Bad Bayesian

Couldn’t find my phone yesterday morning.  I definitely remembered having it in the car on the way home from the kids’ swim lesson, so I knew I hadn’t left it.  “Find my iPhone” told me the phone was on the blacktop of the elementary school, about 1000 feet from my house.  What?  Why?  Then a few minutes later the location updated to the driveway of a bank, closer to my house but in the other direction.  So I went over to the bank and looked around in the driveway, even peering into the garbage shed and seeing if my phone was in their dumpster.

But why did I do that?  It was terrible reason.  There was no chain of events leaving my phone at the bank, or at the school, which wasn’t incredibly a prior unlikely.  I should have reasoned:  “The insistence of Find my iPhone that my phone is at the bank drastically increases the probability my phone is at the bank, but that probability started out so tiny that it remains tiny, and the highest-expected-utility use of my time is to keep looking around my house and my car until I find it.”

Anyway, it was in the basement.




4 thoughts on “Bad Bayesian

  1. Jon Awbrey says:

    Got back from a trip and checked my pocket for my phone — panic ❢ no please ❢ don’t make me go back to Florida ❢ — turns out the TSA checker had me stow it in my carry-on and some other hassle with the death-ray machine drove that out of memory.

    Keep Calm
    Carry On

  2. Kevin says:

    If it’s not already a feature, “Find My iPhone” should tell you the accuracy and not just try to find the pin. I suspect being in the basement meant the phone couldn’t get a GPS signal, so it had to fall back to triangulation via cell towers, which is only good to a kilometer or so.

  3. dratman says:

    From this discussion I learned

    1) Something about the implication of tiny prior probabilities in Bayesian estimation.

    2) Something about cell-tower triangulation as a fallback for iPhone Location Services.

    Thanks to both the questioner and to the answerers!

  4. JSE says:

    Kevin’s fact is really interesting! If I were a really good Bayesian, and knew more about cellphones, I could have reasoned that two estimates a quarter-mile apart in the space of 5 minutes suggested that the phone was somewhere it couldn’t get a GPS signal, and gone straight to the basement.

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