标题： 基于似然的Gompertz模型泊松误差推断 显示英文标题

标题： Likelihood-based inference for the Gompertz model with Poisson errors

摘要： 种群动态模型在许多领域中起着重要作用，如精算科学、人口统计学和生态学。 当除了过程本身的随机性之外，还需要考虑抽样误差时，这些模型的统计推断可能会变得困难。 忽略后者可能导致估计中的偏差，进而导致对系统行为的错误结论。 Gompertz模型被广泛用于推断种群规模动态，但当考虑抽样误差时，完整的似然方法在计算上可能不可行。 我们通过基于完整似然的Gompertz模型的高效计算工具来弥补这一差距。 该方法在贝叶斯和频率论范式中进行了说明。 性能通过模拟和数据分析进行了说明。 显示英文摘要

摘要： Population dynamics models play an important role in a number of fields, such as actuarial science, demography, and ecology. Statistical inference for these models can be difficult when, in addition to the process' inherent stochasticity, one also needs to account for sampling error. Ignoring the latter can lead to biases in the estimation, which in turn can produce erroneous conclusions about the system's behavior. The Gompertz model is widely used to infer population size dynamics, but a full likelihood approach can be computationally prohibitive when sampling error is accounted for. We close this gap by developing efficient computational tools for statistical inference in the Gompertz model based on the full likelihood. The approach is illustrated in both the Bayesian and frequentist paradigms. Performance is illustrated with simulations and data analysis.