Epilepsy is a disorder characterized by paroxysmal transitions between multistable states. Dynamical systems have been useful for modeling the paroxysmal nature of seizures. At the same time, intracranial electroencephalography (EEG) recordings have recently discovered that an electrographic measure of epileptogenicity, interictal epileptiform activity, exhibits cycling patterns ranging from ultradian to multidien rhythmicity, with seizures phase-locked to specific phases of these latent cycles. However, many mechanistic questions about seizure cycles remain unanswered. Here, we provide a principled approach to recast the modeling of seizure chronotypes within a statistical dynamical systems framework by developing a Bayesian switching linear dynamical system (SLDS) with variable selection to estimate latent seizure cycles. We propose a Markov chain Monte Carlo algorithm that employs particle Gibbs with ancestral sampling to estimate latent cycles in epilepsy and apply unsupervised learning on spectral features of latent cycles to uncover clusters in cycling tendency. We analyze the largest database of patient-reported seizures in the world to comprehensively characterize multidien cycling patterns among 1,012 people with epilepsy, spanning from infancy to older adulthood. Our work advances knowledge of cycling in epilepsy by investigating how multidien seizure cycles vary in people with epilepsy, while demonstrating an application of an SLDS to frame seizure cycling within a nonlinear dynamical systems framework. It also lays the groundwork for future studies to pursue data-driven hypothesis generation regarding the mechanistic drivers of seizure cycles.