Re: Testable Predictions by HdB

*** T. Winter wrote:

I am now trying to thoroughly look at it, and much of it does not make
sense to me.  (And I tried to implement it, but the results were completely
wrong.)  First question.  Given a set of t_k and function values f_k, you
define a continuation:

f(t) = sum{k} f_k.exp(-[(t - t_k)/sigma]^2/2) 

Yes. That's a consequence of my sloppy documentation. At first, the t_k
should be _equidistant_ (: essential). And a  norm = 1/sqrt(2.pi.sigma)
(: the "well-known constant", see below) must be included:

     f(t) = norm . sum{k} f_k.exp(-[(t - t_k)/sigma]^2/2)

in what way is that a continuation?  When I fill in any t_k for t, it is
not f_k that comes out.  (You also mention a well-known constant in that
context.  Well, that constant is not known to me.)


That's true: f_k is _not_ equal to f(t_k) . That's the penalty you pay
for the ease later on. But if you choose the sigma = 2.|t_(k+1) - t_k|
then the approximation should be good where f''(x) is not large. Order
of magnitude of the error = f''(x).sigma^2/2 . Any comments on my non-
standard terminology would be welcome as well. And no, I don't have a
decent theory (in my head) for non-equidistant samples. Not yet. Hope
this helps, anyway.

Han de Bruijn

.

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