Related papers: Birth/birth-death processes and their computable t…
Consider the following birth and death process with the following infinitesimal transition probabilities {\lambda}(k) ={\lambda}/(1+k) and {\mu}(k) = {\mu}k with {\lambda},{\mu}> 0. This process has known as a discouragement queue [5].…
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…
Bayesian inference provides a principled framework for probabilistic reasoning. If inference is performed in two steps, uncertainty propagation plays a crucial role in accounting for all sources of uncertainty and variability. This becomes…
We present a class of SEIR Markov chain models for infectious diseases observed over discrete time in a random human population living in a closed environment. The population changes over time through random births, deaths, and transitions…
Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…
Linear birth-and-death processes (LBDPs) are foundational stochastic models in population dynamics, evolutionary biology, and hematopoiesis. Estimating parameters from discretely observed data is computationally demanding due to irregular…
Using the continuous-time susceptible-infected-susceptible (SIS) model on networks, we investigate the problem of inferring the class of the underlying network when epidemic data is only available at population-level (i.e. the number of…
Why are the epidemic patterns of COVID-19 so different among different cities or countries which are similar in their populations, medical infrastructures, and people's behavior? Why are forecasts or predictions made by so-called experts…
Discrete distributions derived from renewal processes, ie distributions of the number of events by some time t are beginning to be used in econometrics and health sciences. A new fast method is presented for computation of the probabilities…
Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights…
Competing risks occur in survival analysis when multiple causes of death are present. They play a prominent role in several domains extending beyond biostatistics to encompass epidemiology, actuarial sciences, and reliability theory. This…
The focus of the present paper is to forecast mortality rates for small sub-populations that are parts of a larger super-population. In this setting the assumption is that it is possible to produce reliable forecasts for the…
Many biological studies involve inferring the evolutionary history of a sample of individuals from a large population and interpreting the reconstructed tree. Such an ascertained tree typically represents only a small part of a…
Computational models are invaluable in capturing the complexities of real-world biological processes. Yet, the selection of appropriate algorithms for inference tasks, especially when dealing with real-world observational data, remains a…
We propose a generalization of the classical M/M/1 queue process. The resulting model is derived by applying fractional derivative operators to a system of difference-differential equations. This generalization includes both non-Markovian…
Bayesian networks (BNs) are graphical models that are useful for representing high-dimensional probability distributions. There has been a great deal of interest in recent years in the NP-hard problem of learning the structure of a BN from…
We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
This work provides a brief introduction to continuous-state branching processes (CB-processes) and continuous-state branching processes with immigration (CBI-processes) accessible to graduate students with reasonable background in…
Although the analysis of human mortality has a well-established history, the attempt to accurately forecast future death-rate patterns for different age groups and time horizons still attracts active research. Such a predictive focus has…