## HCOL 196, February 25, 2011

Short one today, since we didn’t have class due to the slippery roads.

Please, if anyone has a question about the quiz on Monday, please let me know by adding a comment to this post or by emailing me.

Bill

### One Response to “HCOL 196, February 25, 2011”

1. bayesrules Says:

Got the following question from a student. Here is the question and my response. I hope this helps.

> Hello Professor, I hope you are enjoying the weekend now that the snow has calmed down.

> May you please explain how exactly I would answer the question pertaining to plagiarism on the study guide? I tried to set it up but I’m not certain if I did it correctly.
>
> Thank you!!
>

Here’s the idea. Of course you have to have a prior on copying/no copying; this could for example be based on experience (how often have people violated copyright in the past, for example). In this example, the prior doesn’t matter much because the likelihood is very strong.

OK, the likelihood. Again, the SONs are copying, no copying. If the table were copied, the probability that we’d get exact duplication, given copying, is 1, of course. And the probability of exact duplication, given no copying (the table was computed from scratch) is 1/2^100 (^ means “raise to power”) since in the 1000 entries, there are 100 that could have gone either way, and the probability is 1/2 that it would be raised exactly the same as in the original table.

Then we use the approximation 2^10 is approximately 10^3 to rewrite 1/2^100 as approximately 1/10^30 or 10^{-30}. So that’s the likelihood for no copying.

When you compute the joint, marginal, and posterior, the probability of copying is almost 1, the probability of no copying is (for the “noncommital” prior 1/2, 1/2) approximately 10^{-30}, which is very, very small.

Does this help?