Related papers: Likelihood for generally coarsened observations fr…
Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and…
Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks…
Joint modelling of longitudinal observations and event times continues to remain a topic of considerable interest in biomedical research. For example, in HIV studies, the longitudinal bio-marker such as CD4 cell count in a patient's blood…
The paper concerns the probabilistic evaluation of plans in the presence of unmeasured variables, each plan consisting of several concurrent or sequential actions. We establish a graphical criterion for recognizing when the effects of a…
Hidden Markov Models, HMM's, are mathematical models of Markov processes with state that is hidden, but from which information can leak. They are typically represented as 3-way joint-probability distributions. We use HMM's as denotations of…
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…
State-switching models such as hidden Markov models or Markov-switching regression models are routinely applied to analyse sequences of observations that are driven by underlying non-observable states. Coupled state-switching models extend…
We propose a copula-based extension of the hidden Markov model (HMM) which applies when the observations recorded at each time in the sample are multivariate. The joint model produced by the copula extension allows decoding of the hidden…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
In this work we consider time series with a finite number of discrete point changes. We assume that the data in each segment follows a different probability density functions (pdf). We focus on the case where the data in all segments are…
For the continuous-time and the discrete-time three-state hidden Markov model, the flux of the likelihood function up to 3-dimension of the observed process is shown explicitly. As an application, the sufficient and necessary condition of…
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…
Multistate dynamical processes on networks, where nodes can occupy one of a multitude of discrete states, are gaining widespread use because of their ability to recreate realistic, complex behaviour that cannot be adequately captured by…
We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…
For many neurological disorders, prediction of disease state is an important clinical aim. Neuroimaging provides detailed information about brain structure and function from which such predictions may be statistically derived. A multinomial…
In order to give quantitative estimates for approximating the ergodic limit, we investigate probabilistic limit behaviors of time-averaging estimators of numerical discretizations for a class of time-homogeneous Markov processes, by…
Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…
There have been significant efforts devoted to solving the longevity risk given that a continuous growth in population ageing has become a severe issue for many developed countries over the past few decades. The Cairns-Blake-Dowd (CBD)…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
Hidden Markov models (HMM) have been widely used by scientists to model stochastic systems: the underlying process is a discrete Markov chain and the observations are noisy realizations of the underlying process. Determining the number of…