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

  • 4
    $\begingroup$ They refer to the likelihood function of assumed model. $\endgroup$
    – utobi
    Dec 3, 2022 at 15:28
  • $\begingroup$ Is there then a way to take known uncertainties in the data into account? $\endgroup$ Dec 3, 2022 at 16:37
  • $\begingroup$ Why do they talk then of 'gaussian error' eg here: stats.stackexchange.com/questions/483801/… ? $\endgroup$ Dec 3, 2022 at 17:19


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