Bayesian methodologies for handling count-valued time series have gained prominence due to their ability to infer interpretable latent structures and to estimate uncertainties. Among these Bayesian models, Poisson-Gamma Dynamical Systems (PGDSs) are proven to be effective in capturing the evolving dynamics underlying observed count sequences. However, the state-of-the-art PGDS still falls short in capturing the transition dynamics that are commonly observed in real-world count time series. To mitigate this limitation, a PGDS with time-varying transition kernel (TV-PGDS), is proposed to allow the underlying transition matrices to evolve over time. Three specifically-designed Dirichlet Markov chains (Dir-Dir, Dir-Gam-Dir, PR-Gam-Dir) are constructed to accommodate heterogeneous structural mutations within these dependencies. Leveraging Dirichlet-Multinomial-Beta data augmentation techniques, a fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. Experiments show that, in comparison with related models, the proposed PGDS achieves improved predictive performance due to its capacity to learn time-varying dependency structure captured by the time-evolving transition matrices.
The p(parameter)-CSMC algorithm is proposed, which incorporates both parameter learning and ancestor sampling, leading to much better mixing properties compared to (particle) Gibbs sampling in settings where strong internal correlations may challenge effective exploration.
We study prediction and smoothing in hidden Markov models with a latent signal given by a multi-type Wright-Fisher diffusion and discrete-time categorical observations, motivated by repeated-sampling time-series settings, including temporally binned ancient-DNA data, in which noisy frequency counts are recorded at fini...
Luigi M. Malgieri, F. Ascolani, M. Giordano et al.· 0 citations
A hierarchical Ornstein–Uhlenbeck stochastic differential equation with event-conditional drift for latent-state dynamics around life events detected in text and establishes existence and uniqueness of strong solutions, identifiability of the population-level parameters under sparse panel observation, and a posterior-b...
I. Naskinova, Mariyan Milev, Nikolay Netov et al.· Wseas Transactions on Busine...· 0 citations
The proposed additive ODE–SDE model produces a close fit with coherent uncertainty quantification and a flexible seasonal reconstruction, while keeping the mechanistic transmission model interpretable.
Miracle Amadi, J. García-Merino, H. Haario· Bulletin of Mathematical Bio...· 0 citations
High-dimensional count data are common in scientific applications, but most diffusion and flow models are designed for continuous or categorical data, and generation often requires many sequential model evaluations. We propose Count Flow Map, a generative model that learns finite-time transitions directly in count spac...
The Causal Regime Bayesian (CaReBayes) forecasting framework is proposed, which integrates regime detection, causal discovery, and Bayesian forecasting within a unified approach and produces regime-dependent causal graphs that summarize candidate structural relationships in the system, enhancing interpretability.
Assistant Professor Benjamin Lindquist studies how engineers deliberately injected randomness into early AI, giving rise to deep-learning models that sometimes hallucinate.
