We consider mark-recapture models for non-invasive sampling of genetic material left by animals. Examples of such data include scat collected from the ground, or hair caught on a sticky trap. An advantage of this approach is that we do not physically catch the animals, with individual identification obtained through genotyping the material collected. The prob­­lem is that errors often occur in the genotyping process. The most common error is due to drop-out, which is when the pcr amplification fails for one allele at a heterozygous locus. This makes each of the affected loci appear to be homozygous even though they are truly heterozygous, leading to considerable overestimation of the abundance of the population. Here we explore modeling the drop-out process within a statistical model. We do this by specifying a complete data likelihood that includes both the observed genotype and the true genotype. We discuss how we can use data augmentation and trans-dimensional algorithms to fit such a model using MCMC.
A necessary part of this model is describing the sampling model conditional on the “true” identities. We model the observations as arising in continuous time from a (possibly non­­homogeneous) Poisson process. Depending on the assumptions we place on the Poisson parameter, we show the relationship to previously used sampling models using arguments involving S-and Bayes-ancillarity. Throughout we illustrate the model with data from the European badger (Meles meles).