# Which statistics method should I use to model events that barely occurs? [closed]

I have a dataset with information of different individuals and I want to create a model to predict if the individual will take some action or if he won't (1 or 0). E.g.: the individual will buy a product (event = 1) or if he won't (event = 0). Normally, I would use a decision tree or a logistic regression to predict if the event will happen. However, I'm not sure if this is the case for this dataset, since the number of times the event happened in my historical data is very rare (less than 1% of the time). How can I model this?

• How many actual ones do you have in the data? Commented Jun 5, 2018 at 17:08
• @DimitriyV.Masterov I have 7,000 ones and 1,000,000 zeros Commented Jun 5, 2018 at 17:15
• That sounds like enough data for MLE to work reasonably well, but predictions might still not be all that great. Search this site for "firth logit" or "rare events logit". Commented Jun 5, 2018 at 17:39
• How about the method from extreme value theory, would it helps? There will be some distributions regarding extreme events Commented Jun 5, 2018 at 18:11
• I wrote an answer, but then I thought, it is too general. So I deleted it. This question needs to be less broad. "How can I model this?" with only information that there is a small amount of data, is not a very specific question. Commented Apr 4, 2023 at 13:00

Imbalanced problems like this often appear to pose problems, because they often result in few, if any, of the rare events being caught. Much of this comes from using a predicted probability of $$0.5$$ as a threshold for making hard classifications based on the continuous predictions. Because of how low the prior probability of your rare event is, it is only natural that, unless something in the data is screaming out about a rare event,$$^{\dagger}$$ the posterior probability (your model prediction) will be low. In this case, you might consider the ratio of the predicted to the prior probability. If the rare event happens with a probability of just $$7000/(1000000+7000)=0.006951341$$, yet you predict a probability of $$0.1$$, that prediction, despite favoring the common event ($$90\%$$ chance of the common event), is more than fourteen times higher than the usual probability of a rare event.
$$^{\dagger}$$This can happen. Have you ever seen/heard/smelled something highly unexpected yet quickly known what it was?