Related papers: Markov models for accumulating mutations
We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…
A Markov process is registered. At random moment $\theta$ the distribution of observed sequence changes. Using probability maximizing approach the optimal stopping rule for detecting the change is identified. Some explicit solution is…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
Continuous-time multistate models are widely used for analyzing interval-censored data on disease progression over time. Sometimes, diseases manifest differently and what appears to be a coherent collection of symptoms is the expression of…
Owing to the influence of real-world networks both in science and society, numerous mathematical models have been developed to understand the structure and evolution of these systems, particularly in a temporal context. Recent advancements…
Adaptive time series forecasting is essential for prediction under regime changes. Several classical methods assume linear Gaussian state space model (LGSSM) with variances constant in time. However, there are many real-world processes that…
Deterministic compartmental models are predominantly used in the modeling of infectious diseases, though stochastic models are considered more realistic, yet are complicated to estimate due to missing data. In this paper we present a novel…
This paper introduces a Bayesian framework that combines Markov chain Monte Carlo (MCMC) sampling, dimensionality reduction, and neural density estimation to efficiently handle inverse problems that (i) must be solved multiple times, and…
This paper considers maximum likelihood (ML) estimation in a large class of models with hidden Markov regimes. We investigate consistency of the ML estimator and local asymptotic normality for the models under general conditions which allow…
More than ever, today we are left with the abundance of molecular data outpaced by the advancements of the phylogenomic methods. Especially in the case of presence of many genes over a set of species under the phylogeny question, more…
We present a continuous time model of maturation and survival, obtained as the limit of a compartmental evolution model when the number of compartments tends to infinity. We establish in particular an explicit formula for the law of the…
The latent stochastic block model is a flexible and widely used statistical model for the analysis of network data. Extensions of this model to a dynamic context often fail to capture the persistence of edges in contiguous network…
Multitype branching processes are ideal for studying the population dynamics of stem cell populations undergoing mutation accumulation over the years following transplant. In such stochastic models, several quantities are of clinical…
The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous…
Over time, a population acquires neutral genetic substitutions as a consequence of random drift. A famous result in population genetics asserts that the rate, $K$, at which these substitutions accumulate in the population coincides with the…
We propose a generative model and an inference scheme for epidemic processes on dynamic, adaptive contact networks. Network evolution is formulated as a link-Markovian process, which is then coupled to an individual-level stochastic SIR…
Arguing about the equilibrium distribution of continuous-time Markov chains can be vital for showing properties about the underlying systems. For example in biological systems, bistability of a chemical reaction network can hint at its…
We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises…
In this paper, we explore the class of the Hidden Semi-Markov Model (HSMM), a flexible extension of the popular Hidden Markov Model (HMM) that allows the underlying stochastic process to be a semi-Markov chain. HSMMs are typically used less…