For the past 2 weeks I have been trying to cram in all the information I can on what is called "Maximum Likelihood". This is a mathematical technique for figuring out, probably among other things, a tree that best represents how a given set of DNA, Protein or whatever is related to each other. From what I gather so far the maximum likelihood method does this by plotting out all the possible trees that could fit the data set and then it computes which tree is the most probable given whatever model parameters you feed in. In other words the maximum likelihood is the highest probably of your data given the best model. A simple example often used is tossing a coin. Say you toss one 100 times and you get 47 heads and 53 tails. Now we have to chose a model. The model is our theory about how the coin flipping works. I will propose 2 and we will see which results in the maximum likelihood. The first model is the "fair coin" model, that you get 1/2 heads and 1/2 tails. Next I will propose a weighted model, say 1/4 heads and 3/4 tails. In the "fair coin" model we get a high likelihood because of the fact that 47/53 is so close to our expected value of 50/50. The second model doesn't seem to be a very good picture of what is really going on, 25/75 is pretty far away from our actual result of 47/53. Thus given the two models I proposed the one that leads to the maximum likelihood given our coin flipping data is the "fair coin" model. That process I just went through is called Model Selection and it is more specifically what I am going to be working on. It is not an exact science and what I gather is that I am going to be working on ways to improve the models used for inferring how much evolution takes place between two sets of data sequences.
When I figure this out to a fuller extent I will be sure to write a more accurate entry on the subject. If you are really interested in it though check out the wikipedia page on Maximum likelihood at http://en.wikipedia.org/wiki/Maximum_likelihood also you could check out the wiki on model selection at http://en.wikipedia.org/wiki/Model_selection.
Take care and have a great day!
-हवे अ ग्रेट दय!