Simulated Goats? 

 In this week's Gov 2001 class, Gary was showing how to get around difficult statistical problems by simulation rather than using complex analytics. That got me thinking about the trade-offs between the two approaches. 


 One class example was the Monte Hall game that you can probably recite backwards in your sleep: a contestant is asked to choose between 3 doors, 1 of which has a car behind it. Once the choice is made, the game show host opens one of the remaining doors that only has a goat. The contestant is offered to switch from her initial choice to the remaining door, and the question is whether that's a good strategy. 

 One can solve this analytically by thinking hard about the problem. Alternatively one can simulating the conditional probabilities of getting the prize given switching or not switching, and use this to get the intuition for the result. 

 During the debate in class I was wondering whether simulations are really such a good thing. Sure, they solve the particular problem at hand and it may be the only way to handle very complex problems fast. But it doesn't contribute to solving even closely related problems whereas one could glean insights from the analytic approach. 

 Maybe the simulation is still useful since writing code structures one's thoughts. But it also seems like it might depreciate critical skills. (Apart from the very real possibility that one makes a mistake in the code and tries to convince oneself of the wrong result.) Imagine you show up at Monty's show and they changed the game without telling you. It won't help if you would know how to implement a new simulation if you can't actually run it. Having solid practice in the analytical approach might be more useful. 

 I don't want to suggest that simulations are generally evil, but maybe they come at a cost. Oh, and the answer is yes, switch.