# To the likelihood of what does the loglikelihood in AIC, BIC refer?

Both Akaike's information criterion and Bayesian information criterion are calculated from the loglikelihood, eg AIC= -2 log-likelihood +2k.

To the likelihood of what does it refer to? The likelihood of 1) the model that I fit to the data or of 2) the distribution I draw my data from at each point? So, with 2) I mean, if I have data points at {(x_i,y_i)} and take some fixed x the distribution for drawing y.

Or phrased with an example: If I have some data, each point with an gaussian error, to which I fit an exponential function, do I compute the log-likelihood of the gaussian or of the exponential function?

Edit: here the question also came up in the comments, but wasn't answered

• They refer to the likelihood function of assumed model. Dec 3, 2022 at 15:28
• Is there then a way to take known uncertainties in the data into account? Dec 3, 2022 at 16:37
• Why do they talk then of 'gaussian error' eg here: stats.stackexchange.com/questions/483801/… ? Dec 3, 2022 at 17:19