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Over the last decade, ingenuous developments in Monte Carlo methods have enabled the unbiased estimation of adjoint-weighted reactor parameters expressed as bilinear forms, such as kinetics parameters and sensitivity coefficients. A…
The $k$-core decomposition is a widely studied summary statistic that describes a graph's global connectivity structure. In this paper, we move beyond using $k$-core decomposition as a tool to summarize a graph and propose using $k$-core…
We present an exclusion process based approach for sampling densest $k$-sub-graphs from regular graphs $L$ with connected complement. By interpreting an exclusion process as a Markov chain on a corresponding Token Graph $\mathfrak{L}_k$, we…
We observe a length-$n$ sample generated by an unknown,stationary ergodic Markov process (\emph{model}) over a finite alphabet $\mathcal{A}$. Given any string $\bf{w}$ of symbols from $\mathcal{A}$ we want estimates of the conditional…
We reconsider the Moran model in continuous time with population size $N$, two allelic types, and selection. We introduce a new particle representation, which we call the labelled Moran model, and which has the same distribution of type…
Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…
The edge partition model (EPM) is a generative model for extracting an overlapping community structure from static graph-structured data. In the EPM, the gamma process (GaP) prior is adopted to infer the appropriate number of latent…
We consider the question of existence of a unique invariant probability distribution which satisfies some evolutionary property. The problem arises from the random graph theory but to answer it we treat it as a dynamical system in the…
The space of graphs is often characterised by a non-trivial geometry, which complicates learning and inference in practical applications. A common approach is to use embedding techniques to represent graphs as points in a conventional…
There exists a range of different models for estimating and simulating credit risk transitions to optimally manage credit risk portfolios and products. In this chapter we present a Coupled Markov Chain approach to model rating transitions…
We investigate the dynamics of a broad class of stochastic copying processes on a network that includes examples from population genetics (spatially-structured Wright-Fisher models), ecology (Hubbell-type models), linguistics (the utterance…
Natural microbial populations often have complex spatial structures. This can impact their evolution, in particular the ability of mutants to take over. While mutant fixation probabilities are known to be unaffected by sufficiently…
The Laplacian-constrained Gaussian Markov Random Field (LGMRF) is a common multivariate statistical model for learning a weighted sparse dependency graph from given data. This graph learning problem can be formulated as a maximum likelihood…
Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…
Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice,…
The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…
We study properties and parameter estimation of finite-state homogeneous continuous-time bivariate Markov chains. Only one of the two processes of the bivariate Markov chain is observable. The general form of the bivariate Markov chain…
We study asymptotic behaviour of the correlation functions of bipartite sparse random $N\times N$ matrices. We assume that the graphs have $N$ vertices, the ratio of parts is $\displaystyle\frac{\alpha}{1-\alpha}$ and the average number of…
Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…
Motivated by the question of the impact of selective advantage in populations with skewed reproduction mechanims, we study a Moran model with selection. We assume that there are two types of individuals, where the reproductive success of…