Related papers: $\pi$-Girsanov: A Generalized Method to Construct …

Learning dynamical models from data is not only fundamental but also holds great promise for advancing principle discovery, time-series prediction, and controller design. Among various approaches, Gaussian Process State-Space Models…

Computer simulations generate microscopic trajectories of complex systems at a single thermodynamic state point. We recently introduced a Maximum Caliber (MaxCal) approach for dynamical reweighting. Our approach mapped these trajectories to…

Markov community models have been applied to sessile organisms because such models facilitate estimation of transition probabilities by tracking species occupancy at many fixed observation points over multiple periods of time. Estimation of…

Graphical continuous Lyapunov models offer a new perspective on modeling causally interpretable dependence structure in multivariate data by treating each independent observation as a one-time cross-sectional snapshot of a temporal process.…

A novel strategy that combines a given collection of $\pi$-reversible Markov kernels is proposed. At each Markov transition, one of the available kernels is selected via a state-dependent probability distribution. In contrast to random-scan…

Ising models are a simple generative approach to describing interacting binary variables. They have proven useful in a number of biological settings because they enable one to represent observed many-body correlations as the separable…

This paper is concerned with a state-space approach to deep Gaussian process (DGP) regression. We construct the DGP by hierarchically putting transformed Gaussian process (GP) priors on the length scales and magnitudes of the next level of…

Probabilistic generative models based on measure transport, such as diffusion and flow-based models, are often formulated in the language of Markovian stochastic dynamics, where the choice of the underlying process impacts both algorithmic…

This letter proposes a new method for joint state and parameter estimation in uncertain dynamical systems. We exploit the partial errors-in-variables (PEIV) principle and formulate a regression problem in the sense of weighted total least…

Latent autoregressive processes are a popular choice to model time varying parameters. These models can be formulated as nonlinear state space models for which inference is not straightforward due to the high number of parameters. Therefore…

Molecular Dynamics (MD) is a powerful computational microscope for probing protein functions. However, the need for fine-grained integration and the long timescales of biomolecular events make MD computationally expensive. To address this,…

We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods (MCMC). Our results can be used…

Generalized autoregressive score (GAS) models are a class of observation-driven time series models that employ the score to dynamically update time-varying parameters of the underlying probability distribution. GAS models have been…

Markov Population Models are a widespread formalism used to model the dynamics of complex systems, with applications in Systems Biology and many other fields. The associated Markov stochastic process in continuous time is often analyzed by…

In the last decade, advances in molecular dynamics (MD) and Markov State Model (MSM) methodologies have made possible accurate and efficient estimation of kinetic rates and reactive pathways for complex biomolecular dynamics occurring on…

This research presents a comprehensive framework for transitioning financial diffusion models from the risk-neutral (RN) measure to the real-world (RW) measure, leveraging results from probability theory, specifically Girsanov's theorem.…

Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…

Reversibility is a key concept in Markov models and Master-equation models of molecular kinetics. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model relies heavily on the reversibility…

With the next generation of both electromagnetic and gravitational wave observatories beginning to come online, rapid analysis methods for kilonova data are becoming increasingly important in astronomy. Traditional Bayesian parameter…

Many chemical reactions and molecular processes occur on timescales that are significantly longer than those accessible by direct simulation. One successful approach to estimating dynamical statistics for such processes is to use many short…