Abstract Motivation Polygenic embryo screening (PES) is a new, controversial technology, whereby human in vitro fertilization embryos are screened for their genetic risk of complex, polygenic diseases. PES aims to reduce the disease burden in offspring by prioritizing the selection of low-risk embryos. However, given that polygenic diseases are usually late-onset, PES outcomes must be estimated by epidemiological modeling. The liability threshold model has been previously used to predict outcomes. However, predictions rely on complex sets of equations, some of which require numerical integration or simulation. Further, previous models failed to account for the possibility that the selected embryo will not be born. Results Here, we present PEStimate, a freely available online app for predicting PES outcomes when screening for a single disease. PEStimate predicts the offspring risk with and without PES, as well as generates plots of the risk reduction versus key parameters. Users can adjust the number of available embryos, the live birth rate, the disease prevalence, the accuracy of the genetic risk predictor, the embryo selection method, the genetic risk of parents, and the disease status of parents, siblings, uncles/aunts, and grandparents of the embryos. Our model includes, for the first time, the possibility of embryo implantation failure, showing that risk reductions have been previously overestimated. PEStimate provides geneticists, healthcare professionals, patients, and other stakeholders with a necessary tool for examining the impact of PES and weighing its potential benefits against possible personal and societal harms. Availability and implementation PEStimate: https://polygenicembryo.shinyapps.io/pestimate. Source code: https://github.com/Lirazk/PEStimate.

MOTIVATION: The rise in the number of genotyped ancient individuals provides an opportunity to estimate population admixture models for many populations. However, in models describing modern populations as mixtures of ancient ones, it is typically difficult to estimate the model mixing coefficients and to evaluate its fit to the data. RESULTS: We present LINADMIX, designed to tackle this problem by solving a constrained linear model when both the ancient and the modern genotypes are represented in a low-dimensional space. LINADMIX estimates the mixing coefficients and their standard errors, and computes a P-value for testing the model fit to the data. We quantified the performance of LINADMIX using an extensive set of simulated studies. We show that LINADMIX can accurately estimate admixture coefficients, and is robust to factors such as population size, genetic drift, proportion of missing data and various types of model misspecification. AVAILABILITY AND IMPLEMENTATION: LINADMIX is available as a python code at https://github.com/swidler/linadmix. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Hidden Markov models (HMMs) are powerful tools for modeling processes along the genome. In a standard genomic HMM, observations are drawn, at each genomic position, from a distribution whose parameters depend on a hidden state, and the hidden states evolve along the genome as a Markov chain. Often, the hidden state is the Cartesian product of multiple processes, each evolving independently along the genome. Inference in these so-called Factorial HMMs has a naïve running time that scales as the square of the number of possible states, which by itself increases exponentially with the number of sub-chains; such a running time scaling is impractical for many applications. While faster algorithms exist, there is no available implementation suitable for developing bioinformatics applications. RESULTS: We developed FactorialHMM, a Python package for fast exact inference in Factorial HMMs. Our package allows simulating either directly from the model or from the posterior distribution of states given the observations. Additionally, we allow the inference of all key quantities related to HMMs: (i) the (Viterbi) sequence of states with the highest posterior probability; (ii) the likelihood of the data and (iii) the posterior probability (given all observations) of the marginal and pairwise state probabilities. The running time and space requirement of all procedures is linearithmic in the number of possible states. Our package is highly modular, providing the user with maximal flexibility for developing downstream applications. AVAILABILITY AND IMPLEMENTATION: https://github.com/regevs/factorial_hmm. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this problem, based on the eigenvectors of both the second order moment matrix and third order moment tensor of the observed data. We prove that under mild non-degeneracy conditions, our method consistently estimates the model parameters at the optimal parametric rate. Our tensor-based method generalizes previous orthogonal tensor decomposition approaches, where the hidden units were assumed to be either statistically independent or mutually exclusive. We illustrate the consistency of our method on simulated data and demonstrate its usefulness in learning a common model for population mixtures in genetics.