Interesting comparison! The criticism of julia is certainly valid, especially in terms of documentation. However, I wouldn't say that core language documentation should necessarily be geared towards any specific field.

In the implementation of the julia code there is a slight performance bug though (not sure if the authors submitted the article - the username certainly suggests it):

    function likelihood(o, a, b, h, y2, N)
        local lik = 0.0
       for i in 2:N
        @inbounds h = o+a*y2[i-1]+b*h
         lik += log(h)+y2[i]/h
        end
        return(lik)
    end

Only one use of y2 is marked @inbounds - in this case, either the second use too or the whole loop could be marked @inbounds (or the loop could be modified to run for all of eachindex(y2), with the first index being explicitly skipped).