Tuesday, April 30, 2013
Probability and Likelihood: two similarly different terms
Let us start the discussion with 2 very simple examples:-
Let us assume that each of the above 10mer DNA sequences are the experimentally derived binding sites of a Transcription Factor(TF), say X. So, which of the following questions will be correct?
a) what is the probability that G will come at position 4 of the binding site of X?
b) what is the likelihood of G at position 4?
| 1 2 3 4 5 6 7 8 9
A | 3 6 1 0 0 6 7 2 1
C | 2 2 1 0 0 2 1 1 2
G | 1 1 7 10 0 1 1 5 1
T | 4 1 1 0 10 1 1 2 6
The above matrix is the position specific frequency matrix derived from the sequences of example 1. Now, which of the following questions is correct?
a) what is the probability that the sequence CAGGTTGGA is a binding site of the TF X?
b) what is the likelihood that the sequence CAGGTTGGA is a binding site of X?
See, in both the cases it seems like both answers are correct since both the terms sounds very similar unless we carefully review the definition of the terms.
The term likelihood is used when we describe a function of a parameter given a fixed outcome.
In both of the examples, the outcome, that is the experimentally derived sequences are given. So the out come is fixed and based on this observations we are asking a question. So, in both of the cases the therm Likelihood will be used.
What? Not convinced?????? ok, let me give you an example of the situation where the term "probability" will be used.
a) What is the probability that the 10mer sequence CAGGTTGGA will come in our genome?
b) what is the likelihood that the 10mer sequence CAGGTTGGA will come in our genome?
See, this time no prior data, that is, no observation is given (our genome size is fixed). So, likelihood is not the word meant for used in this case. So, the 10mer has a probability, not likelihood to be there in our genome.
Clear??? A bit?? I hope so. If not, feel free to post your query using the comment box below. Time to go, will return soon with more such topics. Till then, bbyeee!!!! :)