Dear Beatrice

thanks for your questions, please see some replies inline below

 

First, is there a way to choose the best HRF basis function based on my data?

There's no universal rule. The gamma mixtures will best reproduce a wide variety of shapes. FIR is more agnostic and data driven, and possibly more suitable if your target property is the whole hrf shape, for example with afni 3dMSS. It's also more suitable for unusual shapes, like animal or pathology.

Could be a correct approach to estimate both canonical and gamma functions and then compare them? If so, how should I do it operatively?

Unless there's a "ground truth" to compare to, then it's difficult. Indicators such as spatial or temporal variance can be useful though.

In the case of gamma function, how can I estimate the number of basis functions?

It's a choice you make, rather than an estimation. To avoid overfitting, the number should not be too high.

In Threshold (SD) for event detection should I change the value (i.e 1)? (considering both the options: canonical and gamma function)

This is not necessary, but it's indeed a parameter that you can choose to tune.

Also, what is K (local peak)? How is it calculated?

See eq. [3] of the tutorial paper, where K is defined as the range of x values in which we look for a peak.: 

y(i) is defined as peak: y(i)>y(i+x),  x=[-K: K];     

 

I hope this helps