We introduce a new class of semiparametric latent variable models for long memory discretized event data. The proposed methodology is motivated by a study of bird vocalizations in the Amazon rain forest; the timings of vocalizations exhibit self-similarity and long range dependence ruling out models based on Poisson processes. The proposed class of FRActional Probit (FRAP) models is based on thresholding of a latent process consisting of an additive expansion of a smooth Gaussian process with a fractional Brownian motion. We develop a Bayesian approach to inference using Markov chain Monte Carlo, and show good performance in simulation studies. Applying the methods to the Amazon bird vocalization data, we find substantial evidence for self-similarity and non-Markovian/Poisson dynamics. To accommodate the bird vocalization data, in which there are many different species of birds exhibiting their own vocalization dynamics, a hierarchical expansion of FRAP is provided in Supplementary Materials.

翻译：我们为长期记忆离散事件数据引入了新型半半参数潜在变量模型。拟议方法的动机是研究亚马逊雨林中的鸟类声学;声学时间显示自异性和长期依赖性,排除了基于 Poisson 过程的模式。拟议的FRActional Probit (FRAP) 模型类别基于一个潜在过程的临界值,该潜在过程由光滑高山过程的增量扩展和微小的布朗运动组成。我们利用Markov 链 Monte Carlo 开发了一种巴伊西亚推理方法,并展示了模拟研究的好性能。对亚马逊鸟声学数据应用这些方法,我们找到了关于自我相似性和非马可维亚/波斯逊动态的大量证据。为了容纳鸟类声学数据,在补充材料中提供了多种不同鸟类展示其声学动态的鸟类的分级扩展。