Consider the distribution of places you spend your time during peak shelter in place. It was probably mostly at home. Your bedroom, the kitchen, the bathroom, and occasionally going out to the store.
Take the math out of it for a second. I’m not nearly smart enough to predict which room you’ll be in during a specific minute of a specific day. Predicting that you’re going to be hungry at exactly 12:42 and you’ll go to the store this Sunday at 9:21 is well beyond me.
But I could be much more accurate if I abstract it a bit to a few important properties. During shelter in place, you probably spend 25-35% of the time asleep, maybe 0.1-0.5% at the store (once every 1-3 weeks maybe), etc. I can even confidently predict that as shelter in place relaxes, you’ll likely go out more often, but probably still very rarely to the grocery store more than twice per week.
Your precise movements are impossible to accurately predict more than a few moments out, but their distribution from one day to the next during shelter in place is pretty stable. On a longer timescale, that distribution will shift once shelter in place lifts, and it’s even reasonable to predict how it’ll change.
Another timely analogy might be modeling specifically who has COVID-19 at a point in time versus modeling the distribution. The percent of people in a place who have it is the distribution in question here: the probability that any given person there has it is a simple distribution over true or false. There’s no question of stability over time here because it’s a distribution over people instead of time. You can model how that spreads over time and location so much more easily than predicting the specific individuals who will get it and transmit it.
Take the math out of it for a second. I’m not nearly smart enough to predict which room you’ll be in during a specific minute of a specific day. Predicting that you’re going to be hungry at exactly 12:42 and you’ll go to the store this Sunday at 9:21 is well beyond me.
But I could be much more accurate if I abstract it a bit to a few important properties. During shelter in place, you probably spend 25-35% of the time asleep, maybe 0.1-0.5% at the store (once every 1-3 weeks maybe), etc. I can even confidently predict that as shelter in place relaxes, you’ll likely go out more often, but probably still very rarely to the grocery store more than twice per week.
Your precise movements are impossible to accurately predict more than a few moments out, but their distribution from one day to the next during shelter in place is pretty stable. On a longer timescale, that distribution will shift once shelter in place lifts, and it’s even reasonable to predict how it’ll change.
Another timely analogy might be modeling specifically who has COVID-19 at a point in time versus modeling the distribution. The percent of people in a place who have it is the distribution in question here: the probability that any given person there has it is a simple distribution over true or false. There’s no question of stability over time here because it’s a distribution over people instead of time. You can model how that spreads over time and location so much more easily than predicting the specific individuals who will get it and transmit it.