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

Bayesian semiparametric long memory models for discretized event data