The 1000 Genomes Project set out to provide a comprehensive description of common human genetic variation by applying whole-genome sequencing to a diverse set of individuals from multiple populations. Here we report completion of the project, having reconstructed the genomes of 2,504 individuals from 26 populations using a combination of low-coverage whole-genome sequencing, deep exome sequencing, and dense microarray genotyping. We characterized a broad spectrum of genetic variation, in total over 88 million variants (84.7 million single nucleotide polymorphisms (SNPs), 3.6 million short insertions/deletions (indels), and 60,000 structural variants), all phased onto high-quality haplotypes. This resource includes >99% of SNP variants with a frequency of >1% for a variety of ancestries. We describe the distribution of genetic variation across the global sample, and discuss the implications for common disease studies.

https://cdr.lib.unc.edu/downloads/v692t8920

A global reference for human genetic variation.

Summary. We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure pD for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest. In general pD approximately corresponds to the trace of the product of Fisher's information and the posterior covariance, which in normal models is the trace of the ‘hat’ matrix projecting observations onto fitted values. Its properties in exponential families are explored. The posterior mean deviance is suggested as a Bayesian measure of fit or adequacy, and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. Adding pD to the posterior mean deviance gives a deviance information criterion for comparing models, which is related to other information criteria and has an approximate decision theoretic justification. The procedure is illustrated in some examples, and comparisons are drawn with alternative Bayesian and classical proposals. Throughout it is emphasized that the quantities required are trivial to compute in a Markov chain Monte Carlo analysis.

/pdf/bayesian-measures-of-model-complexity-and-fit-1ouzmtfu7x.pdf

Bayesian measures of model complexity and fit

Statistics for Spatial Data.

The brms package implements Bayesian multilevel models in R using the probabilistic programming language Stan. A wide range of distributions and link functions are supported, allowing users to fit - among others - linear, robust linear, binomial, Poisson, survival, ordinal, zero-inflated, hurdle, and even non-linear models all in a multilevel context. Further modeling options include autocorrelation of the response variable, user defined covariance structures, censored data, as well as meta-analytic standard errors. Prior specifications are flexible and explicitly encourage users to apply prior distributions that actually reflect their beliefs. In addition, model fit can easily be assessed and compared with the Watanabe-Akaike information criterion and leave-one-out cross-validation.

brms: An R Package for Bayesian Multilevel Models Using Stan

Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.

/pdf/approximate-bayesian-inference-for-latent-gaussian-models-by-2m3x22eic2.pdf

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

SECTION 1 - INTRODUCTION: HEALTH AND POPULATION DATA 1. Spatial epidemiology: methods and applications 2. Health event data 3. The use of population data in spatial epidemiology 4. Socio-economic factors at area level and their relationship with health 5. Bias and confounding in spatial epidemiology SECTION 2 - STATISTICAL METHODS 6. Overview of statistical methods for disease mapping and its relationship to cluster detection 7. Bayesian approaches to disease mapping 8. Clustering, cluster detection and spatial variation in risk 9. Assessment of disease risk in relation to a pre-specified source 10. Geostatistical methods for mapping environmental exposures 11. Ecological correlation studies SECTION 3 - DISEASE MAPPING AND CLUSTERING 12. Disease mapping: a historical perspective 13. Mapping mortality data in the United States 14. Geographical analysis of communicable disease data 15. Bayesian mapping of Hodgkin's disease in France 16. Investigating the genetic association between diabetes and malaria: an application of Bayesian ecological regression models with errors in covariates 17. Do cancers cluster? 18. Geographical variations in childhood leukaemia incidence SECTION 4 - EXPOSURE DATA AND THE LINK TO HEALTH 19. Exposure assessment 20. Personal exposure monitoring in environmental epidemiology 21. Dispersion modelling 22. Combining models of health and exposure data: the SAVIAH study 23. The role of geographical studies in risk assessment 24. Water quality and health 25. Climate change and human health: mapping and modelling potential impacts

Spatial epidemiology: methods and applications.

In light of the vast amounts of genomic data that are now being generated, we propose a new measure, the Bayesian false-discovery probability (BFDP), for assessing the noteworthiness of an observed association. BFDP shares the ease of calculation of the recently proposed false-positive report probability (FPRP) but uses more information, has a noteworthy threshold defined naturally in terms of the costs of false discovery and nondiscovery, and has a sound methodological foundation. In addition, in a multiple-testing situation, it is straightforward to estimate the expected numbers of false discoveries and false nondiscoveries. We provide an in-depth discussion of FPRP, including a comparison with the q value, and examine the empirical behavior of these measures, along with BFDP, via simulation. Finally, we use BFDP to assess the association between 131 single-nucleotide polymorphisms and lung cancer in a case-control study.

/pdf/a-bayesian-measure-of-the-probability-of-false-discovery-in-1pt20t8ws1.pdf

A Bayesian Measure of the Probability of False Discovery in Genetic Epidemiology Studies

The Bayes factor is a summary measure that provides an alternative to the P-value for the ranking of associations, or the flagging of associations as "significant". We describe an approximate Bayes factor that is straightforward to use and is appropriate when sample sizes are large. We consider various choices of the prior on the effect size, including those that allow effect size to vary with the minor allele frequency (MAF) of the marker. An important contribution is the description of a specific prior that gives identical rankings between Bayes factors and P-values, providing a link between the two approaches, and allowing the implications of the use of P-values to be more easily understood. As a summary measure of noteworthiness P-values are difficult to calibrate since their interpretation depends on MAF and, crucially, on sample size. A consequence is that a consistent decision-making procedure using P-values requires a threshold for significance that reduces with sample size, contrary to common practice.

Bayes factors for genome‐wide association studies: comparison with P‐values

Summary. We demonstrate the use of auxiliary (or latent) variables for sampling non-standard densities which arise in the context of the Bayesian analysis of non-conjugate and hierarchical models by using a Gibbs sampler. Their strategic use can result in a Gibbs sampler having easily sampled full conditionals. We propose such a procedure to simplify or speed up the Markov chain Monte Carlo algorithm. The strength of this approach lies in its generality and its ease of implementation. The aim of the paper, therefore, is to provide an alternative sampling algorithm to rejection-based methods and other sampling approaches such as the Metropolis-Hastings algorithm.

/pdf/gibbs-sampling-for-bayesian-non-conjugate-and-hierarchical-590b053380.pdf

Gibbs sampling for Bayesian non‐conjugate and hierarchical models by using auxiliary variables

Although Neandertal sequences that persist in the genomes of modern humans have been identified in Eurasians, comparable studies in people whose ancestors hybridized with both Neandertals and Denisovans are lacking. We developed an approach to identify DNA inherited from multiple archaic hominin ancestors and applied it to whole-genome sequences from 1523 geographically diverse individuals, including 35 previously unknown Island Melanesian genomes. In aggregate, we recovered 1.34 gigabases and 303 megabases of the Neandertal and Denisovan genome, respectively. We use these maps of archaic sequences to show that Neandertal admixture occurred multiple times in different non-African populations, characterize genomic regions that are significantly depleted of archaic sequences, and identify signatures of adaptive introgression.

https://science.sciencemag.org/content/sci/352/6282/235.full.pdf

Jon Wakefield

Papers

Spatial epidemiology: methods and applications.

A Bayesian Measure of the Probability of False Discovery in Genetic Epidemiology Studies

Bayes factors for genome‐wide association studies: comparison with P‐values

Gibbs sampling for Bayesian non‐conjugate and hierarchical models by using auxiliary variables

Excavating Neandertal and Denisovan DNA from the genomes of Melanesian individuals