Multiple regression: 1 statement for all components or many stat. for each

Maybe is a stupid question, but I was wondering if in principle this:

simplex[N] pi;
observed[g] ~ normal(a[1,g]*pi[1] + a[2,g]*pi[2] + ... , sigma);

is equivalent, to this:

simplex[N] pi;
observed[g] ~ normal(a[n,g]*pi[n], sigma); //with sigma that might potentially vary per "n"

I am trying to think what are the differences in what “the model sees”.

I am not sure how the R linear regression and support vector regression (svm) implement their cost functions.


This helped understanding better the implementation of error model.

Least squares is pretty obvious when you realize that the log of the normal density is negative one half the squared, scaled distance from the mean, i.e., -0.5 * ((y - mu)/sigma)^2. You can code a simple regression in Stan on unit scale as simply

  target -= 0.5 * dot_self(y - mu);