Related papers: Semi-Markov Arnason-Schwarz models
Transition probability estimation plays a critical role in multi-state modeling, especially in clinical research. This paper investigates the application of semi-Markov and Markov renewal frameworks to the EBMT dataset, focusing on six…
Continuous-time state-space models (SSMs) are flexible tools for analysing irregularly sampled sequential observations that are driven by an underlying state process. Corresponding applications typically involve restrictive assumptions…
We consider a finite state discrete time process X. Without loss of generality the finite state space can be identified with the set of unit vectors {e1, e2, . . . , eN} with ei = (0, . . . , 0, 1, 0, . . . , 0)0 2 RN. For a Markov chain…
Motivated by techniques developed in recent progress on lower bounds for sublinear time algorithms (Behnezhad, Roghani and Rubinstein, STOC 2023, FOCS 2023, and STOC 2024) we introduce and study a new class of randomized algorithmic…
The COVID-19 pandemic has been characterised by multiple waves of transmission driven by interventions and emerging variants, challenging epidemic models that assume gradually evolving transmission dynamics. We propose a class of…
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain…
Data sets comprised of sequences of curves sampled at high frequencies in time are increasingly common in practice, but they can exhibit complicated dependence structures that cannot be modelled using common methods of Functional Data…
Many applications in medical statistics as well as in other fields can be described by transitions between multiple states (e.g. from health to disease) experienced by individuals over time. In this context, multi-state models are a popular…
Markov models are often used to capture the temporal patterns of sequential data for statistical learning applications. While the Hidden Markov modeling-based learning mechanisms are well studied in literature, we analyze a…
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…
We consider the problem of performing parameter and state inference in a state-space model (SSM) parametrized by a static parameter $\theta$. A popular idea to address this problem consists of incorporating $\theta$ in the state of the…
Experiments, in particular on biological systems, typically probe lower-dimensional observables which are projections of high-dimensional dynamics. In order to infer consistent models capturing the relevant dynamics of the system, it is…
Progressive diseases worsen over time and are characterised by monotonic change in features that track disease progression. Here we connect ideas from two formerly separate methodologies -- event-based and hidden Markov modelling -- to…
The conformational kinetics of enzymes can be reliably revealed when they are governed by Markovian dynamics. Hidden Markov Models (HMMs) are appropriate especially in the case of conformational states that are hardly distinguishable.…
Markovian memory embedded in a binary system is shaping its evolution on the basis of its current state and introduces either clustering or dispersion of binary states. The consequence is directly observed in the lengthening or shortening…
Isolating slower dynamics from fast fluctuations has proven remarkably powerful, but how do we proceed from partial observations of dynamical systems for which we lack underlying equations? Here, we construct maximally-predictive states by…
We compare different selection criteria to choose the number of latent states of a multivariate latent Markov model for longitudinal data. This model is based on an underlying Markov chain to represent the evolution of a latent…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
In this paper, the recurrent events that can occur more than one over the follow-up time have been modeled by phase-type distributions. We use the finite-state continuous-time Markov process with multi states for patients with recurrent…
Multi-type Markov point processes offer a flexible framework for modelling complex multi-type point patterns where it is pertinent to capture both interactions between points as well as large scale trends depending on observed covariates.…