I have the following problem:
I have estimates pi_0 * f_0 / ( pi_0 * f_0 + pi_1*f_1 )
where f_0 are the density estimates of p-values under the null and f_1 are
the alternative density estimates of p-values under the alternative. We also
have that p_0 + p_1 = 1 where p_0 are the proportion of p-values under the
null and p_1 is the proportion of p-values under the alternative.
My question is this, how can I change to pi_0 *F_0 / ( pi_0 * F_0 +
pi_1*F_1 ) where F are the corresponding cdfs. I don't have the actual
p-values. I just have 1,000 f_0 values and 1,000 f_1 values.
Is there an approximation somewhere that can do this?
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