Statistics for Spatial Data.

1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

Massively parallel short-read sequencing technologies, coupled with powerful software platforms, are enabling investigators to analyse tens of thousands of genetic markers. This wealth of data is rapidly expanding and allowing biological questions to be addressed with unprecedented scope and precision. The sizes of the data sets are now posing significant data processing and analysis challenges. Here we describe an extension of the Stacks software package to efficiently use genotype-by-sequencing data for studies of populations of organisms. Stacks now produces core population genomic summary statistics and SNP-by-SNP statistical tests. These statistics can be analysed across a reference genome using a smoothed sliding window. Stacks also now provides several output formats for several commonly used downstream analysis packages. The expanded population genomics functions in Stacks will make it a useful tool to harness the newest generation of massively parallel genotyping data for ecological and evolutionary genetics.

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Stacks: an analysis tool set for population genomics

Machine learning (ML) encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. This article reviews in a selective way the recent research on the interface between machine learning and the physical sciences. This includes conceptual developments in ML motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross fertilization between the two fields. After giving a basic notion of machine learning methods and principles, examples are described of how statistical physics is used to understand methods in ML. This review then describes applications of ML methods in particle physics and cosmology, quantum many-body physics, quantum computing, and chemical and material physics. Research and development into novel computing architectures aimed at accelerating ML are also highlighted. Each of the sections describe recent successes as well as domain-specific methodology and challenges.

Machine learning and the physical sciences

Genotyping by sequencing (GBS) is a next generation sequencing based method that takes advantage of reduced representation to enable high throughput genotyping of large numbers of individuals at a large number of SNP markers. The relatively straightforward, robust, and cost-effective GBS protocol is currently being applied in numerous species by a large number of researchers. Herein we describe a bioinformatics pipeline, tassel-gbs, designed for the efficient processing of raw GBS sequence data into SNP genotypes. The tassel-gbs pipeline successfully fulfills the following key design criteria: (1) Ability to run on the modest computing resources that are typically available to small breeding or ecological research programs, including desktop or laptop machines with only 8–16 GB of RAM, (2) Scalability from small to extremely large studies, where hundreds of thousands or even millions of SNPs can be scored in up to 100,000 individuals (e.g., for large breeding programs or genetic surveys), and (3) Applicability in an accelerated breeding context, requiring rapid turnover from tissue collection to genotypes. Although a reference genome is required, the pipeline can also be run with an unfinished “pseudo-reference” consisting of numerous contigs. We describe the tassel-gbs pipeline in detail and benchmark it based upon a large scale, species wide analysis in maize (Zea mays), where the average error rate was reduced to 0.0042 through application of population genetic-based SNP filters. Overall, the GBS assay and the tassel-gbs pipeline provide robust tools for studying genomic diversity.

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TASSEL-GBS: a high capacity genotyping by sequencing analysis pipeline

DIYABC is a software package for a comprehensive analysis of population history using approximate Bayesian computation on DNA polymorphism data. Version 2.0 implements a number of new features and analytical methods. It allows (i) the analysis of single nucleotide polymorphism data at large number of loci, apart from microsatellite and DNA sequence data, (ii) efficient Bayesian model choice using linear discriminant analysis on summary statistics and (iii) the serial launching of multiple post-processing analyses. DIYABC v2.0 also includes a user-friendly graphical interface with various new options. It can be run on three operating systems: GNU/Linux, Microsoft Windows and Apple Os X. Freely available with a detailed notice document and example projects to academic users at http://www1.montpellier.inra.fr/CBGP/diyabc CONTACT: estoup@supagro.inra.fr SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

DIYABC v2.0: a software to make approximate Bayesian computation inferences about population history using single nucleotide polymorphism, DNA sequence and microsatellite data

Approximate Bayesian Computation (ABC) methods, also known as likelihood-free techniques, have appeared in the past ten years as the most satisfactory approach to intractable likelihood problems, first in genetics then in a broader spectrum of applications. However, these methods suffer to some degree from calibration difficulties that make them rather volatile in their implementation and thus render them suspicious to the users of more traditional Monte Carlo methods. In this survey, we study the various improvements and extensions brought on the original ABC algorithm in recent years.

Approximate Bayesian computational methods

Also known as likelihood-free methods, approximate Bayesian computational (ABC) methods have appeared in the past ten years as the most satisfactory approach to untractable likelihood problems, first in genetics then in a broader spectrum of applications. However, these methods suffer to some degree from calibration difficulties that make them rather volatile in their implementation and thus render them suspicious to the users of more traditional Monte Carlo methods. In this survey, we study the various improvements and extensions made to the original ABC algorithm over the recent years.

Approximate Bayesian Computational methods

Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior probabilities may be poorly evaluated by standard ABC techniques.Results: We propose a novel approach based on a machine learning tool named random forests (RF) to conduct selection among the highly complex models covered by ABC algorithms. We thus modify the way Bayesian model selection is both understood and operated, in that we rephrase the inferential goal as a classification problem, first predicting the model that best fits the data with RF and postponing the approximation of the posterior probability of the selected model for a second stage also relying on RF. Compared with earlier implementations of ABC model choice, the ABC RF approach offers several potential improvements: (i) it often has a larger discriminative power among the competing models, (ii) it is more robust against the number and choice of statistics summarizing the data, (iii) the computing effort is drastically reduced (with a gain in computation efficiency of at least 50) and (iv) it includes an approximation of the posterior probability of the selected model. The call to RF will undoubtedly extend the range of size of datasets and complexity of models that ABC can handle. We illustrate the power of this novel methodology by analyzing controlled experiments as well as genuine population genetics datasets.Availability and implementation: The proposed methodology is implemented in the R package abcrf available on the CRAN.

Reliable ABC model choice via random forests.

Inexpensive short-read sequencing technologies applied to reduced representation genomes is revolutionizing genetic research, especially population genetics analysis, by allowing the genotyping of massive numbers of single-nucleotide polymorphisms (SNP) for large numbers of individuals and populations. Restriction site-associated DNA (RAD) sequencing is a recent technique based on the characterization of genomic regions flanking restriction sites. One of its potential drawbacks is the presence of polymorphism within the restriction site, which makes it impossible to observe the associated SNP allele (i.e. allele dropout, ADO). To investigate the effect of ADO on genetic variation estimated from RAD markers, we first mathematically derived measures of the effect of ADO on allele frequencies as a function of different parameters within a single population. We then used RAD data sets simulated using a coalescence model to investigate the magnitude of biases induced by ADO on the estimation of expected heterozygosity and F(ST) under a simple demographic model of divergence between two populations. We found that ADO tends to overestimate genetic variation both within and between populations. Assuming a mutation rate per nucleotide between 10(-9) and 10(-8), this bias remained low for most studied combinations of divergence time and effective population size, except for large effective population sizes. Averaging F(ST) values over multiple SNPs, for example, by sliding window analysis, did not correct ADO biases. We briefly discuss possible solutions to filter the most problematic cases of ADO using read coverage to detect markers with a large excess of null alleles.

Pierre Pudlo

Papers

DIYABC v2.0: a software to make approximate Bayesian computation inferences about population history using single nucleotide polymorphism, DNA sequence and microsatellite data

Approximate Bayesian computational methods

Approximate Bayesian Computational methods

Reliable ABC model choice via random forests.

The effect of RAD allele dropout on the estimation of genetic variation within and between populations