Related papers: State occupation probabilities in non-Markov model…
The Aalen-Johansen estimator generalizes the Kaplan-Meier estimator for independently left-truncated and right-censored survival data to estimating the transition probability matrix of a time-inhomogeneous Markov model with finite state…
Multi-state models are increasingly being used to model complex epidemiological and clinical outcomes over time. It is common to assume that the models are Markov, but the assumption can often be unrealistic. The Markov assumption is…
The conditional Aalen--Johansen estimator, a general-purpose non-parametric estimator of conditional state occupation probabilities, is introduced. The estimator is applicable for any finite-state jump process and supports conditioning on…
Various estimators for modelling the transition probabilities in multi-state models have been proposed, e.g., the Aalen-Johansen estimator, the landmark Aalen-Johansen estimator, and a hybrid Aalen-Johansen estimator. While the…
In this article, weak convergence of the general non-Markov state transition probability estimator by Titman (2015) is established which, up to now, has not been verified yet for other general non-Markov estimators. A similar theorem is…
Asymptotic properties of Markov Processes, such as steady state probabilities or hazard rate for absorbing states can be efficiently calculated by means of linear algebra even for large-scale problems. This paper discusses the methods for…
In multi-state life insurance, incidental policyholder behavior gives rise to expected cash flows that are not easily targeted by classic non-parametric estimators if data is subject to sampling effects. We introduce a scaled version of the…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
We consider finite-state time-nonhomogeneous Markov chains where the probability of moving from state $i$ to state $j\neq i$ at time $n$ is $G(i,j)/n^\zeta$ for a ``generator'' matrix $G$ and strength parameter $\zeta>0$. In these chains,…
This paper presents a nonparametric method for estimating the conditional density associated to the jump rate of a piecewise-deterministic Markov process. In our framework, the estimation needs only one observation of the process within a…
This study of occupation time densities for continuous-time Markov processes was inspired by the work of E.Nir et al (2006) in the field of Single Molecule FRET spectroscopy. There, a single molecule fluctuates between two or more states,…
The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations…
The need to model a Markov renewal on-off process with multiple off-states arise in many applications such as economics, physics, and engineering. Characterization of the occupation time of one specific off-state marginally or two…
We propose an individual claims reserving model based on the conditional Aalen-Johansen estimator, as developed in Bladt and Furrer (2023b). In our approach, we formulate a multi-state problem, where the underlying variable is the…
This paper introduces a class of non-linear and continuous-time opinion dynamics model with additive noise and state dependent interaction rates between agents. The model features interaction rates which are proportional to a negative power…
Case-I interval-censored (current status) data from multistate systems are often encountered in biomedical and epidemiological studies. In this article, we focus on the problem of estimating state entry distribution and occupation…
We develop an Onsager-Machlup-type theory for nonequilibrium semi-Markov processes. Our main result is an exact large time asymptotics for the joint probability of the occupation times and the currents in the system, establishing some…
Interval-censored multi state data is collected when the state of a subject is observed periodically. The analysis of such data using non-parametric multi-state models was not possible until recently, but is very desirable as it allows for…
Hidden Markov models (HMMs) are popular tools for analysing animal behaviour based on movement, acceleration and other sensor data. In particular, these models allow to infer how the animal's decision-making process interacts with internal…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…