BAYESIAN STATE-SPACE MODEL FOR JOINT INFERENCE OF OSCILLATORY DYNAMICS AND POINT-PROCESS COUPLING

Abstract

Under a range of behavioral and physiological conditions, spike times and local field potential (LFP) oscillations exhibit phase coupling within specific frequency bands. Classical measures such as spike-field coherence (SFC) and the phase-locking value (PLV) quantify this coupling but estimate the LFP spectrum independently of spike timing. We introduce Joint SSMT, a Bayesian state-space framework that jointly infers LFP spectrograms and spike-field coupling strength. The model treats narrowband LFP activity as a latent process evolving in continuous time, with spike trains linked to the complex spectral state through a Bernoulli-logistic model. In simulations, Joint SSMT accurately recovers coupling strength, denoises the spectrogram, and uses spike timing to resolve fine temporal structure in the LFP. Applied to propofol anesthesia data, the model identifies coupling at a specific slow-oscillation frequency where SFC and PLV report only broad low-frequency coupling. We extend Joint SSMT to trial-structured experiments and apply it to primate recordings during an associative learning task, revealing frequency-specific coupling in hippocampus and prefrontal cortex. We also derive closed-form expressions for SFC and PLV as functions of the generative model parameters. Across simulations and two primate datasets, Joint SSMT provides more frequency-specific coupling estimates with principled uncertainty quantification than classical PLV and SFC.