Sure I think that
Of course you do, you’ve known that since you first started walking. Since you stick to your beliefs there is no changing that.
You’ve known since day 1 that the sun will always rise just like you will.
But here’s a tip from a mechanic of 60 years…The more days that you start your car the less likely it is to start the next day.
Both of these are empirical reasoning: the first is your prior probability, the second is your posterior probability.
Neither is the hypothetical case I describe, where the fairness of the coin isn’t a prior, it’s a given. Is that a meaningful distinction for you?
The “fairness” of a coin is basically “how often.” It is information that is known about the coin that affects “how often” a given outcome will occur.
The “fairness” of a coin does not affect the number of possible outcomes. If you want to talk about “fairness” then you are speaking about “how often” which is not a calculation of possible outcomes.
Is the distinction between a “prior” and a “given” a meaningful distinction for you?
If it’s a given it’s prior, right? If it’s prior then it’s a given, right?
Do you agree that the more days the sun rises the less likely it is to rise the next day?
Good, no, this is not right.
A given is a fact that’s stipulated as true at the outset. It’s not a best guess or estimate, it’s a known fact about the hypothetical situation.
A prior is a best guess or estimate. The truth of the matter is unknown, and before any observation you have only your best guess about what the truth is.
A prior can be mistaken, and when it is that mistake can be revealed by observation. A given cannot be mistaken within the context of the hypothetical.
If it’s a prior that the coin is fair, you could say “I don’t know if this is a fair coin, but my best guess is that it is.”
If it’s a given that the coin is fair, you could say “I know that the coin is fair.”
If you have different words that you use for these concepts, I’m happy to use them, but I want to make sure you see the distinction between the concepts.
It is YOU that is playing word games with words.
If I say I am going to sweep my porch prior to going to the store, what does that mean to you?
Prior to me means something about the order of things on a timeline, prior being earlier on the timeline compared to some other thing.
So we have now 4 shoes that are 6 pair of shoes, and prior is a best guess…
WTF?? Word game much?
Carleas, You forgot to answer my question:
Do you agree that the more days the sun rises the less likely it is to rise the next day?
Again, I want to talk about those concepts, I’m happy to use different words.
I’m not using prior as an adverb, I’m using it as a noun, as a short form of the phrase “prior probability distribution”. It’s the estimate of the probability distribution before an observation (contrast “posterior probability distribution”, the estimate of the probability distribution after an observation).
Flannel said words are a popularity contest.
Nobody I know would think “prior probability distribution” when saying the word “prior.”
Ask anyone what prior means and see how many people respond with
“prior probability distribution” or “best guess.”
If you are going to use some word that is totally off base with the standard understanding then it behooves you to explain the meaning and context PRIOR to using it.
I agree it’s not it’s most common meaning, it’s a technical meaning used in discussions of probability. From wikipedia:
A prior probability distribution of an uncertain quantity, often simply called the prior, is its assumed probability distribution before some evidence is taken into account.
But I will stop using it if you find it misleading. Will “prior probability distribution” work for you, or is there a different word you’d prefer to use? Or is the concept unclear?
Wikipedia also suggests axiom, postulate, or assumption as synonyms for “given” in the sense I am using it, would one of those work better for you?
You are misunderstanding that quote. They are using the word “prior” exactly as I described it, “before” which in simple terms is a “before” probability distribution, ie a probability distribution “before” the evidence.
It is not a “guess” it is “before” the evidence. On a timeline the probability distribution is PRIOR (before) to the evidence.
Great, we’ll call it a “guess before the evidence”.
Now compare to what I’ve called a “given”, which is not a guess, it is not uncertain, it is stipulated as true. Do you see how this is a different concept?
The probability distribution is the guess. The fact that it is prior to the evidence means it occurs before the evidence.
The sole meaning of the word “prior” in that quote is used as “before.”
I’m not talking about the word, I’m talking about the concept.
And that concept is different from the concept that I’ve called a “given”
Like I explained before this went into a tailspin because you claimed “prior” means “best guess”, something prior is a given, and something given is a prior, right?
“Given the fact that a bicycle has 2 wheels, how many wheels do 2 bicycles have?”
You are given a fact prior to the question of how many wheels for 2 bicycles. The given was prior and the prior was a given.
Is the distinction between a ‘guess before the evidence’ and a ‘given’ a meaningful distinction for you?
Not really. A “guess before the evidence” is a guess given prior to the evidence. If a guess is given prior to the evidence then it is a given prior to the evidence.
Given HP = Torque x RPM / 5252, how much torque at 5252 RPM is 100 HP?
You are GIVEN the formula PRIOR to answering the question. Or you could say a “given” was prior information, or prior guess, or prior facts.