A1 Journal article (refereed)
Bayesian semiparametric long memory models for discretized event data (2022)

Chakraborty, A., Ovaskainen, O., & Dunson, D. B. (2022). Bayesian semiparametric long memory models for discretized event data. Annals of Applied Statistics, 16(3), 1380-1399. https://doi.org/10.1214/21-AOAS1546

JYU authors or editors

Publication details

All authors or editors: Chakraborty, Antik; Ovaskainen, Otso; Dunson, David B.

Journal or series: Annals of Applied Statistics

ISSN: 1932-6157

eISSN: 1941-7330

Publication year: 2022

Publication date: 19/07/2022

Volume: 16

Issue number: 3

Pages range: 1380-1399

Publisher: Institute of Mathematical Statistics

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1214/21-AOAS1546

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/82484

Publication is parallel published: https://arxiv.org/abs/2004.08309


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. This rules out Poisson process based models where the rate function itself is not long range dependent. The proposed class of FRActional Probit (FRAP) models is based on thresholding, a latent process. This latent process is modeled by a smooth Gaussian process and a fractional Brownian motion by assuming an additive structure. 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 the Supplementary Material.

Keywords: modelling (representation); fractals; Bayesian analysis; Monte Carlo methods; Markov chains; Gaussian processes; time series; mathematical statistics; probability calculation; bird sounds; nature sounds; natural diversity; rain forests

Free keywords: fractal; fractional Brownian motion; latent Gaussian process models; long range dependence; nonparametric Bayes; probit; time series

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2022

JUFO rating: 3

Last updated on 2023-30-08 at 08:57