Related papers: Markov jump processes in modeling coalescent with …
Genetic recombination can produce heterogeneous phylogenetic histories within a set of homologous genes. Delineating recombination events is important in the study of molecular evolution, as inference of such events provides a clearer…
We provide a characterisation of the continuous-time Markov models where the Markov matrices from the model can be parameterised directly in terms of the associated rate matrices (generators). That is, each Markov matrix can be expressed as…
Simulation experiments are typically conducted repeatedly during the model development process, for example, to re-validate if a behavioral property still holds after several model changes. Approaches for automatically reusing and…
Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…
A recombination reaction model for high-temperature chemical kinetics is derived from ab initio simulations data. A kinetic recombination rate model is derived using a recently developed ab initio state-specific dissociation model and the…
The advent of modern data collection and processing techniques has seen the size, scale, and complexity of data grow exponentially. A seminal step in leveraging these rich datasets for downstream inference is understanding the…
In this paper, we consider statistical estimation of time-inhomogeneous aggregate Markov models. Unaggregated models, which corresponds to Markov chains, are commonly used in multi-state life insurance to model the biometric states of an…
The molecular evolution in a gene regulatory network is classically modeled by Markov jump processes. However, the direct simulation of such models is extremely time consuming. Indeed, even the simplest Markovian model, such as the…
Hidden Markov jump processes are an attractive approach for modeling clinical disease progression data because they are explainable and capable of handling both irregularly sampled and noisy data. Most applications in this context consider…
We extend the spatial $\Lambda$-Fleming-Viot process introduced in [Electron. J. Probab. 15 (2010) 162-216] to incorporate recombination. The process models allele frequencies in a population which is distributed over the two-dimensional…
Quantum Markov networks are a generalization of quantum Markov chains to arbitrary graphs. They provide a powerful classification of correlations in quantum many-body systems---complementing the area law at finite temperature---and are…
Information theory and machine learning are inextricably linked and have even been referred to as "two sides of the same coin". One particularly elegant connection is the essential equivalence between probabilistic generative modeling and…
Advances in sampling schemes for Markov jump processes have recently enabled multiple inferential tasks. However, in statistical and machine learning applications, we often require that these continuous-time models find support on…
Markov chain Monte Carlo methods for exponential family models with intractable normalizing constant, such as the exchange algorithm, require simulations of the sufficient statistics at every iteration of the Markov chain, which often…
The computer revolution has been driven by a sustained increase of computational speed of approximately one order of magnitude (a factor of ten) every five years since about 1950. In natural sciences this has led to a continuous increase of…
Understanding the interplay between recombination and resampling is a significant challenge in mathematical population genetics and of great practical relevance. Asymptotic results about the distribution of samples when recombination is…
In the present article, we investigate the effects of dormancy on an abstract population genetic level. We first provide a short review of seed bank models in population genetics, and the role of dormancy for the interplay of evolutionary…
The deterministic selection-recombination equation describes the evolution of the genetic type composition of a population under selection and recombination in a law of large numbers regime. So far, an explicit solution has seemed out of…
Conditionally Markov (CM) sequences are powerful mathematical tools for modeling random phenomena. There are several classes of CM sequences one of which is the reciprocal sequence. Reciprocal sequences have been widely used in many areas…
We consider sampling and enumeration problems for Markov equivalence classes. We create and analyze a Markov chain for uniform random sampling on the DAGs inside a Markov equivalence class. Though the worst case is exponentially slow…