1. Bayesian methods have been developed for inferring the true year of extinction of a species from sighting records that have both certain and uncertain sightings. These methods typically make the restrictive assumption that all sighting types (i.e. certain, valid uncertain, invalid uncertain) derive from constant rate Poisson processes.
2. In this study, the constant rate assumption in the homogeneous Poisson process is relaxed by allowing certain and uncertain sightings to follow independent non‐homogeneous Poisson processes. The model can thus identify whether any of the sighting rates were increasing, decreasing or constant. In addition, a change‐point is introduced to model the uncertain sightings, where the sighting rates before and after the change‐point vary.
3. We have used Markov Chain Monte Carlo (MCMC) sampling to generate the posterior distributions for model parameters including species extinction time. The proposed method was applied to the sighting records of the black‐footed ferret Mustela nigripes and the ivory‐billed woodpecker Campephilus principalis (IBW) species.
4. Based on a hypothesis test, the results of the model indicate that the species both went extinct in the years 1988 and 1956 respectively. Moreover, a decline in the certain sighting rate was also inferred for both these species, possibly indicating the decrease in the species abundance as it converges to extinction. Thus, earlier models that assume a constant sighting rate may well be biased. Uncertain sighting rates for the IBW were found to increase before extinction (indicating possibly some additional ecological attention received near extinction) and remained constant after extinction.

中文翻译：

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使用具有变化点的非均匀泊松过程推断物种的灭绝日期

1. 已经开发出贝叶斯方法，以从具有确定目击和不确定目击的目击记录中推断出物种的真实灭绝年。这些方法通常做出限制性假设，即所有瞄准类型（即某些，有效的不确定性，无效的不确定性）都来自恒定速率的泊松过程。
2. 在这项研究中，通过允许确定且不确定的目视遵循独立的非均质Poisson过程，放宽了均质Poisson过程中的恒定速率假设。因此，该模型可以识别任何瞄准率是在增加，减少还是恒定。此外，引入了一个更改点来对不确定的目击事件进行建模，更改点之前和之后的目击率会发生变化。
3. 我们已使用马尔可夫链蒙特卡洛（MCMC）采样来生成模型参数（包括物种灭绝时间）的后验分布。该方法被应用于黑脚雪貂鼬鼬和象牙嘴啄木鸟CampephilusPrincipalis（IBW）物种的目击记录。
4. 根据假设检验，模型的结果表明该物种均分别在1988年和1956年灭绝。此外，还推断出这两个物种的特定目视率都下降了，这可能表明随着物种趋于灭绝，物种的丰度降低了。因此，假定恒定瞄准率的早期模型可能会产生偏差。灭绝前IBW的不确定观察率增加了（表明灭绝前可能受到了更多的生态关注），灭绝后保持不变。