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I have a pet project to figure out the birth year of a significant person in history.

I'm collecting a lot of data on other people with similar status during that time period. I have data such as education length, year married, year of child bearing, information about siblings and age difference between each child, marriages, etc...

The age of this person is disputed between two years, one making the person very old, and the other making the person young. I want to regress the persons age. My first idea was to draw gaussians over each variable and see if one is more likely to be an outlier than the other.

What way would you tackle this problem?

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It seems like you have a classical bayesian problem. You have some sort of prior distribution, a distribution over years of birth, your prior distribution is bimodal with peaks at the two years, you can probably use a convolution of two normal distributions to model this variable. Then have it spit out a posterior distribution after you feed in some data.

The real problem that I have with this analysis is it seems your features aren't particularly good. It is true these vars might have information about birth year, for example for the 20th century the average age of first marriage has steadily been increasing. But I suspect that the signal is going to be fairly weak. Essentially, if I tell you that I got married at age 24, had my first child at 26, and that my older brother is 3 years older than me and my younger sister is 2 years younger than me, can you tell me in what year was I born, 1956 or 1989?

I suspect that without additional data this information that I provided would be completely useless, mostly because it is a very noisy signal. That information could apply equally to someone born in 1956 or 1989. It isn't very helpful.

Essentially, what I am saying is that when you update your prior, it isn't going to change very much. (Your posterior distribution would look very similar to the prior distribution.) Instead of doing some mustache twirling over what is the right algorithm to crack this problem, I think a much more fruitful exercise would be to think up some better features.

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  • $\begingroup$ Nice! Regarding the features, so if I knew that all your siblings were married at 24, and had their children at 26. The general population with marriages average at 25 at some normal distribution. I don't necessarily know what age you were married (that's what I would be predicting). One year suggests that you were married at 38, the other suggests that you were married at 24. Is it right to say that it's more probable that you were married at 24? $\endgroup$ – Lfa Jul 18 '16 at 15:37
  • $\begingroup$ Well, yes with a normal distribution 24 is closer to the population average of 25 than 38. So without any other data you can say that it is more probable, simply because you already have a distribution in mind. $\endgroup$ – Ryan Jul 19 '16 at 16:07
  • $\begingroup$ My plan is to collect data to create the distributions for this variable (and several others that I will continue thinking about). I feel like I already added biases such as "all the data I collect is nobility only", etc... But these biases were based on a historian's opinion of the class of people we should be drawing distributions for. Thanks for the answers! I'll accept it! $\endgroup$ – Lfa Jul 19 '16 at 17:59

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