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I'm not sure I follow. Say you have P(gene|healthy) = 0.010 and P(no_gene|healthy) = 0.99 P(gene|sick) = 0.011 and P(no_gene|sick) = 0.989 Then you do lar

I'm not sure I follow. Say you have P(gene|healthy) = 0.010 and P(no_gene|healthy) = 0.99 P(gene|sick) = 0.011 and P(no_gene|sick) = 0.989 Then you do large population studies (testing for sick vs healthy is cheaper than testing for genes). You get P(healthy) = 0.90 and P(sick) = 0.10. From the small sample you get the average of the gene's expression frequency: P(gene) = 0.0101 and P(no_gene) = 0.9899. You are interested in what is the probability of a person being sick when they have the gene P(sick|gene) = P(sick,gene) / P(gene) = P(gene|sick) * P(sick) / P(gene) = 0.011 * 0.10 / 0.0101 = 0.109 And conversely, odds of being sick without the gene: P(sick|no_gene) = P(no_gene|sick) * P(sick) / P(no_gene) = 0.989 * 0.10 / 0.9899 = 0.0979 So, based on this data, having the gene increases your probability of having the disease some 11% (0.109/0.0979) or 1.1 percentage points (0,109-0,0979). Or you might want to calculate some other figures from these. If you just want the ratio, then P(sick) does not have a bearing on it. You could perform some sensitivity analysis etc... (I am not a statistician by far)

pcrh 13y ago
I am not a statistician either, apart from a few courses, but your argument starts with: P(gene|healthy) = 0.010 and P(no_gene|healthy) = 0.99 P(gene|sick) = 0.011 and P(no_gene|sick) = 0.989 My point is that in many cases there is no justification for placing any number whatsoever on a prior hypothesis. You can't simply say that the prior probability of a particular gene being involved in a disease is 1%, or 0.00001% or 10%, or whatever. Edit: I'm not saying that Bayesian statistics is without uses, it is very useful in epidemiology, for example. However it is not appropriate for determining molecular and genetic mechanisms.
- Gravityloss 13y ago
  I think you misunderstand. P(gene|healthy), P(gene) and P(healthy) are something we can often measure. P(healthy|gene) is something we can calculate with the Bayes formula from the above values. More generic version: We want to know P(model|data). That's what we always want. What is the probability of some model, based on this data that we measured. But we only have P(model), P(data) and P(data|model). So we use the Bayes formula to get the answer to the interesting conditional probability. It needs all three inputs. We must estimate if we don't have some. Just presenting P(data|model) and not constraining P(model) or P(data) in any way means that we can't say anything about P(model|data). It's like if we start with x + a + b = 5. If we don't know or estimate a and b, it's impossible to say anything about x. Bayes' formula is like saying then, solve it like this: x = 5 - a - b. So, if you say, there is not justification placing any constraint on a or b - then it's just saying we clearly do not have enough data to say anything about x either. There is no way out of it.

pcrh 13y ago

I am not a statistician either, apart from a few courses, but your argument starts with: P(gene|healthy) = 0.010 and P(no_gene|healthy) = 0.99 P(gene|sick) = 0.011 and P(no_gene|sick) = 0.989 My point is that in many cases there is no justification for placing any number whatsoever on a prior hypothesis. You can't simply say that the prior probability of a particular gene being involved in a disease is 1%, or 0.00001% or 10%, or whatever. Edit: I'm not saying that Bayesian statistics is without uses, it is very useful in epidemiology, for example. However it is not appropriate for determining molecular and genetic mechanisms.

Gravityloss 13y ago
I think you misunderstand. P(gene|healthy), P(gene) and P(healthy) are something we can often measure. P(healthy|gene) is something we can calculate with the Bayes formula from the above values. More generic version: We want to know P(model|data). That's what we always want. What is the probability of some model, based on this data that we measured. But we only have P(model), P(data) and P(data|model). So we use the Bayes formula to get the answer to the interesting conditional probability. It needs all three inputs. We must estimate if we don't have some. Just presenting P(data|model) and not constraining P(model) or P(data) in any way means that we can't say anything about P(model|data). It's like if we start with x + a + b = 5. If we don't know or estimate a and b, it's impossible to say anything about x. Bayes' formula is like saying then, solve it like this: x = 5 - a - b. So, if you say, there is not justification placing any constraint on a or b - then it's just saying we clearly do not have enough data to say anything about x either. There is no way out of it.