BAYESIAN SEMIPARAMETRIC LONG MEMORY MODELS FOR DISCRETIZED EVENT DATA.

Area of Science:

• Statistics
• Ecology
• Bioacoustics

Background:

• Discretized event data often exhibit complex temporal patterns.
• Traditional models like Poisson processes may not capture long memory and self-similarity.
• Bird vocalizations display self-similarity and long-range dependence, necessitating advanced modeling.

Purpose of the Study:

• Introduce a novel class of semiparametric latent variable models for long memory discretized event data.
• Address the limitations of existing models in capturing self-similarity and long-range dependence in event timings.
• Provide a flexible modeling framework applicable to ecological event data, such as animal vocalizations.

Main Methods:

• Propose FRActional Probit (FRAP) models based on thresholding a latent process.
• Model the latent process using an additive structure of a smooth Gaussian process and fractional Brownian motion.
• Employ a Bayesian inference approach utilizing Markov chain Monte Carlo (MCMC) methods.

Main Results:

• Demonstrate good performance of the FRAP models in simulation studies.
• Find substantial evidence of self-similarity and non-Markovian/Poisson dynamics in Amazon rainforest bird vocalization data.
• Confirm the inadequacy of standard models for capturing the observed long-range dependence in vocalization patterns.

Conclusions:

• The proposed FRAP models offer a powerful tool for analyzing complex event data with long memory properties.
• The findings highlight the non-Poisson and self-similar nature of bird vocalizations, providing ecological insights.
• The developed methodology and its hierarchical extension can be applied to diverse biological and ecological event series.