27 Nov '16 15:18>1 edit
Originally posted by DeepThoughti will also investigate that next.
Your resu the distribution so plausibly your program is trying to sample too small a subset of the domain.
Originally posted by humyArr I HAVE misunderstood your formula. Correct me if I am wrong but you mean;
Arrr I think I might have misunderstood your formula. I will investigate that next and then come back to you.
Originally posted by humyWell, I misunderstood the entire problem in the first place and then fouled up substituting into my own formula. We're suffering a little from having to use a text system to write maths rather than LaTeX or some such, and my attempt to clarify generated even more confusion...
DeepThought
SUCCESS! (at last)
Your formula is exactly correct and it was me who was in error (as usual).
The reason why I was getting nonsense of my program was simply because I kept entering the wrong formula (rubbish-in, rubbish-out), not because of anything wrong with the behavior with the iteration of my software I especially developed to test such fo ...[text shortened]... normal distribution and based on random walks but with an unknown mean-average parameter value.
Originally posted by humyHum, is this a non-academic work or is it part of a thesis?
-or perhaps instead of writing just
∑[n=1, m] ( x – h{n} )^2
for absolute clarity, write that as;
∑[n=1, m] ( ( x – h{n} )^2 )
or, perhaps even better, write that as;
∑[n=1, m] [ ( x – h{n} )^2 ]
then surely there cannot be any easy misunderstanding?
And if you wanted to change the meaning of that from 'the sum of the squares of the diff ...[text shortened]... of square brackets?
I am now considering adopting this notation permanently and esp in my book.
Originally posted by sonhousesort-of non-academic work;
Hum, is this a non-academic work or is it part of a thesis?
Originally posted by humyJust for clarity, in what I wrote above I was referring to posts in this forum. In your book you should use standard notation unless you have an overriding reason not to.
sort-of non-academic work;
it is a possible recommendation to put in my book to all readers for a new notation for summations to help reduce potential misinterpretations and which hopefully will be widely adopted after publication of my book.
I hope my book does a lot more than put forward a thesis (although it puts forward many theorems with maths proofs) an ...[text shortened]... to apply it to A.I) and the whole of probability theory and the science of statistical analysis.
Originally posted by DeepThoughtI am struggling to see how you can misinterpret 1/exp((1/Q)*(P)) as P/exp(1/Q).
Just for clarity, in what I wrote above I was referring to posts in this forum. In your book you should use standard notation unless you have an overriding reason not to.
The confusion in the first few posts was because you typed in:
1/exp((1/Q)*(P))
where P and Q are placeholders for the sum and the factor of 2K^2 respectively, which I mistook ...[text shortened]... ng possibilities are limited to unicode, and not to media where decent typesetting is available.
Originally posted by humyactually, I think we have agreed that it would be better to write that as;
I just thought of such a simple way to avoid confusion I don't understand why I didn't think of it before.
with expressions like;
∫[–∞, ∞] 1 / e^( ( 0.5/K^2 ) * ∑[n=1, m] ( x – h{n} )^2 ) dx
I could simply use a "where statement" and rewrite that like this;
∫[–∞, ∞] 1 / e^( sum /(2*K^2) ) dx
where sum = ∑[n=1, m] (( x – h{n} )^2 )
Problem solved. I will for now on use that strategy in my book.
Originally posted by humyI am struggling to see how you can misinterpret 1/exp((1/Q)*(P)) as P/exp(1/Q).
I am struggling to see how you can misinterpret 1/exp((1/Q)*(P)) as P/exp(1/Q).
It is my understanding that you must do the maths operations in the brackets first and always to the maths operations within the inner most pair of brackets before the outer most pair?
With that being correct, how can it make any sense to write 1/exp((1/Q)*(P)) to mean P/exp(1/Q) ...[text shortened]... ing "...1/x^y = x^-y and the latter notation is preferable when you are writing inline formula"