Related papers: The coalescent and its descendants
This paper addresses the problem of making statistical inference about a population that can only be identified through classifier predictions. The problem is motivated by scientific studies in which human labels of a population are…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
Some practical results are derived for population inference based on a sample, under the two qualitative conditions of 'ignorability' and exchangeability. These are the 'Histogram Theorem', for predicting the outcome of a non-sampled member…
Phylogeographic methods aim to infer migration trends and the history of sampled lineages from genetic data. Applications of phylogeography are broad, and in the context of pathogens include the reconstruction of transmission histories and…
We review the problem of confounding in genetic association studies, which arises principally because of population structure and cryptic relatedness. Many treatments of the problem consider only a simple ``island'' model of population…
Many biological studies involve inferring the evolutionary history of a sample of individuals from a large population and interpreting the reconstructed tree. Such an ascertained tree typically represents only a small part of a…
For a family of models of evolving population under selection, which can be described by noisy traveling wave equations, the coalescence times along the genealogical tree scale like $\log^\alpha N$, where $N$ is the size of the population,…
We derive exact formulae for the allele frequency spectrum under the coalescent with mutation, conditioned on allele counts at some fixed time in the past. We consider unlinked biallelic markers mutating according to a finite sites, or…
Gene genealogies are frequently studied by measuring properties such as their height ($H$), length ($L$), sum of external branches ($E$), sum of internal branches ($I$), and mean of their two basal branches ($B$), and the coalescence times…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
Coalescent histories are combinatorial structures that describe for a given gene tree and species tree the possible lists of branches of the species tree on which the gene tree coalescences take place. Properties of the number of coalescent…
Discrete diffusion models have recently become competitive with autoregressive models for language modeling, even outperforming them on reasoning tasks requiring planning and global coherence, but they require more computation at inference…
How to model distribution of sequential data, including but not limited to speech and human motions, is an important ongoing research problem. It has been demonstrated that model capacity can be significantly enhanced by introducing…
Many aspects of the historical relationships between populations in a species are reflected in genetic data. Inferring these relationships from genetic data, however, remains a challenging task. In this paper, we present a statistical model…
Assume that individuals alive at time $t$ in some population can be ranked in such a way that the coalescence times between consecutive individuals are i.i.d. The ranked sequence of these branches is called a coalescent point process. We…
A classical problem of statistical inference is the valid specification of a model that can account for the statistical dependencies between observations when the true structure is dense, intractable, or unknown. To address this problem, a…
Correlation of gene histories in the human genome determines the patterns of genetic variation (haplotype structure) and is crucial to understanding genetic factors in common diseases. We derive closed analytical expressions for the…
In the absence of selection, the structure of allelic diversity is described by the elegant sampling formula of Ewens. This formula has helped shape our expectations of empirical patterns of molecular variation. Along with coalescent…
The recent realization that entire communities fuse and separate (community coalescence) has led to a reappraisal of the forces determining species diversity and dynamics, especially in microbial communities where coalescence is likely…
Understanding patterns of selectively neutral genetic variation is essential in order to model deviations from neutrality, caused for example by different forms of selection. Best understood is neutral genetic variation at a single locus,…