guys I've proven that absense of evidence is evidence of absence. what should I so with this discovery?
the only assumption necessary for this proof is that none of the events have a probability of 0 of occuring. let x be some event and e be an event which makes x more likely when e is true , aka evidence for x so P(x|e)>P(x) and let x' and e' be the complements/negation of x and e and let denote a 2 way implication, in other words "if and only if" then P(x|e)>P(x) 1-P(x|e)P(x) by bayes theorem P(e|x)P(x)/P(e) > P(x) P(e|x) > P(e) now apply result (1.) P(e'|x) < P(e') by bayes theorem P(x|e')P(e')/P(x) < P(e') P(x|e') < P(x) applying result 1 again P(x'|e') > P(x') Q.E.D.
So e being evidence for x is equivalent to not e being evidence for not x. And before you complain that absence does not mean negation, look at the original phrase >absence of evidence is not evidence of absence here evidence of absence clearly means the absence of something, meaning there is no such thing, meaning the thing does not exist, meaning more generally that the event is not true i.e. the negation of the event. therefore rigorously speaking, absence does mean negation.
dude... absence of evidence is NOT evidence of absence!
Hunter Jackson
Where does the absence of evidence appear in your "proof"? I see evidence in every single inequality.
Christian Fisher
Suppose probability of evidence is certain: P(e) = 1
Your second line becomes P(x) > P(x).
Nah.
Adrian Reed
event e is evidence for event x === P(x|e) > P(x) e' i.e. the complement or negation of e is the absence of evidence.
Ian Bennett
Logical negation is not a good representation of what "absence" means, if we haven't found e then the probability of x given the absence of e is P(x|e'). But then after finding e, our new probability is P(x|e',e)=0.
The issue is the illogical assumption that the phrase "absence of evidence" ought to be modeled mathematically as a construction that actually models presence of evidence to the contrary.
Leo Jones
>e' i.e. the complement or negation of e is the absence of evidence. But e' is evidence, since P(x'|e') > P(x'), so it cannot not be evidence.
Kevin Morris
yes, like I said this proof holds whenever and only when none of the probabilities are 0 . P(e) = 1 would mean P(e') = 0
your fault for not reading the proof properly.
Colton Richardson
in that case x' is not absence, it is presence of not-x
I believe your complaint is already answered in the OP post: And before you complain that absence does not mean negation, look at the original phrase >absence of evidence is not evidence of absence here evidence of absence clearly means the absence of something, meaning there is no such thing, meaning the thing does not exist, meaning more generally that the event is not true i.e. the negation of the event. therefore rigorously speaking, absence does mean negation.
Camden Green
>in that case x' is not absence, it is presence of not-x What would it mean for something to "be absence"?
John Garcia
>it's not valid for the trivial cases that show the whole thing is wrong >but trust me it's right the rest of the time :^)
Parker Howard
>But then after finding e, our new probability is P(x|e',e)=0.
the new probability is actually P(x|e) e' is no longer the case so it is not "given" so we do not have probability of x given e and not e. we simply have the probability of x given e.
John Richardson
as explained, negation.
>hurr look guys bayes theorem doesn't apply when conditioned on probabilities of measure 0 therefore bayes theorem is wrong!! YESSS EPIIICCC WIIIIIINNNNNNNN ;^)
Grayson Anderson
>as explained, negation. What does it mean for something to "be negation"?
Asher Barnes
>the new probability is actually P(x|e) e' is an event though, either it occurred or it didn't.
Brandon Powell
>>hurr look guys bayes theorem doesn't apply when conditioned on probabilities of measure 0 therefore bayes theorem is wrong!! YESSS EPIIICCC WIIIIIINNNNNNNN ;^) Who are you quoting?
Christopher Sanders
>Veeky Forums got baited again Not surprised desu
Brandon Clark
The truth value of a proposition is independent of the evidence. Also, outside quantum mechanics the actuality of something existing is either 1 or 0. So there is no, "Evidence adds to the probability." There is only actuality and it is independent of the evidence.
>the negation of something is the complement of that thing Yes but what does it mean to "be negation"?
Julian Kelly
probability isn't a branch of physics or applied mathematics, it's a branch of pure mathematics.
also it is very brainletish of you to claim that only quantum mechanics gives probability meaning or validity when you could just adopt the de-broglie-bohm interpretation of quantum mechanics and say that the "actuality" of anything being the case or existing is 1 or 0.
Camden Williams
>probability isn't a branch of physics or applied mathematics, it's a branch of pure mathematics. Probability is applied mathematics, actually.
Joshua Rogers
I don't know. I didn't write "be negation" I did my best to interpret your post that said "be negation".
>I don't know. I didn't write "be negation" I did my best to interpret your post that said "be negation". see > x' is not absence
Ethan Garcia
Wrong, brainlet.
Jose Scott
>wikipedia's article categorisation is a greater authority on probability than Kolmogorov please , kid . you're just embarrassing yourself
nevertheless, probability is not applied because it is not predicated whatsoever on the real world anymore than analysis is.
the foundations of probability aren't based on doing experiments in real life, they're based on measure theory and were formulated by kolmogorov at the beginning of the 20th century.
Benjamin Rivera
>>wikipedia's article categorisation is a greater authority on probability than Kolmogorov >please , kid . you're just embarrassing yourself Where does Kolmogorov say probability is pure mathematics? It doesn't say that anywhere in the Wikipedia article you linked.
Juan Barnes
that should probably say absence of x
Jack Martin
Probability doesn't describe real life, which is where you went wrong in the OP.
Juan Anderson
when he formulated probability from measure theory rather than any reference to experiments or the real world.
Levi Gonzalez
>when he formulated probability from measure theory rather than any reference to experiments or the real world. Did you misread my post? I asked "Where does Kolmogorov say probability is pure mathematics?". You answered with why "you" think probability is pure mathematics.
Benjamin Lee
on the contrary, probability does describe real life very well. It describes situations where were are uncertain about all the information or unable to do all the necessary calculations to reach a certain answer and does so well. The proof that it does so well is that we are able to use probability to solve many problems much better than we would if we tried to model the situation deterministically or if we gave up trying to address the problem at all because we lack the informtion or computational power necessary to reach a deterministic answer.
e.g. medical diagnoses e.g. failure/reliability engineering. e.g. network queues
Oliver Reed
no, I answered with what he did , and what he did means that probability is pure mathematics.
You're throwing a hissyfit because when you learnt probability you learnt about dice and bernoulli trials and so are unaware that probability is actually a pure branch of mathematics whose formulation is based on measure theory.
Camden Jones
A mental model is not reality. Your uncertainty about your mental model's accuracy is not reality's uncertainty about its own truth value. Reality is either 1 or 0.
Asher Brooks
>You're throwing a hissyfit because when you learnt probability you learnt about dice and bernoulli trials and so are unaware that probability is actually a pure branch of mathematics whose formulation is based on measure theory. But I learned probability both ways, and irregardless, how I personally learned it doesn't change its nature of being applied maths.
Hudson Cook
What is applied mathematics in your opinion?
Jonathan Reyes
>A mental model is not reality. and a description is not reality either. probability is a description and a model of reality and may or may not be reality (it is if the non-deterministic interpretations of QM are right, it is not if they are not).
in that case arithmetic is applied maths because cavemen used to formulate arithmetic in terms of visible, distinct objects in the real world good one brainlet also >irregardless heh...sheesh kid...
Lincoln Brooks
applied mathematics is formulated in terms of the real, physical world, pure maths is formulated totally independent of the real world.
Jeremiah Rivera
>applied mathematics is formulated in terms of the real, physical world, pure maths is formulated totally independent of the real world. Can you give an example?
Aaron Williams
>in that case arithmetic is applied maths because cavemen used to formulate arithmetic in terms of visible, distinct objects in the real world How exactly does that follow?
Jose Phillips
operational research
Ryan Nguyen
>probability is a description Only of meatspace. You can't break it out of that. Trying to say that your meatspace interpretation of the evidence creates the Universe is just as illogical as trying to define God into existence.
Wyatt Cox
>people used to formulate arithmetic in terms of the real world so arithmetic is applied mathematics >people used to formulate probability in terms of the real world so probability is applied mathematics
Oliver Hall
>>people used to formulate probability in terms of the real world so probability is applied mathematics Who are you quoting?
Brayden Reed
you when you insisted that probability is applied mathematics despite supposedly learning its rigorous formulation in terms of measure theory.
Matthew Morris
t. Freshman.
Charles Miller
>you when you insisted that probability is applied mathematics despite supposedly learning its rigorous formulation in terms of measure theory. Can you point to the post where I said it? I don't recall saying such nonsense.
Cooper Moore
>operational research What part of operations research can not be formulated independently of the real world?
Eli Robinson
I'm changing my answer.
Applied mathematics is actually a branch of mathematics that deals with mathematical methods that find use in science, engineering, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.
probability requires no specialised knowledge , unlike say operational research.
Robert Moore
Probability also doesn't describe reality.
Logan Sanders
here >But I learned probability both ways, and irregardless, how I personally learned it doesn't change its nature of being applied maths.
Christian Kelly
yes it does. It's a model of reality that is accurate in useful ways so it describes reality.
Jace Robinson
I meant the part where I allegedly said "people used to formulate probability in terms of the real world so probability is applied mathematics".
Xavier White
>Applied mathematics is actually a branch of mathematics that deals with mathematical methods that find use in science, engineering, business, computer science, and industry. So you're saying probability does not find use in engineering, business, computer science, and industry?
Lucas Stewart
>probability requires no specialised knowledge , unlike say operational research. What specialized knowledge does operations research require?
Brayden Murphy
A description of a model of a thing is not a description of the thing.
Benjamin White
the fact that you insist that probability is applied mathematics despite knowing that it's rigorous formulation and modern study is founded in measure theory can only be explained by you thinking that because probability used to be part of applied mathematics by virtue of people doing it in a way that necessarily related to the real world it must still count as an applied branch of mathematics.
Connor Butler
You understood the maxim wrongly. Both e and e' are evidence. e is evidence that supports the claim, e' is evidence that disproves it. "evidence of absence" is correctly modeled by negation, but "absence of evidence" is not. True "absence of evidence" would make you unable to conjure a suitable e (or e', for that matter).
Dylan Wood
>the fact that you insist that probability is applied mathematics despite knowing that it's rigorous formulation and modern study is founded in measure theory can only be explained by you thinking that because probability used to be part of applied mathematics by virtue of people doing it in a way that necessarily related to the real world it must still count as an applied branch of mathematics. Why can it only be explained that way? I don't follow. And my position is that "probability is a part of applied mathematics", not that "probability used to be part of applied mathematics".
Game theory has also been formulated axiomatically, but that doesn't prevent it from still being applied mathematics (as it always has been).
Michael Ross
that is not what "deals with" means. by equating "deals with" with "finds use" you thereby make number theory, abstract algebra, algebraic topology, mathematical logic all branches of applied mathematics so your attempt to twist the meaning is absurd. specialist insight into what suitable modelling assumptions of the factory/road system/network are.
probability is not a description of a model of reality. it is something that can be used to model and thus to describe reality. en.oxforddictionaries.com/definition/model >model >a representation >a description
Ayden Cox
>that is not what "deals with" means. >by equating "deals with" with "finds use" you thereby make number theory, abstract algebra, algebraic topology, mathematical logic all branches of applied mathematics so your attempt to twist the meaning is absurd. Can you explain what "deals with" means?
Levi Johnson
using the same word in the same sentence to mean 2 totally different things would be illogical and very poor english.
the fact that absence is used later in the sentence to mean negation/complement means that earlier in the sentence it must also mean that.
Or else I could just as easily say that "absence of evidence is not evidence of absence" means "being ignorant of the evidence is not evidence of being ignorant of "
Colton Ortiz
I don't need to. It is sufficient for me to point out that according to your interpretation branches of mathematics that are definitely pure would count as applied and therefore your interpretation is incorrect.
Luis Morris
"There being no evidence is not evidence of there being no [what we are talking about]."
John Carter
>probability is not a description of a model of reality. it is something that can be used to model and thus to describe reality. Things either exist or they don't. Probability does not describe reality.
Jack Long
That was rhetorical exaggeration. It can't only be explained that way. perhaps you chose your words at random and produced those sentences by chance, or through some other inscrutable and incorrect thought process. the explanation I provided was simply my best guess at why you believe something incorrect.
Logan Hernandez
>specialist insight into what suitable modelling assumptions of the factory/road system/network are. Why do you need specialist insight into suitable modelling assumptions? You can do research on general road systems and general networks and on factories (assuming you're talking about facility location) using graphs.
Jason Young
>by equating "deals with" with "finds use" When did I do that? "find use" is in YOUR definition of applied mathematics.
Connor Taylor
>the explanation I provided was simply my best guess at why you believe something incorrect. Your guess was wholly incorrect.
Julian Stewart
>It is sufficient for me to point out that according to your interpretation branches of mathematics that are definitely pure would count as applied and therefore your interpretation is incorrect. What do you mean by "my interpretation"? We're using your definition of applied mathematics (see ), in which case either probability is applied mathematics, or it does not find use in in engineering, business, computer science, and industry (which is absurd).
Leo Harris
>the fact that absence is used later in the sentence to mean negation/complement means that earlier in the sentence it must also mean that. The English language is not commutative.
Christopher Cox
yes it does. it models parts of reality very well, therefore it describes those parts of reality very well since the words are synonyms that differ only in connotations. A description does not need to be an exact specification to be a description.
Hudson Brown
without specialist insight your model and attempt to solve the problem would probably be worthless.
If you need convincing of this you can attempt to become an operational researcher and attempt to solve problems for companies with only a lay person's knowledge about the the system you are trying to solve a problem for and see how successful you are.
Jeremiah Peterson
>without specialist insight your model and attempt to solve the problem would probably be worthless. How does this not apply to probability?
Adam Hall
you're only using part of the criteria I gave. as I said before:
Applied mathematics is actually a branch of mathematics that deals with mathematical methods that find use in science, engineering, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.
probability requires no specialised knowledge , unlike say operational research.
Lucas Gonzalez
>probability requires no specialised knowledge without specialist insight your model and attempt to solve the problem would probably be worthless.
If you need convincing of this you can attempt to become an probability researcher and attempt to solve problems for companies with only a lay person's knowledge about the the system you are trying to solve a problem for and see how successful you are.
Mason Edwards
in probability the axioms are chosen by the mathematician and so fully specified thus do not require specialist knowledge. You already possess all the knowledge necessary to derive probability.
Dylan Cox
wrong. see
Aaron Miller
>in probability the axioms are chosen by the mathematician and so fully specified thus do not require specialist knowledge. without specialist insight your model and attempt to solve the problem would probably be worthless.
If you need convincing of this you can attempt to become an probability researcher and attempt to solve problems for companies with only a lay person's knowledge about the the system you are trying to solve a problem for and see how successful you are.
Michael Lee
repeating your point after it's been answered and refuted just makes you look stupid and like a sore loser.
Jose Hall
>refuted Where was it refuted?
Easton Gutierrez
You know where. if you think I'm wrong then refute my post.
Jaxson Gomez
>if you think I'm wrong then refute my post. Wrong about what?
without specialist insight your model and attempt to solve the problem would probably be worthless.
If you need convincing of this you can attempt to become an probability researcher and attempt to solve problems for companies with only a lay person's knowledge about the the system you are trying to solve a problem for and see how successful you are.
Landon Hall
>You know where. if you think I'm wrong then refute my post. There's an absence of evidence for anything you've posted that resembling a "refutation" (note that this is not evidence of absence).
Daniel Thomas
If you think that what my post has stated is wrong then refute it.
Jacob Brown
here's the evidence if you think that this post fails to answer and refute your point then demonstrate so.
Isaac Edwards
>If you think that what my post has stated is wrong then refute it. Probability researchers can't solve problems for companies with only a lay person's knowledge about the the system they are trying to solve a problem for.
Grayson Brown
What you're describing isn't researching probability, that's simply using probability in an applied setting. Researching probability would mean deriving theorems from axioms and other theorems. in probability the axioms are chosen by the mathematician and so fully specified thus do not require specialist knowledge. You already possess all the knowledge necessary to derive probability.
the fact that a field of mathematics can be used in an applied setting does not make the field applied. If this were the case then arithmetic, alegbraic topology and linear algebra would all be applied branches of mathematics . We know that they are not applied branches of mathematics therefore the fact that a branch of mathematics can be used in an applied setting does not make that branch of mathematics applied.
Thomas Kelly
>What you're describing isn't researching probability Then what you're describing isn't researching operations research.
Ethan Turner
You are saying that a statement about absence of evidence doesn't apply when evidence cannot be absent. That's simply irrelevant.
Ryan Scott
>Researching probability would mean deriving theorems from axioms and other theorems Why can't this be done in an applied setting?
the difference that you do not seem to grasp is that you can make progress in probability in a vacuum , the same with all fields of pure mathematics. you simply choose axioms then you can derive all the other theorems with logic.
Specialist knowledge is required in operational research because you cannot do operational research without specialized knowledge because the study is fundamentally linked with solving real world problems in companies, armies, road systems, etc. and you need to actually know about the real world and those systems and behaviour in order to model them suitably and find the best or a very good solution for the problem they are having.
John Thompson
>The truth value of a proposition is independent of the evidence. I don't see how that's relevant. Evidence is something which when known increases the probability of something else being true. That is all one needs to interpret the phrase "the absence of evidence is (not) evidence of absence."
Charles Nguyen
because without specialist insight your model and attempt to solve the problem would probably be worthless.
If you need convincing of this you can attempt to become an operational researcher and attempt to solve problems for companies with only a lay person's knowledge about the the system you are trying to solve a problem for and see how successful you are. see also
If having evidence supporting the claim is possible, then there cannot be an absence of evidence supporting the claim and against the claim, since the lack of one is the presence of the other. So your interpretation is basically useless.
Cooper Hall
>If having evidence supporting the claim is possible, then there cannot be an absence of evidence supporting the claim and against the claim, since the lack of one is the presence of the other. How does that follow?
