We consider the problem of estimating the number of species (denoted by S) of a biological community located in a region divided into n quadrats. To address this question, different hierarchical parametric approaches have been recently developed. Despite a detailed modeling of the underlying biological processes, they all have some limitations. Indeed, some assume that n is theoretically infinite; as a result, n and the sampling fraction are not a part of such models. Others require some prior information on S to be efficiently implemented. Our approach is more general in that it applies without limitation on the size of n, and it can be used in the presence, as well as in the absence, of prior information on S. Moreover, it can be viewed as an extension of the approach of Dorazio and Royle (2005, Journal of the American Statistical Association 100, 389-398) in that n is a part of the model and a prior distribution is placed on S. Despite serious computational difficulties, we have perfected an efficient Markov chain Monte Carlo algorithm, which allows us to obtain the Bayesian estimate of S. We illustrate our approach by estimating the number of species of a bird community located in a forest.
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机译：我们考虑估计位于一个分为n个四足动物的区域中的生物群落的物种数量（用S表示）的问题。为了解决这个问题，最近已经开发了不同的分层参数方法。尽管对潜在的生物过程进行了详细的建模，但它们都有一定的局限性。实际上，有人认为n在理论上是无限的。结果，n和采样分数不是此类模型的一部分。其他要求有效地实施有关S的一些先验信息。我们的方法更具通用性，因为它适用于n的大小，没有限制，并且可以在存在和不存在有关S的先验信息的情况下使用。此外，可以将其视为对n的扩展。 Dorazio and Royle（2005，美国统计协会杂志100，389-398）的方法，其中n是模型的一部分，并且先验分布放在S上。尽管存在严重的计算困难，我们仍完善了有效的马尔可夫链蒙特卡洛算法，它使我们能够获得S的贝叶斯估计。我们通过估计位于森林中的鸟类群落的物种数来说明我们的方法。
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