论文标题
观鸟和其他时间顺序抽样活动的模型
A Model for Birdwatching and other Chronological Sampling Activities
论文作者
论文摘要
在许多现实生活中，人们都有$ m $类型的随机事件在一个时间间隔内按时间顺序进行，并且希望预测有关这些事件或其子集的各种里程碑。一个例子是观鸟。假设我们可以在一个季节观察多达$ m $不同类型的鸟类。在任何时候，都会观察到$ i $的鸟。观鸟者可能有许多自然的问题：在记录所有类型的鸟类之前，应该期望有多少观察结果？是否有时间间隔，研究人员最有可能观察到所有物种？或者，在重叠时间间隔中观察到几只鸟类的可能性是多少？我们的论文使用基于随机间隔图的新模型回答了这些问题。该模型是著名优惠券收藏家问题的自然跟进。
In many real life situations one has $m$ types of random events happening in chronological order within a time interval and one wishes to predict various milestones about these events or their subsets. An example is birdwatching. Suppose we can observe up to $m$ different types of birds during a season. At any moment a bird of type $i$ is observed with some probability. There are many natural questions a birdwatcher may have: how many observations should one expect to perform before recording all types of birds? Is there a time interval where the researcher is most likely to observe all species? Or, what is the likelihood that several species of birds will be observed at overlapping time intervals? Our paper answers these questions using a new model based on random interval graphs. This model is a natural follow up to the famous coupon collector's problem.
