# Borrowing observations for prior probability in Bayesian Inference

For the purposes of Bayesian Inference, is it assumed that the historical observations used for the prior probability values must be from the exact entity for which you are looking to calculate the posterior probability?

By way of an example, say I am an automobile insurer. I take on a new covered entity, a 22 year old male from the midwest. In the first week, this new covered entity files a claim for an accident, we don't know who was at fault. I have no prior observational data on this covered entity, but I am curious how likely it is that they are "average" in their attention to safety, and just had a bad day. Can I borrow historical observations from other covered entities who are statistically similar (22 years old, male, live in the midwest, drive with the same frequency, etc) and use it to calculate my prior probabilities for the Bayesian Inference? My assumption is yes, but in that case, I am curious of the following:

Are there any assumptions that will be violated in doing this?

How can I weight the "more similar" historical observations (22 years old, midwest, male) differently than my "less similar" historical observations (23 years old, midwest, female, drives less frequently)?

Prior distributions can come from anywhere as long as the information content impinges on the problem at hand.

For example, if you have developed a new variety of green beans, it is highly reasonable to take information on caloric content from existing green bean varietals. If you were interested in forming a prior on corporate bankruptcy rates, the spread between B+++ and D could act as rough bounding information as the default rate must be less than that spread.

Last year's overall batting average for the major leagues could be used as a prior for the batting average of a new rookie, although absent any other information, it should likely be the case that the average should be shifted downward since rookies tend to have lower averages than seasoned players.

There are no assumptions that would be violated by that.

The best weight would be to ask an experienced actuary.

• Thank you for your response. Interesting to consider. Commented Sep 17, 2019 at 20:29

I would look into hierarchical models that allow you "learn" the prior. Hierarchical models allow you give each entity their own unique models parameters, but they can be informed in part by the parameters of other entities.

The extent to which they are informed depends on how much data you have for that entity and how similar entities are to each other.

• Thanks! Any specific statistical packages in Python or R that do this nicely? Commented Sep 17, 2019 at 20:28