or maybe they're busy playing un updated version of reality.

I think the use of matrices is pretty clear in the computer world. It requires no judicious rearranging techniques and solves its general form. Matrics I guess are sort of like the quadratic formula for all linear equations. But perhaps these are the "certain problems" you are refering to.

Actually there are competitions in math theories!
for example, staticians are debating whether classical or Bayesian for decades! Econometritians are debating whether (Ax)'=A or (Ax)'=A' for a long time!

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~

Bayesians are good at helping court. In that case, only Bayesians could help.

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)

After a tiring investigation I find Classical is not as solid as many people think. Probablity is a hard subject, and neither classical nor Bayesian can make progress without sacrificing something.

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.

Last edited by George,Y (2006-06-24 14:21:37)

Luckily S₁=0 and S₂=1 satisfy this formula too.

for example
0,1,1,2,3,5,8,13,21,34
S₁₀=34 here

and using the formula approximation
(1.618⁹+0.618⁹)/√5=33.99
for n a large number

S_n≈Golden Ratio^n-1 /√5,