Title: Mendel mixtures of genuine and fake $p$-values in meta analysis
Authors: Dinis Pestana - FCiencias.ID, Universidade de Lisboa and CEAUL (Portugal) [presenting]
Maria Brilhante - FCiencias.ID (Portugal)
Sandra Mendonca - Universidade da Madeira and CEAUL (Portugal)
Abstract: Meta-analysing $p$-values is simple under the naive and optimistic assumption that the null hypothesis $H_0$ is true in each of the independent tests performed, i.e. that the reported $p$-values come from independent standard uniforms. Assuming that $H_0$ holds in all cases is farfetched; on the other hand, one of the sources of bad science is the repetition of experiments in order to report a more convenient $p$-value. Fisher suggested that Mendel used such `fake' $p$-values, so that assuming that $H_0$ holds some of the $p$-values are genuine (uniforms), but others are fake, namely a Beta(1,k) or a Beta(k,1) extremes of uniforms. It seems therefore sensible to assume that the appropriate model for the sequence of $p$-values, if $H_0$ is true, is a mixture of uniforms and extremes of uniforms, that in the sequel is named Mendel model. We present results on the estimation of the mixing parameter, and discuss auto-regressive versus independent setups.