Thread: Exercises and Problems View Single Post
#24
09-09-2015, 10:17 AM
 giridhar1202 Junior Member Join Date: Sep 2015 Posts: 2
Re: Exercises and Problems

I conducted experiment mentioned in 1.10(b), and i got following result.

V1 = 90, 999, 4375, 11803, 20329, 24793, 20411, 11685, 4450, 988, 77
Vrand = 103, 1022, 4389, 11691, 20444, 24489, 20653, 11669, 4502, 941, 97
Vmin = 62376, 37622, 2, 0, 0, 0, 0, 0, 0, 0, 0

i.e; 90 times out of 100,000 times, i get 0 heads in 10 tosses of first coin
999 times out of 100,000 times, i get 1 head in 10 tosses of first coin
....
77 times out of 100,000 times, i get 10 heads in 10 tosses of first coin

and

103 times out of 100,000 times, i get 0 heads in 10 tosses of coin chosen at random
....
97 times out of 100,000 times, i get 10 heads in 10 tosses of coin chosen at random

and

62376 times out of 100,000 times, i get 0 heads in 10 tosses of coin for which number of heads was minimum across 1000 coins

So, it is as expected that distribution of V1 and Vrand are similar.
Can someone please explain how we should interpret result for Vmin?

Is distribution of Vmin suggesting that one should be careful about overfitting ? Because if we have many hypothesis there will almost always be some hypothesis which fits data set exactly. So what should be one's strategy for selecting hypothesis ?