Wednesday, April 7, 2010

A princess story part II

As it's been pointed out to me, girlfriend's got some issues. I'm making the poor princess a little bit too needy, jumping from one prince right on to the next. She needs time to really focus on herself, time to figure out what SHE likes, time to just enjoy being single. She's no sitting around waiting for Prince Charming, delicate flower of a Snow White.... no, she's got the sass of Princess Jasmine.

In terms of modeling assumptions, the slight tweak required to accommodate our dear princess's independent spirit (or desire to never have to utter the words "I don't know who my babydaddy is."-- thanks, L, for that.) is the addition of a component that determines the wait time between relationships. In the current incarnation of this simulation, the princes arrive back to back, and she is constantly collecting data. Exhausting!

Alternatively, let's consider a model in which there is a period of latency between princes. At the end of each prince's tenure, let's now suppose that the princess waits some exponentially distributed amount of time with mean independent of her mean relationship duration.

How does this change the best strategy?

As expected, she should auto-reject fewer princes on average if she's going to wait a long time between them. Makes sense. Keep in mind that this is under the assumption that she is not collecting data on anyone during the waiting period.

Here's another plot of the best strategy for the number of princes to automatically ditch (instead of do or marry?) for my settings in this experiment, but under conditions where the princess isn't quite so needy. The x-axis shows the average number of days between relationships, and the hot pink region, shows strategies that came within 90% this time of the best one.
I didn't allow for simultaneous data collection on multiple princes (a negative wait time?), but that could be an interesting extension. If you stay tuned, I've got an even more interesting tweak in the works that I'm pretty sure is going to imply that prince_i is still training data.

But first, Bayesian spatial quantile regression awaits...

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