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Summary We present new models and methods for the posterior drift problem where the regression function in the target domain is modelled as a linear adjustment, on an appropriate scale, of that in the source domain, and study the theoretical properties of our proposed estimators in the binary classification problem. The core idea of our model inherits the simplicity and the usefulness of generalized linear models and accelerated failure time models from the classical statistics literature. Our approach is shown to be flexible and applicable in a variety of statistical settings, and can be adopted for transfer learning problems in various domains including epidemiology, genetics and biomedicine. As concrete applications, we illustrate the power of our approach (i) through mortality prediction for British Asians by borrowing strength from similar data from the larger pool of British Caucasians, using the UK Biobank data, and (ii) in overcoming a spurious correlation present in the source domain of the Waterbirds dataset. 

Abstract The Li-Stephens (LS) haplotype copying model forms the basis of a number of important statistical inference procedures in genetics. LS is a probabilistic generative model which supposes that a sampled chromosome is an imperfect mosaic of other chromosomes found in a population. In the frequentist setting which is the focus of this paper, the output of LS is a “copying path” through chromosome space. The behavior of LS depends crucially on two user-specified parameters,$$\theta $$ $\theta$and$$\rho $$ $\rho$, which are respectively interpreted as the rates of mutation and recombination. However, because LS is not based on a realistic model of ancestry, the precise connection between these parameters and the biological phenomena they represent is unclear. Here, we offer an alternative perspective, which considers$$\theta $$ $\theta$and$$\rho $$ $\rho$as tuning parameters, and seeks to understand their impact on the LS output. We derive an algorithm which, for a given dataset, efficiently partitions the$$(\theta ,\rho )$$ $(\theta ,\rho )$plane into regions where the output of the algorithm is constant, thereby enumerating all possible solutions to the LS model in one go. We extend this approach to the “diploid LS” model commonly used for phasing. We demonstrate the usefulness of our method by studying the effects of changing$$\theta $$ $\theta$and$$\rho $$ $\rho$when using LS for common bioinformatic tasks. Our findings indicate that using the conventional (i.e., population-scaled) values for$$\theta $$ $\theta$and$$\rho $$ $\rho$produces near optimal results for imputation, but may systematically inflate switch error in the case of phasing diploid genotypes. 

Abstract Neutrality tests such as Tajima’s D and Fay and Wu’s H are standard implements in the population genetics toolbox. One of their most common uses is to scan the genome for signals of natural selection. However, it is well understood that D and H are confounded by other evolutionary forces—in particular, population expansion—that may be unrelated to selection. Because they are not model-based, it is not clear how to deconfound these tests in a principled way. In this article, we derive new likelihood-based methods for detecting natural selection, which are robust to fluctuations in effective population size. At the core of our method is a novel probabilistic model of tree imbalance, which generalizes Kingman’s coalescent to allow certain aberrant tree topologies to arise more frequently than is expected under neutrality. We derive a frequency spectrum-based estimator that can be used in place of D, and also extend to the case where genealogies are first estimated. We benchmark our methods on real and simulated data, and provide an open source software implementation. 

We developed a novel method for efficiently estimating time-varying selection coefficients from genome-wide ancient DNA data. In simulations, our method accurately recovers selective trajectories and is robust to misspecification of population size. We applied it to a large data set of ancient and present-day human genomes from Britain and identified seven loci with genome-wide significant evidence of selection in the past 4500 yr. Almost all of them can be related to increased vitamin D or calcium levels, suggesting strong selective pressure on these or related phenotypes. However, the strength of selection on individual loci varied substantially over time, suggesting that cultural or environmental factors moderated the genetic response. Of 28 complex anthropometric and metabolic traits, skin pigmentation was the only one with significant evidence of polygenic selection, further underscoring the importance of phenotypes related to vitamin D. Our approach illustrates the power of ancient DNA to characterize selection in human populations and illuminates the recent evolutionary history of Britain. 

In a striking result, Louca and Pennell [S. Louca, M. W. Pennell, Nature 580, 502–505 (2020)] recently proved that a large class of phylogenetic birth–death models is statistically unidentifiable from lineage-through-time (LTT) data: Any pair of sufficiently smooth birth and death rate functions is “congruent” to an infinite collection of other rate functions, all of which have the same likelihood for any LTT vector of any dimension. As Louca and Pennell argue, this fact has distressing implications for the thousands of studies that have utilized birth–death models to study evolution. In this paper, we qualify their finding by proving that an alternative and widely used class of birth–death models is indeed identifiable. Specifically, we show that piecewise constant birth–death models can, in principle, be consistently estimated and distinguished from one another, given a sufficiently large extant timetree and some knowledge of the present-day population. Subject to mild regularity conditions, we further show that any unidentifiable birth–death model class can be arbitrarily closely approximated by a class of identifiable models. The sampling requirements needed for our results to hold are explicit and are expected to be satisfied in many contexts such as the phylodynamic analysis of a global pandemic. 

Abstract The ongoing global pandemic has sharply increased the amount of data available to researchers in epidemiology and public health. Unfortunately, few existing analysis tools are capable of exploiting all of the information contained in a pandemic-scale data set, resulting in missed opportunities for improved surveillance and contact tracing. In this paper, we develop the variational Bayesian skyline (VBSKY), a method for fitting Bayesian phylodynamic models to very large pathogen genetic data sets. By combining recent advances in phylodynamic modeling, scalable Bayesian inference and differentiable programming, along with a few tailored heuristics, VBSKY is capable of analyzing thousands of genomes in a few minutes, providing accurate estimates of epidemiologically relevant quantities such as the effective reproduction number and overall sampling effort through time. We illustrate the utility of our method by performing a rapid analysis of a large number of SARS-CoV-2 genomes, and demonstrate that the resulting estimates closely track those derived from alternative sources of public health data.