Related papers: Exchangeable partitions derived from Markovian coa…
Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadratic dissipation potentials. This paper describes two natural…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
To introduce selection into a model of coalescence, I explore the use of modified integer partitions that allow the identification of a preferred lineage. I show that a partition-partition transition matrix, along with Monte Carlo discrete…
The collective interference of partially distinguishable bosons in multi-mode networks is studied via double-sided Feynman diagrams. The probability for many-body scattering events becomes a multi-dimensional tensor-permanent, which…
We present a sequential sampling methodology for weakly structural Markov laws, arising naturally in a Bayesian structure learning context for decomposable graphical models. As a key component of our suggested approach, we show that the…
We present simple conditions under which the limiting genealogical process associated with a class of interacting particle systems with non-neutral selection mechanisms, as the number of particles grows, is a time-rescaled Kingman…
We consider an infinitely-many neutral allelic model of population genetics where all alleles are divided into a finite number of classes, and each class is characterized by its own mutation rate. For this model the allelic composition of a…
Consider a haploid population which has evolved through an exchangeable reproduction dynamics, and in which all individuals alive at time $t$ have a most recent common ancestor (MRCA) who lived at time $A_t$, say. As time goes on, not only…
We develop a new Markov chain on graph partitions that makes relatively global moves yet is computationally feasible to be used as the proposal in the Metropolis-Hastings method. Our resulting algorithm can be made reversible and able to…
We describe a representation of the Bolthausen-Sznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the coalescent restricted to [n]: we show…
Every exchangeable Feller process taking values in a suitably nice combinatorial state space can be constructed by a system of iterated random Lipschitz functions. In discrete time, the construction proceeds by iterated application of…
We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model.…
Conditional sampling distributions (CSDs), sometimes referred to as copying models, underlie numerous practical tools in population genomic analyses. Though an important application that has received much attention is the inference of…
Bayesian inference for undirected graphical models is mostly restricted to the class of decomposable graphs, as they enjoy a rich set of properties making them amenable to high-dimensional problems. While parameter inference is…
We reconsider the immediate exchange model and define a more general class of models where mass is split, exchanged and merged. We relate the splitting process to the symmetric inclusion process via thermalization and from that obtain…
We argue for the use of separate exchangeability as a modeling principle in Bayesian nonparametric (BNP) inference. Separate exchangeability is de facto widely applied in the Bayesian parametric case, e.g., it naturally arises in simple…
In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…
We consider a model of a population in which individuals are sampled from different species. The Yule-Kingman nested coalescent describes the genealogy of the sample when each species merges with another randomly chosen species with a…
We present an explicit construction of a Markovian random growth process on integer partitions such that given it visits some level $n$, it passes through any partition $\lambda$ of $n$ with equal probabilities. The construction has…
Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…