In real life you would have a users collection and an events collection, and the events field of users would be an array of event ids.
Storing event_ids as an array in the events field defeats the whole purpose of organizing your data into rich documents.
In real life, you very well could build something where the events info was built straight into the user record.
db.events.find({hosted_by: MY_ID})
db.events.find({invited: MY_ID}) // invited is an array of users