  This paper proposes a hierarchical spatial-temporal model for modelling the
spectrograms of animal calls. The motivation stems from analyzing recordings of
the so-called grunt calls emitted by various lemur species. Our goal is to
identify a latent spectral shape that characterizes each species and
facilitates measuring dissimilarities between them. The model addresses the
synchronization of animal vocalizations, due to varying time-lengths and
speeds, with non-stationary temporal patterns and accounts for periodic
sampling artifacts produced by the time discretization of analog signals. The
former is achieved through a synchronization function, and the latter is
modeled using a circular representation of time. To overcome the curse of
dimensionality inherent in the model's implementation, we employ the Nearest
Neighbor Gaussian Process, and posterior samples are obtained using the Markov
Chain Monte Carlo method. We apply the model to a real dataset comprising
sounds from 8 different species. We define a representative sound for each
species and compare them using a simple distance measure. Cross-validation is
used to evaluate the predictive capability of our proposal and explore special
cases. Additionally, a simulation example is provided to demonstrate that the
algorithm is capable of retrieving the true parameters.
