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In the context of the genome rearrangement problem, we analyze two well known models, namely the reversal and the prefix reversal models, by exploiting the connection with the notion of permutation pattern. More specifically, for any $k$,…
Under a markovian evolutionary process, the expected number of substitutions per site (also called branch length) that have occurred when a sequence has evolved from another according to a transition matrix $P$ can be approximated by…
We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other,…
This article presents a novel method for causal discovery with generalized structural equation models suited for analyzing diverse types of outcomes, including discrete, continuous, and mixed data. Causal discovery often faces challenges…
We introduce two models for multi-type random trees motivated by studies of trait dependence in the evolution of species. Our discrete time model, the multi-type ERM tree, is a generalization of Markov propagation models on a random tree…
We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g. exchangeable observational units or features) and contiguous groups, or…
In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…
Whole genome sequencing of pathogens from multiple hosts in an epidemic offers the potential to investigate who infected whom with unparalleled resolution, potentially yielding important insights into disease dynamics and the impact of…
Phylogenetic reconstruction aims at finding plausible hypotheses of the evolutionary history of genes or species based on genomic sequence information. The distinction of orthologous genes (genes that having a common ancestry and diverged…
We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the…
Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…
Not all nodes in a network are created equal. Differences and similarities exist at both individual node and group levels. Disentangling single node from group properties is crucial for network modeling and structural inference. Based on…
The reconstruction of transmission trees for epidemics from genetic data has been the subject of some recent interest. It has been demonstrated that the transmission tree structure can be investigated by augmenting internal nodes of a…
We consider the Moran model of population genetics with two types, mutation, and selection, and investigate the line of descent of a randomly-sampled individual from a contemporary population. We trace this ancestral line back into the…
Probabilistic graphical models (PGMs) are widely used to discover latent structure in data, but their success hinges on selecting an appropriate model design. In practice, model specification is difficult and often requires iterative…
One of the main aims in phylogenetics is the estimation of ancestral sequences based on present-day data like, for instance, DNA alignments. One way to estimate the data of the last common ancestor of a given set of species is to first…
We give a closed form of the discrete-time evolution of a recombination transformation in population genetics. This decomposition allows to define a Markov chain in a natural way. We describe the geometric decay rate to the limit…
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…
Understanding the evolutionary relationship among species is of fundamental importance to the biological sciences. The location of the root in any phylogenetic tree is critical as it gives an order to evolutionary events. None of the…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…