Simultaneous inference of parental admixture proportions and admixture times from unphased local ancestry calls

Population genetic analyses of local ancestry tracts routinely assume that the ancestral admixture process is identical for both parents of an individual, an assumption that may be invalid when considering recent admixture. Here we present Parental Admixture Proportion Inference (PAPI), a Bayesian tool for inferring the admixture proportions and admixture times for each parent of a single admixed individual. PAPI analyzes unphased local ancestry tracts and has two components models: a binomial model that exploits the informativeness of homozygous ancestry regions to infer parental admixture proportions, and a hidden Markov model (HMM) that infers admixture times from tract lengths. Crucially, the HMM employs an approximation to the pedigree crossover dynamics that accounts for unobserved within-ancestry recombination, enabling inference of parental admixture times. We compared the accuracy of PAPI's admixture proportion estimates with those of ANCESTOR in simulated admixed individuals and found that PAPI outperforms ANCESTOR by an average of 46% in a representative set of simulation scenarios, with PAPI's estimates deviating from the ground truth by 0.047 on average. Moreover, PAPI's admixture time estimates were strongly correlated with the ground truth in these simulations (R = 0.76), but have an average downward bias of 1.01 generations that is partly attributable to inaccuracies in local ancestry inference. As an illustration of its utility, we ran PAPI on real African Americans from the PAGE study (N = 5,786) and found strong evidence of assortative mating by ancestry proportion: couples' ancestry proportions are closer to each other than expected by chance (P<10-6), and are highly correlated (R = 0.87). We anticipate that PAPI will be useful in studying the population dynamics of admixture and will also be of interest to individuals seeking to learn about their personal genealogies.

Post-selection Inference

We discuss inference after data exploration, with a particular focus on inference after model or variable selection. We review three popular approaches to this problem: sample splitting, simultaneous inference, and conditional selective inference. We explain how each approach works and highlight its advantages and disadvantages. We also provide an illustration of these post-selection inference approaches. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Compositional learning of mutually recursive procedural systems

This paper presents a compositional approach to active automata learning of Systems of Procedural Automata (SPAs), an extension of Deterministic Finite Automata (DFAs) to systems of DFAs that can mutually call each other. SPAs are of high practical relevance, as they allow one to efficiently learn intuitive recursive models of recursive programs after an easy instrumentation that makes calls and returns observable. Key to our approach is the simultaneous inference of individual DFAs for each of the involved procedures via expansion and projection: membership queries for the individual DFAs are expanded to membership queries of the entire SPA, and global counterexample traces are transformed into counterexamples for the DFAs of concerned procedures. This reduces the inference of SPAs to a simultaneous inference of the DFAs for the involved procedures for which we can utilize various existing regular learning algorithms. The inferred models are easy to understand and allow for an intuitive display of the procedural system under learning that reveals its recursive structure. We implemented the algorithm within the LearnLib framework in order to provide a ready-to-use tool for practical application which is publicly available on GitHub for experimentation.

Joint Alignment and Tree Inference

Multiple sequence alignment and phylogenetic tree inference are connected problems that are often solved as independent steps in the inference process. Several attempts at doing simultaneous inference have been made, however currently the available methods are greatly limited by their computational complexity and can only handle small datasets. In this manuscript we introduce a combinatorial optimisation approach that will allow us to resolve the circularity of the problem and efficiently infer both alignments and trees under maximum likelihood.