Related papers: A primer on coupled state-switching models for mul…
Spiking neural network models characterize the emergent collective dynamics of circuits of biological neurons and help engineer neuro-inspired solutions across fields. Most dynamical systems' models of spiking neural networks typically…
State-space models effectively model multivariate time series by updating over time a representation of the system state from which predictions are made. The state representation is usually a vector without any explicit structure.…
We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to switch from one function…
Recurrent COVID-19 outbreaks have placed immense strain on the hospital system in Quebec. We develop a Bayesian three-state coupled Markov switching model to analyze COVID-19 outbreaks across Quebec based on admissions in the 30 largest…
Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete…
Motivated by recent observations in neuronal systems we investigate all-to-all networks of non-identical oscillators with adaptive coupling. The adaptation models spike-timing-dependent plasticity in which the sum of the weights of all…
We use coupling to study the time taken until the distribution of a statistic on a Markov chain is close to its stationary distribution. Coupling is a common technique used to obtain upper bounds on mixing times of Markov chains, and we…
Multi-state survival analysis considers several potential events of interest along a disease pathway. Such analyses are crucial to model complex patient trajectories and are increasingly being used in epidemiological and health economic…
A key question in brain sciences is how to identify time-evolving functional connectivity, such as that obtained from recordings of neuronal activity over time. We wish to explain the observed phenomena in terms of latent states which, in…
Hidden Markov models are versatile tools for modeling sequential observations, where it is assumed that a hidden state process selects which of finitely many distributions generates any given observation. Specifically for time series of…
Markov chains are simple yet powerful mathematical structures to model temporally dependent processes. They generally assume stationary data, i.e., fixed transition probabilities between observations/states. However, live, real-world…
Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems. But these computational methods, from correlation coefficients to causal inference, rely on distinct quantitative…
A Markov state model of the dynamics of a protein-like chain immersed in an implicit hard sphere solvent is derived from first principles for a system of monomers that interact via discontinuous potentials designed to account for local…
We present a new method for inferring hidden Markov models from noisy time sequences without the necessity of assuming a model architecture, thus allowing for the detection of degenerate states. This is based on the statistical prediction…
Over the last decade, hidden Markov models (HMMs) have become increasingly popular in statistical ecology, where they constitute natural tools for studying animal behavior based on complex sensor data. Corresponding analyses sometimes…
Motivated by disease progression-related studies, we propose an estimation method for fitting general non-homogeneous multi-state Markov models. The proposal can handle many types of multi-state processes, with several states and various…
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…
A freely walking fly visits roughly 100 stereotyped states in a strongly non-Markovian sequence. To explore these dynamics, we develop a generalization of the information bottleneck method, compressing the large number of behavioral states…
In this paper, two-state Markov switching models are proposed to study accident frequencies. These models assume that there are two unobserved states of roadway safety, and that roadway entities (roadway segments) can switch between these…
In medicine, comorbidities refer to the presence of multiple, co-occurring diseases. Due to their co-occurring nature, the course of one comorbidity is often highly dependent on the course of the other disease and, hence, treatments can…