We consider the problem of inference in a probabilistic model for transient populations where we wish to learn about arrivals, departures, and population size over all time, but the only available data are periodic counts of the population size at specific observation times. The underlying model arises in queueing theory (as an M_t/G/∞ queue) and also in ecological models for short-lived animals such as insects. Our work applies to both systems. Previous work in the ecology literature focused on maximum likelihood estimation and made a simplifying independence assumption that prevents inference over unobserved random variables such as arrivals and departures. The contribution of this paper is to formulate a latent variable model and develop a novel Gibbs sampler based on Markov bases to perform inference using the correct, but intractable, likelihood function. We empirically validate the convergence behavior of our sampler and demonstrate the ability of our model to make much finer-grained inferences than the previous approach.
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机译：我们认为推理的问题在哪里，我们希望了解到达，离开，并在所有的时间人口规模流动人口的概率模型，但唯一可用的数据是在特定的观察时间人口规模的周期性计数。潜在模型出现在排队理论（作为M_T / G /∞队列）以及昆虫等短期动物的生态模型中。我们的工作适用于两个系统。在生态文学以前的工作集中在最大似然估计，并提出了简化的独立性假设，即防止过度推断不可观测的随机变量，如抵港及离港。本文的贡献是制定潜在的变量模型，并基于Markov碱基开发新的GIBBS采样器，以使用正确但棘手的似然函数进行推断。我们经验验证了我们采样器的收敛行为，并展示了我们模型制作比以前的方法更精细的粒度推论的能力。
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