Chang Xuan Mao

TL;DR: In this paper, a binomial mixture model is proposed for the species accumulation function based on presence-absence (incidence) of species in a sample of quadrats or other sampling units, which covers interpolation between zero and the observed number of samples, as well as extrapolation beyond the observed sample set.

TL;DR: In this paper, the authors provide new unconditional variance estimators for classical, individual-based rarefaction and for Coleman Rarefaction under two sampling models: sampling-theoretic predictors for the number of species in a larger sample (multinomial model), a larger area (Poisson model) or a larger number of sampling units (Bernoulli product model), based on an estimate of asymptotic species richness.

TL;DR: By considering the contributions of rare species and the role of undetected species for a fixed sampling effort, it is shown why the problem of richness estimation is so difficult, and what statistical models can provide.

TL;DR: The problem of estimating the species accumulation curve based on an empirical data set arising from quadrat sampling is studied in a nonparametric binomial mixture model and a likelihood-based procedure is developed for the purpose of extrapolation, associated with bootstrap confidence intervals.

TL;DR: In this paper, the problem of estimating the unknown number of classes in a population has been reduced to estimating the odds that a class is undetected in a sample, and a sequence of lower bounds to the odds is developed and used to define pseudo maximum likelihood estimators for the number of classifications.