A probability theory problem - page 12

[Vladimir]

I read the article, but I didn't manage to put in a comment, I guess I'm not right enough. That's why I'm writing the comment here. It concerns only these words of the article:

The correlations of these functions and their derivatives are zero.

R(cos(x), sin(x)) = 0 (7)

R(cos(x), -sin(x)) = 0

Therefore the use of the first derivative of the indicator is in general a good candidate for consideration as an additional independent indicator.

End of quotation.

Note: Sine and cosine are related by the condition Sin^2+Cos^2=1 and are simply calculated from each other, they are highly dependent. The conditions of Bayes' theorem require exactly independence of events, uncorrelation is not enough.

On the merits, frankly, I don't see why you need to involve statistical inference theory. To think, whether indicator readings or signals are events or not, whether we deal with realizations of a random variable or a random process etc. Anyway, we will have to check the result by history of quotes. The check itself will be a justification without formulas. It doesn't matter how dependent the indicators are. For example, we often see recommendations to check the signals of two moving averages crossover by the behavior of the third one with a larger period. The environment developed in the article for checking different indicators could give a direct answer to the question if there is an effect and what effect.

[Mesaoria]

Vladimir:

The use of the first derivative of an indicator is therefore generally a good candidate for consideration as an additional independent indicator.

Independent of what?

[Stanislav Korotky]

Mesaoria:
Independent of what?

This is from the article. It was about the independence of indicator signals (from each other). The example, indeed, was purely theoretical, based on the uncorrelation (which we can calculate). We will consider that the expressed assumption about the uncorrelation of signals from the derivative indicators, although it requires checking, is much more probable than the uncorrelation of the signals of the indicators, built on one principle - for them we exactly observe the dependence and the constant coincidence.