I am beginner in mathematics/statistics and apologise in advance for my faulty use of language. Especially because I assume this to be a simple problem.
I am working on a problem in statistical genetics, where I would like to calculate a metric which I can use to compare probabilities of genotypes across multiple individuals.
For a given individual at a certain genetic position, I have three possible genotype states: AA, AB, and BB. Using an algorithm that estimates how likely it is to observe a genotype, I obtained probabilities for each genotype state at a given position: $p_{AA}$, $p_{AB}$, and $p_{BB}$; which is a posterior probability distribution (probabilities sum to 1).
Let's say I have 2 individuals with 5 corresponding genetic positions each. The resulting probably matrices are
Individual 1:
position pAA pAB pBB 00000001 0.1 0.2 0.7 00000002 0.8 0.1 0.1 00000003 0.3 0.2 0.5 00000004 0.3 0.3 0.4 00000005 0.8 0.0 0.2
Individual 2:
position pAA pAB pBB 00000001 0.2 0.2 0.6 00000002 0.6 0.4 0.0 00000003 0.3 0.4 0.3 00000004 0.3 0.3 0.4 00000005 0.4 0.3 0.3
For the two individuals, the estimation resulted in different genotype probabilities for the same positions (because they are different individuals and can have different genotypes), but for the second individual, estimation was less accurate.
I would like to calculate a metric which allows me to compare the estimation quality.
For this, I simply could use the mean of the max genotype probability in each row. However, I assume this to be less robust when a few positions where estimated with higher probability than the others.
Also, a second problem arrises when individual 2 has more genetic positions:
Individual 2:
position pAA pAB pBB 00000001 0.2 0.2 0.6 00000002 0.6 0.4 0.0 00000003 0.3 0.4 0.3 00000004 0.3 0.3 0.4 00000005 0.4 0.3 0.3 00000006 0.0 0.0 1.0 00000007 0.0 0.0 1.0 00000008 0.0 0.0 1.0
Hence, my question comes down to this: Can I compute a metric with which I can compare the estimation results of multiple individuals, which have a variable number of genetic positions?