Bayesian Inference in Recurrent Explicit Duration Switching Linear Dynamical Systems

The paper states the REDSLDS model and derives the same closed-form conditional posteriors and augmentation used by the candidate: MNIW conjugacy for linear-Gaussian dynamics and emissions (their Eqs. (16)–(17) in Appendix A) and Pólya–Gamma augmentation for stick-breaking logistic hyperplanes with κk,t = I[st=k] − 1/2 I[st≥k] leading to conditionally Gaussian updates (their Eqs. (18)–(20)) . The model’s duration/state transition kernel with gating at boundaries (dt−1=1) matches the candidate’s FFBS decomposition for zt=(st,dt) (cf. Eqs. (11)–(15) in the main text and Eq. (37) in Appendix C) . The paper’s message-passing for x (Appendix B) incorporates the same I[dt−1=1] gating and PG terms used by the candidate, yielding backward information-form recursions compatible with Kalman smoothing . Minor differences are present only in exposition (e.g., the paper samples ω ~ PG(1, v) for the active stick terms, whereas the candidate writes b=I[st≥k], which is an equivalent gating convention) and a few typos (e.g., a stray “+ xt−1” in Eq. (16)). Overall, both arguments align in substance and steps.