Given the independence of each event, the overall log-likelihood of intersection equals the sum of the log-likelihoods of the individual events. This is analogous to the fact that the overall log-probability is the sum of the log-probability of the individual events. In addition to the mathematical convenience from this, the adding process of log-likelihood has an intuitive interpretation, as often expressed as "support" from the data. When the parameters are estimated using the log-likelihood for the maximum likelihood estimation, each data point is used by being added to the total log-likelihood. As the data can be viewed as an evidence that support the estimated parameters, this process can be interpreted as "support from independent evidence adds", and the log-likelihood is the "weight of evidence". Interpreting negative log-probability as information content or surprisal, the support (log-likelihood) of a model, given an event, is the negative of the surprisal of the event, given the model: a model is supported by an event to the extent that the event is unsurprising, given the model.
Given the independence of each event the overall log-likelihood of intersection equals the sum of the log-likelihoods of the individual events This is analogous to the fact that the overall log-probability is the sum of the log-probability of the individual events In addition to the mathematical convenience from this the adding process of log-likelihood has an intuitive interpretation as often expressed as "support" from the data When the parameters are estimated using the log-likelihood for the maximum likelihood estimation each data point is used by being added to the total log-likelihood As the data can be viewed as an evidence that support the estimated parameters this process can be interpreted as "support from independent evidence adds" and the log-likelihood is the "weight of evidence" Interpreting negative log-probability as information content or surprisal the support (log-likelihood) of a model given an event is the negative of the surprisal of the event given the model a model is supported by an event to the extent that the event is unsurprising given the model