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Abstract:
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In any latent variable problem, in which the ideal test statistic is a function of latent variables S, one may consider the p-value p(S). The latent p-value is then defined as the probability distribution of p(S) given the observed data Y. A randomized test and confidence sets for the parameter of interest follow. Here we apply this idea to testing for genetic linkage for a quantitative trait, and to estimating the location of DNA affecting a trait, given genetic marker data on a pedigree structure. The approach provides not only an exact p-value as a measure of significance, including a natural correction for multiple testing over the genome, but also a measure of the uncertainty associated with that p-value given that S is not observable. Confidence sets are a natural extension that reveal the asymmetry between absence and presence of linkage.
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