Board Thread:General Discussion/@comment-26006155-20200107155350/@comment-32182236-20200204211306

I'll probably make one last response, and then just get to my Mother Analysis.

...An actual ban? Seriously?

..And this time, no reference to what the ban was for, though there is a link to ask questions about it.

@Jacky:I second that-It likely was meant for Merc!THA. After all, my account was created in 2017, which is less than 4 years ago, so it can't just be to me.

@Ferret, you're not the reason why I left FNAF. That happened before we even met. You're better at solving the lore than Matpat. And while I still don't believe Sans is Ness, you made a stronger case than he did.

The Game Theorist channel simply starts with an idea, and then tries to collect evidence for that theory. Take a look here:https://youtu.be/EeHzGEgDcig?t=565

"You control the story. Don't feel like you have to talk about everything. Focus on the stronger evidence and brush aside some of the weaker moments and parts that may contradict what you're trying to prove. For a good example, look at the Mario is Mental series of videos-- I really focus in on that shoe grinding moment and avoid all mention of the good things Mario has done throughout the series. In that way, I'm able to direct viewer focus to what is going to be most compelling for the overall story I'm trying to tell. ".

That's not how you theorize games.

During the "Nazi" incident, where I was trying to explain how I figured out some members of the Afton Family had an African American mother, Merc was my very loudest and most personal detractor. Loudly shouting about the Holocaust and calling my theories personally "disgusting".

..That just isn't right.. That has nothing to do with the topic at hand.

If that's what happened, then Triss should have given a strike to Merc. ...Though I'm not sure if they could, considering the fact that Merc is a moderator. Is Triss above Merc?

Time and again, they all say that I have "no evidence" for my theories. Even after I've submitted a mountain of evidence. They keep saying small details don't matter. The child pictures on the walls, don't matter. Because they say so. Even if I can positive-ID several members of the Afton Family in those pictures now, that's still just trying to use my theories as evidence. Which should be ignored. Because it is No Evidence.

That's one broad way of thinking, actually.

But perhaps we need a more formalized version of my take on the matter. Perhaps it'll help resolve what might look like inconsistencies in my take (like times where I've said every detail is important, while also saying three rocks are just three rocks.)

Let's use Bayes' Theorem-This will help us find the strength of evidence. (I was going to use this either in Part 4 or Part 5 in my series, because it's important for inductive reasoning.)

P(A|B)= (P(B|A)P(A)/P(B)

..Hm, we should probably rename our variables.

P(H|E)= (P(E|H)P(H)/(P(E)

H stands for a particular hypothesis, and E stands for a particular kind of evidence.

What this formula is telling us is the probability of a hypothesis after finding evidence E is based on the likelihood of hypothesis E appearing if hypothesis H is true, the prior probability of hypothesis H, and, of course, the likelihood of just seeing that evidence anyway. After all, it could have appeared randomly. Maybe that rock is there because we're in ruins, where rocks are commonly found, not that someone brought it underground and hit Toriel with it.

P(E) can be calculated by adding P(H)P(E|H) to P(¬H)P(E|¬H).

Now, let's calculate the Bayes' probability of a coin being rigged to always show heads.

We'll assume prior probability of .001. That is, 1 in 1000. (The prior probability's the hardest to figure out-Sometimes, we really only have a guess for it. If we're trying to see if someone has a rare disease, we use the rarity of the disease as the prior probability, for example.)

So our hypothesis, H, is that the coin is rigged. We'll see what happens if we flip 12 heads in a row.

P(rigged coin|E)= (P(E|H)P(H)/(P(E)

P(H) is .001, and the probability of seeing the evidence IF the coin is rigged is 1. So multiplying them gives us .001. Now to calculate the denominator.

P(E)=P(H)P(E|H)+P(¬H)P(E|¬H)

We already calculated the first part to be true-As you can see, the first part is the same as the numerator. Keep it in mind, so you can use it as a shortcut. You can just copy/paste the numerator into the first part of the denominator, and only manually calculate the second part of it.

P(E)=.001+P(¬H)P(E|¬H)

P(¬H)=1-P(H) (This is always true.)

P(E)=.001+.999P(E|¬H)

As you can see, the last bit that matters is the odds of the evidence showing up anyway if the hypothesis is false.

This is what I mean when I say sometimes three rocks are three rocks. If it's reasonably likely to see them anyway, there's no reason to assume they mean something. But if it's abnormal, then it probably means something.

12 heads has odds of 1/2^12. Or 1/4096. Or .00024414063. So we multiply it by .999 to get .00024389649, and add it to .001 to get .00124389649. And that's the denominator. Now we divide the numerator (.001) by the denominator to get 0.80392541344. So there's about an 80.39% chance that the coin is rigged. That's the new probability.

When there's multiple pieces of evidence, we calculate them one at a time, but we make sure to use the new probability we got from the previous calculation as the new prior probability. We continue doing this, until all the evidence has been presented.

In the case of counter-evidence, we flip the probability around and plug that in, basically swapping ¬H with H.

..Perhaps we should start formally using Bayes' theorem. We can start discussing each piece of evidence, and find out exactly where we disagree.

Perhaps breaking the evidence into parts, and going over probability theory if we disagree on P(E|¬H).

"Going too deep" is never a problem. Going the wrong way is, but it's not because it's "too deep". So let's go deeper, by actually looking into the probabilities themselves.

If we calculated each of the 12 individual flips into Bayes' Theorem this way, using the result from the first iteration as the prior probability for the new iteration, we'd get the same answer.

So it does allow for many small pieces of evidence to combine and form one strong case.

It'll be a fine tool to continue the discussion.