Statistics in Service of Metascience: Measuring Replication Distance with Reproducibility Rate.

Motivated by the recent putative reproducibility crisis, we discuss the relationship between the replicability of scientific studies, the reproducibility of results obtained in these replications, and the philosophy of statistics. Our approach focuses on challenges in specifying scientific studies for scientific inference via statistical inference and is complementary to classical discussions in the philosophy of statistics. We particularly consider the challenges in replicating studies exactly, using the notion of the idealized experiment.

Approximate Bayesian computational methods to estimate the strength of divergent selection in population genomics models.

Statistical estimation of parameters in large models of evolutionary processes is often too computationally inefficient to pursue using exact model likelihoods, even with single-nucleotide polymorphism (SNP) data, which offers a way to reduce the size of genetic data while retaining relevant information. Approximate Bayesian Computation (ABC) to perform statistical inference about parameters of large models takes the advantage of simulations to bypass direct evaluation of model likelihoods. We develop a mechanistic model to simulate forward-in-time divergent selection with variable migration rates, modes of reproduction (sexual, asexual), length and number of migration-selection cycles.

Rigorous exploration in a model-centric science via epistemic iteration.

Urgent attention is needed to address generalizability problems in psychology. However, the current dominant paradigm centered on dichotomous results and rapid discoveries cannot provide the solution because of its theoretical inadequacies. We propose a paradigm shift towards a model-centric science, which provides the sophistication to understanding the sources of generalizability and promote systematic exploration.

The logical structure of experiments lays the foundation for a theory of reproducibility.

The scientific reform movement has proposed openness as a potential remedy to the putative reproducibility or replication crisis. However, the conceptual relationship among openness, replication experiments and results reproducibility has been obscure. We analyse the logical structure of experiments, define the mathematical notion of idealized experiment and use this notion to advance a theory of reproducibility.

Scientific discovery in a model-centric framework: Reproducibility, innovation, and epistemic diversity.

Consistent confirmations obtained independently of each other lend credibility to a scientific result. We refer to results satisfying this consistency as reproducible and assume that reproducibility is a desirable property of scientific discovery. Yet seemingly science also progresses despite irreproducible results, indicating that the relationship between reproducibility and other desirable properties of scientific discovery is not well understood.

Inference on admixture fractions in a mechanistic model of recurrent admixture.

Signatures of recent historical admixture are ubiquitous in human populations. We present a mechanistic model of admixture with two source populations, encompassing recurrent admixture periods and study the distribution of admixture fractions for finite but arbitrary genome size. We provide simulation-based methods to estimate the introgression parameters and discuss the implications of reaching stationarity on estimability of parameters when there are recurrent admixture events with different rates.

Inference from the stationary distribution of allele frequencies in a family of Wright-Fisher models with two levels of genetic variability.

The distribution of allele frequencies obtained from diffusion approximations to Wright-Fisher models is useful in developing intuition about the population level effects of evolutionary processes. The statistical properties of the stationary distributions of K-allele models have been extensively studied under neutrality or under selection. Here, we introduce a new family of Wright-Fisher models in which there are two hierarchical levels of genetic variability.

Recent selective sweeps in North American Drosophila melanogaster show signatures of soft sweeps.

Adaptation from standing genetic variation or recurrent de novo mutation in large populations should commonly generate soft rather than hard selective sweeps. In contrast to a hard selective sweep, in which a single adaptive haplotype rises to high population frequency, in a soft selective sweep multiple adaptive haplotypes sweep through the population simultaneously, producing distinct patterns of genetic variation in the vicinity of the adaptive site. Current statistical methods were expressly designed to detect hard sweeps and most lack power to detect soft sweeps.

AABC: approximate approximate Bayesian computation for inference in population-genetic models.

Approximate Bayesian computation (ABC) methods perform inference on model-specific parameters of mechanistically motivated parametric models when evaluating likelihoods is difficult. Central to the success of ABC methods, which have been used frequently in biology, is computationally inexpensive simulation of data sets from the parametric model of interest. However, when simulating data sets from a model is so computationally expensive that the posterior distribution of parameters cannot be adequately sampled by ABC, inference is not straightforward.

Genotype imputation in a coalescent model with infinitely-many-sites mutation.

Empirical studies have identified population-genetic factors as important determinants of the properties of genotype-imputation accuracy in imputation-based disease association studies. Here, we develop a simple coalescent model of three sequences that we use to explore the theoretical basis for the influence of these factors on genotype-imputation accuracy, under the assumption of infinitely-many-sites mutation. Employing a demographic model in which two populations diverged at a given time in the past, we derive the approximate expectation and variance of imputation accuracy in a study sequence sampled from one of the two populations, choosing between two reference sequences, one sampled from the same population as the study sequence and the other sampled from the other population.

Efficient simulation and likelihood methods for non-neutral multi-allele models.

Throughout the 1980s, Simon Tavaré made numerous significant contributions to population genetics theory. As genetic data, in particular DNA sequence, became more readily available, a need to connect population-genetic models to data became the central issue. The seminal work of Griffiths and Tavaré (1994a , 1994b , 1994c) was among the first to develop a likelihood method to estimate the population-genetic parameters using full DNA sequences.

Inference on the strength of balancing selection for epistatically interacting loci.

Existing inference methods for estimating the strength of balancing selection in multi-locus genotypes rely on the assumption that there are no epistatic interactions between loci. Complex systems in which balancing selection is prevalent, such as sets of human immune system genes, are known to contain components that interact epistatically. Therefore, current methods may not produce reliable inference on the strength of selection at these loci.

Estimation of selection intensity under overdominance by Bayesian methods.

A balanced pattern in the allele frequencies of polymorphic loci is a potential sign of selection, particularly of overdominance. Although this type of selection is of some interest in population genetics, there exists no likelihood based approaches specifically tailored to make inference on selection intensity. To fill this gap, we present Bayesian methods to estimate selection intensity under k-allele models with overdominance.