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Family studies provide an important tool for understanding etiology of diseases, with the key aim of discovering evidence of family aggregation and to determine if such aggregation can be attributed to genetic components. Heritability and…
As whole genomes become widely available, maximum likelihood and Bayesian phylogenetic methods are demonstrating their limits in meeting the escalating computational demands. Conversely, distance-based phylogenetic methods are efficient,…
The collection of immunoglobulin genes in an individual's germline, which gives rise to B cell receptors via recombination, is known to vary significantly across individuals. In humans, for example, each individual has only a fraction of…
Phylogenetic analyses of gene expression have great potential for addressing a wide range of questions. These analyses will, for example, identify genes that have evolutionary shifts in expression that are correlated with evolutionary…
Partial clonality is widespread across the tree of life, but most population genetics models are designed for exclusively clonal or sexual organisms. This gap hampers our understanding of the influence of clonality on evolutionary…
Our goal is to study the genetic composition of a population in which each individual has 2 parents, who contribute equally to the genome of their ospring. We use a biparental Moran model, which is characterized by its xed number N of…
The evolutionary edit distance between two individuals in a population, i.e., the amount of applications of any genetic operator it would take the evolutionary process to generate one individual starting from the other, seems like a…
The log-det distance between two aligned DNA sequences was introduced as a tool for statistically consistent inference of a gene tree under simple non-mixture models of sequence evolution. Here we prove that the log-det distance, coupled…
We consider cross-sectional genetic association studies (common and rare variants) where non-genetic information is available, or feasible to obtain for $N$ individuals, but where it is infeasible to genotype all $N$ individuals. We…
Lexical resemblances among a group of languages indicate that the languages could be genetically related, i.e., they could have descended from a common ancestral language. However, such resemblances can arise by chance and, hence, need not…
Genetic association study is an essential step to discover genetic factors that are associated with a complex trait of interest. In this paper we present a novel generalized quasi-likelihood score (GQLS) test that is suitable for a study…
Plant breeding and variety trials are usually conducted in multiple environments sampled from a defined target population of environments in order to characterize the performance of breeding lines or varieties. When the population is large…
Motivated by the goals of dataset pruning and defect identification, a growing body of methods have been developed to score individual examples within a dataset. These methods, which we call "example difficulty scores", are typically used…
Recently, a special case of precision matrix estimation based on a distributionally robust optimization (DRO) framework has been shown to be equivalent to the graphical lasso. From this formulation, a method for choosing the regularization…
We present a mathematical model, and the corresponding mathematical analysis, that justifies and quantifies the use of principal component analysis of biallelic genetic marker data for a set of individuals to detect the number of…
Genetic data are often used to infer demographic history and changes or detect genes under selection. Inferential methods are commonly based on models making various strong assumptions: demography and population structures are supposed…
The broad sense genetic heritability, which quantifies the total proportion of phenotypic variation in a population due to genetic factors, is crucial for understanding trait inheritance. While many existing methods focus on estimating…
Rare diseases are collectively common, affecting approximately one in twenty individuals worldwide. In recent years, rapid progress has been made in rare disease diagnostics due to advances in DNA sequencing, development of new…
Selection bias affects Mendelian randomization investigations when selection into the study sample depends on a collider between the genetic variant and confounders of the risk factor-outcome association. However, the relative importance of…
We consider the problem of finding anomalies in a $d$-dimensional field of independent random variables $\{Y_i\}_{i \in \left\{1,...,n\right\}^d}$, each distributed according to a one-dimensional natural exponential family $\mathcal F =…