseudo-probability-pill ?

would make a great movie? how will the story end?

Image
Last edited by Collector on November 9th, 2016, 10:12 pm, edited 4 times in total.