Guess stability based on filter coefficients is it possible to guess the stability of a filter with given coefficients a and b? I know that the right way would be to calculate the pole positions and check if they are in the unit circle but I think I read that there also is another method. 

Cheers
In the general case there is no simple way to determine the stability of a discrete-time system (unless it is FIR, in which case it is always stable). In order to check stability you don't necessarily need to compute the poles of the transfer function, but you can use the Jury stability criterion, which does not explicitly compute the poles, because the latter is generally a numerically ill-conditioned problem.

For a second-order system the denominator coefficients have to be inside the stability triangle, which can be checked very easily.