We define likelihood of parameters $\theta$ given observations $x$ (assuming $x$ is sampled according to density $f$) as: $$\mathcal{L}(\theta | x)=f_\theta(x). $$ Is it correct to speak about "[l]ikelihood of the data" (The Elements of Statistical Learning before equation (2.35)), or should we only speak about the likelihood of parameters?
I also get such remark during oral presentation, but I'm still confused to know if this misnomer is accepted.
In addition, the first equation comes from the English Wikipedia, but in the French ones it is written: $$\mathcal{L}(x | \theta)=f(x;\theta).$$ I think this notation $\mathcal{L}(x | \theta)$ is incorrect, but is it accepted somehow? Are there some authoritative notation rules for likelihood, or each author picks as he wants?