On continuous-time capture-recapture in closed populations

Schofield et al. (2018, Biometrics 74, 626-635) presented simple and efficient algorithms for fitting continuous-time capture-recapture models based on Poisson processes. They also demonstrated by real examples that the standard method of discretizing continuous-time capture-recapture data and then fitting traditional discrete-time models may lead to information loss in population size estimation. In this article, we aim to clarify that key to the approach of Schofield et al. (2018) is the Poisson model assumed for the number of captures of each individual throughout the study, rather than the fact of data being collected in continuous time. We further show that the method of data discretization works equally well as the method of Schofield et al. (2018), provided that a Poisson model is applied instead of the traditional Bernoulli model to the number of captures for each individual on each sampling occasion.