for example
0,1,1,2,3,5,8,13,21,34
S[sub]10[/sub]=34 here
and using the formula approximation
(1.618[sup]9[/sup]+0.618[sup]9[/sup])/√5=33.99
for n a large number
S[sub]n[/sub]≈Golden Ratio[sup]n-1[/sup] /√5,
This could explain why
S[sub]n[/sub]/S[sub]n-1[/sub]≈Golden Ratio
since the coefficient for S[sub]n-1[/sub] and S[sub]n-2[/sub] are 1, l and k should satisfy:
we get l and k are
. Which is bigger? We can only leave this question here.On the other hand,
,since
and so on,The "bigger" question does not matter here, so we get the final formula:
]]>95% in confidence interval is the probablity generated by samples. Actually it's the X-bar probablity. If you want expectation(parameter) probability, (if you want more), you have to make assumptions that expectation u couid be everywhere and initially its probablity in everywhere is equal. By adding new knowledge of samples you can get conditional (treamed) probility of u. And this time whole distribution, better than just interval. Though the distribution is fake due to assumption.
Luckily, they get a same answer with classical until now. But Bayesians'competitive advantage is to change the equal assumption for expert prejudice. By doing that they can make the predicted interval narrower.
The difference is like if you allow a forecaster to add his personal intuition according to his experience beyond given theory and compution or not. If you allow him to do so, he may get a narrower forecast but more subjective one.
And it's a philophical debate whether a person's experience is more subjective than staticians' theory. Is their theory qualified enough to be truth?
And there's some time that a narrower but more risky forecast overweighs the less risky but broader one.
]]>I discover that many people believe in Classical and are against Bayesian just because they think they understand Classical. So may I ask you a question: what does 95% in confidence interval mean? (what does it stand for)
]]>for example, staticians are debating whether classical or Bayesian for decades!
As far as I know, Bayesian theory is a lame attempt to gather a probability in which scientific theory is correct. It amounts to going around and asking people, "How much do you believe in theory X?"
Unless you are talking about something else the Bayesians did?
]]>So I would rather put existing theories as the competitive theories that win their opponents or at least due than being the truth.
But my view looks tricky, lol~
]]>Then why complicated matrices combining multiplication and addition together?(Actually it took me a long time to accept that concept)
Matices multiplication and determinants are some kind of winners , as there are actually many other competing definations that are not as poplular as them.(A lot of mathematicians are inventing new definations to arrange numbers) The reason why they win over might be that their usefulness are not limited to linear equations solving - matrices multiplication is good at handling data, especially in statistics, and determinant is popular among physicians.
And I guess determinant's application in physics is quite lucky- the inventor wouldn't have ever dreamed about it!
]]>for example, negative numbers, dot product, and matrices initially seem a waste of time. But when they just fit the certain problems, they become very useful indeed!
]]>And we could all be simulations in that very computer, and not even know it!
perhaps, but im pretty sure theyd have been getting bored of watching us after the billions upon billions of years, and cut off the program, and even so, i think they would be having, well fun with us, rather than just letting existance get on with it, that is, unless theyre preoccupied with the other side of our universe.
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