currently I have a terminology issue to accurately write a text. I read up on the definitions on probability and likelihood. Given some continuous random variable(s) as far as I can infer, probability is calculated between to datapoint given some fixed parameters via the integration, whereas we refer to likelihood as a reversed thing, namely varying parameters under fixed data. So far so good.

Now let's assume that we have some observation x from a sample space which is represented by a multivariate normal distribution $\mathcal{N}(\mathbf{x}|\mu,\,\Sigma )\,$. If the parameters vary, then we call this quantity the likelihood function according to Christopher Bishop's Pattern Recognition book. However, if the what if simple want to calculate the function value given some fixed parameters? I think we can't call it probability, as for continuous random variables there is nothing like a probability at any datapoint x. Nonetheless, if we want to talk about it, what proper name is given to this? Simply the 'function value' or the 'probability density function value' or ... as the 'relative likelihood' [https://en.wikipedia.org/wiki/Probability_density_function] ?

Thanks for clarification in advance.


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