A Study of Mexican Free-Tailed Bat Chirp Syllables: Bayesian Functional Mixed Modeling of Nonstationary Time Series Data with Time-Dependent Spectra

Josue G. Martinez
Kirsten M. Bohn, School of Integrated Science, Florida International University
Raymond J. Carroll, Department of Statistics, Texas A & M University
Jeffrey S. Morris, The University of Texas M.D. Anderson Cancer Center

Abstract

We propose a general multi-domain strategy for modeling and performing inference on nonstationary time series with a time-dependent spectrum. The strategy involves mapping the original data via a two-stage transformation to a space where modeling is more amenable. The two-stage transformation involves a mapping from the time domain to the time-frequency domain via the spectrogram, where results are more interpretable, followed by a second mapping to the wavelet domain, where flexible, parsimonious modeling can be done using Bayesian functional mixed models. We describe this modeling strategy and apply it to characterize bat chirps which are represented by time series of auditory calls, finding insights that would have been missed by the simplistic analysis approaches typical to the field. We study the chirp syllable derived from mating type songs and look for systematic differences between groups of bat captured in two different locations in the central Texas region.