Related papers: Bessel-like birth-death process
We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields to a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish…
In modern life insurance, Markov processes in continuous time on a finite or at least countable state space have been over the years an important tool for the modelling of the states of an insured. Motivated by applications in disability…
Sequential neuronal activity underlies a wide range of processes in the brain. Neuroscientific evidence for neuronal sequences has been reported in domains as diverse as perception, motor control, speech, spatial navigation and memory.…
Renewal processes are broadly used to model stochastic behavior consisting of isolated events separated by periods of quiescence, whose durations are specified by a given probability law. Here, we identify the minimal sufficient statistic…
We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on…
The mean residual life function is a key functional for a survival distribution. It has a practically useful interpretation as the expected remaining lifetime given survival up to a particular time point, and it also characterizes the…
Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…
The dynamics of a population exhibiting exponential growth can be modelled as a birth-death process, which naturally captures the stochastic variation in population size over time. In this article, we consider a supercritical birth-death…
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…
This paper introduces a discrete-time fractional Poisson process defined as a renewal process, where the waiting times follow a discrete Mittag-Leffler distribution. We investigate its fundamental properties by explicitly deriving the…
We continue to explore the hypothesis that neuronal populations represent and process analog variables in terms of probability density functions (PDFs). A neural assembly encoding the joint probability density over relevant analog variables…
For a Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE's) time discretization numerical schemes usually destroy the property of…
One of the key features of non-equilibrium steady states (NESS) is the presence of nontrivial probability currents. We propose a general classification of NESS in which these currents play a central distinguishing role. As a corollary, we…
We consider birth-and-death processes of objects (animals) defined in ${\bf Z}^d$ having unit death rates and random birth rates. For animals with uniformly bounded diameter we establish conditions on the rate distribution under which the…
Various and ubiquitous information systems are being used in monitoring, exchanging, and collecting information. These systems are generating massive amount of event sequence logs that may help us understand underlying phenomenon. By…
This paper explores and develops alternative statistical representations and estimation approaches for dynamic mortality models. The framework we adopt is to reinterpret popular mortality models such as the Lee-Carter class of models in a…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…
We study a class of Stochastic Differential Equations (SDEs) with jumps modeling multistage Michaelis--Menten enzyme kinetics, in which a substrate is sequentially transformed into a product via a cascade of intermediate complexes. These…
We propose a constructive approach to building temporal point processes that incorporate dependence on their history. The dependence is modeled through the conditional density of the duration, i.e., the interval between successive event…