Graham
Senior Moment
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- 5,188
- Location
- Sussex, UK
Hi Valentijn. Suddenly my brain feels very inadequate! I must admit that I know very little about the biology here. But I can comment on the probabilities. They are slippery little devils to deal with.
First of all, as you suggested, if they are inherited in a clump, then you cannot treat them as though they are independent probabilities. Blond hair and blue eyes spring to mind as an example. They tend to occur together.
Now this is where I am guessing about the biology, so if I misunderstand, please excuse me. If one minor allele has a 1% occurrence, then the odds of a person picked at random having that is 1 in 100. The probability that you and me both have that specific minor allele would be 1 in 10,000. But if you discover that I have a specific minor allele, then the probability that you have it too is 1 in 100. If you have a list of 5 people, then the chance that someone in the list besides me has it drops to 1 in 20.
The second problem is that of picking "coincidences" in a group. The chance of two people picked at random having a shared birthday is 1 in 365 (ignoring leap years), but in a class of 30 I believe the chance of finding two people with a birthday in common is over a half. This is closer to what you are doing with your lists: you are looking for pairs with common features.
So when you say "what are the chances that Sea and Valentijn both have ..." you can't just multiply the probabilities together. First of all I guess it is almost certain that both of them will have a number of rare alleles. Then if you pick one of Sea's, and look for a match somewhere that is not the same as calculating the probability that, picked at random, they both share one particular rare allele. If you start by looking for two people in a group that share a rare allele (like shared birthdays), it would be very very time consuming to calculate the odds. What you can say is that if several people share that rare allele, then that would be against the odds.
I have a similar personal gripe when my wife complains to the GP about a side effect of blood pressure medication, and is told that it can't be because the odds are 10,000 to 1 against. It is the wrong probability. Suppose the very rare side effect is to produce a nose that glows in the dark. If, after taking the medication, her nose starts to glow in the dark then we are no longer dealing with theoretical probabilities (a priori). Instead we now need to know, given that she is taking the medication, what is the probability of it being the medication in comparison with all of the other probabilities? (and that is very different). These are conditional probabilities.
I think I have got that straight, and I hope it is useful. Certainly the data that you have found is potentially very interesting, I'd just be wary of working out the odds. Now to rest my brain. I'll go and open up the greenhouse.
First of all, as you suggested, if they are inherited in a clump, then you cannot treat them as though they are independent probabilities. Blond hair and blue eyes spring to mind as an example. They tend to occur together.
Now this is where I am guessing about the biology, so if I misunderstand, please excuse me. If one minor allele has a 1% occurrence, then the odds of a person picked at random having that is 1 in 100. The probability that you and me both have that specific minor allele would be 1 in 10,000. But if you discover that I have a specific minor allele, then the probability that you have it too is 1 in 100. If you have a list of 5 people, then the chance that someone in the list besides me has it drops to 1 in 20.
The second problem is that of picking "coincidences" in a group. The chance of two people picked at random having a shared birthday is 1 in 365 (ignoring leap years), but in a class of 30 I believe the chance of finding two people with a birthday in common is over a half. This is closer to what you are doing with your lists: you are looking for pairs with common features.
So when you say "what are the chances that Sea and Valentijn both have ..." you can't just multiply the probabilities together. First of all I guess it is almost certain that both of them will have a number of rare alleles. Then if you pick one of Sea's, and look for a match somewhere that is not the same as calculating the probability that, picked at random, they both share one particular rare allele. If you start by looking for two people in a group that share a rare allele (like shared birthdays), it would be very very time consuming to calculate the odds. What you can say is that if several people share that rare allele, then that would be against the odds.
I have a similar personal gripe when my wife complains to the GP about a side effect of blood pressure medication, and is told that it can't be because the odds are 10,000 to 1 against. It is the wrong probability. Suppose the very rare side effect is to produce a nose that glows in the dark. If, after taking the medication, her nose starts to glow in the dark then we are no longer dealing with theoretical probabilities (a priori). Instead we now need to know, given that she is taking the medication, what is the probability of it being the medication in comparison with all of the other probabilities? (and that is very different). These are conditional probabilities.
I think I have got that straight, and I hope it is useful. Certainly the data that you have found is potentially very interesting, I'd just be wary of working out the odds. Now to rest my brain. I'll go and open up the greenhouse.