New Routes to Phylogeography: A Bayesian Structured Coalescent Approximation

Phylogeographic methods aim to infer migration trends and the history of sampled lineages from genetic data. Applications of phylogeography are broad, and in the context of pathogens include the reconstruction of transmission histories and the origin and emergence of outbreaks. Phylogeographic inference based on bottom-up population genetics models is computationally expensive, and as a result faster alternatives based on the evolution of discrete traits have become popular. In this paper, we show that inference of migration rates and root locations based on discrete trait models is extremely unreliable and sensitive to biased sampling. To address this problem, we introduce BASTA (BAyesian STructured coalescent Approximation), a new approach implemented in BEAST2 that combines the accuracy of methods based on the structured coalescent with the computational efficiency required to handle more than just few populations. We illustrate the potentially severe implications of poor model choice for phylogeographic analyses by investigating the zoonotic transmission of Ebola virus. Whereas the structured coalescent analysis correctly infers that successive human Ebola outbreaks have been seeded by a large unsampled non-human reservoir population, the discrete trait analysis implausibly concludes that undetected human-to-human transmission has allowed the virus to persist over the past four decades. As genomics takes on an increasingly prominent role informing the control and prevention of infectious diseases, it will be vital that phylogeographic inference provides robust insights into transmission history.     

Bayesian Inference of Local Trees Along Chromosomes by the Sequential Markov Coalescent

We propose a genealogy-sampling algorithm, Sequential Markov Ancestral Recombination Tree (SMARTree), that provides an approach to estimation from SNP haplotype data of the patterns of coancestry across a genome segment among a set of homologous chromosomes. To enable analysis across longer segments of genome, the sequence of coalescent trees is modeled via the modified sequential Markov coalescent (Marjoram and Wall, Genetics 7:16, 2006). To assess performance in estimating these local trees, our SMARTree implementation is tested on simulated data. Our base data set is of the SNPs in 10 DNA sequences over 50 kb. We examine the effects of longer sequences and of more sequences, and of a recombination and/or mutational hotspot. The model underlying SMARTree is an approximation to the full recombinant-coalescent distribution. However, in a small trial on simulated data, recovery of local trees was similar to that of LAMARC (Kuhner et al. Genetics 156:1393-1401, 2000a), a sampler which uses the full model.     

Inferring Epidemiological Dynamics with Bayesian Coalescent Inference: The Merits of Deterministic and Stochastic Models

Estimation of epidemiological and population parameters from molecular sequence data has become central to the understanding of infectious disease dynamics. Various models have been proposed to infer details of the dynamics that describe epidemic progression. These include inference approaches derived from Kingman’s coalescent theory. Here, we use recently described coalescent theory for epidemic dynamics to develop stochastic and deterministic coalescent susceptible–infected–removed (SIR) tree priors. We implement these in a Bayesian phylogenetic inference framework to permit joint estimation of SIR epidemic parameters and the sample genealogy. We assess the performance of the two coalescent models and also juxtapose results obtained with a recently published birth–death-sampling model for epidemic inference. Comparisons are made by analyzing sets of genealogies simulated under precisely known epidemiological parameters. Additionally, we analyze influenza A (H1N1) sequence data sampled in the Canterbury region of New Zealand and HIV-1 sequence data obtained from known United Kingdom infection clusters. We show that both coalescent SIR models are effective at estimating epidemiological parameters from data with large fundamental reproductive number R₀ and large population size S₀. Furthermore, we find that the stochastic variant generally outperforms its deterministic counterpart in terms of error, bias, and highest posterior density coverage, particularly for smaller R₀ and S₀. However, each of these inference models is shown to have undesirable properties in certain circumstances, especially for epidemic outbreaks with R₀ close to one or with small effective susceptible populations.     

Statistical Detection of EEG Synchrony Using Empirical Bayesian Inference

There is growing interest in understanding how the brain utilizes synchronized oscillatory activity to integrate information across functionally connected regions. Computing phase-locking values (PLV) between EEG signals is a popular method for quantifying such synchronizations and elucidating their role in cognitive tasks. However, high-dimensionality in PLV data incurs a serious multiple testing problem. Standard multiple testing methods in neuroimaging research (e.g., false discovery rate, FDR) suffer severe loss of power, because they fail to exploit complex dependence structure between hypotheses that vary in spectral, temporal and spatial dimension. Previously, we showed that a hierarchical FDR and optimal discovery procedures could be effectively applied for PLV analysis to provide better power than FDR. In this article, we revisit the multiple comparison problem from a new Empirical Bayes perspective and propose the application of the local FDR method (locFDR; Efron, 2001) for PLV synchrony analysis to compute FDR as a posterior probability that an observed statistic belongs to a null hypothesis. We demonstrate the application of Efron''s Empirical Bayes approach for PLV synchrony analysis for the first time. We use simulations to validate the specificity and sensitivity of locFDR and a real EEG dataset from a visual search study for experimental validation. We also compare locFDR with hierarchical FDR and optimal discovery procedures in both simulation and experimental analyses. Our simulation results showed that the locFDR can effectively control false positives without compromising on the power of PLV synchrony inference. Our results from the application locFDR on experiment data detected more significant discoveries than our previously proposed methods whereas the standard FDR method failed to detect any significant discoveries.     

Fully Bayesian Inference for Structural MRI: Application to Segmentation and Statistical Analysis of T2-Hypointensities

Aiming at iron-related T2-hypointensity, which is related to normal aging and neurodegenerative processes, we here present two practicable approaches, based on Bayesian inference, for preprocessing and statistical analysis of a complex set of structural MRI data. In particular, Markov Chain Monte Carlo methods were used to simulate posterior distributions. First, we rendered a segmentation algorithm that uses outlier detection based on model checking techniques within a Bayesian mixture model. Second, we rendered an analytical tool comprising a Bayesian regression model with smoothness priors (in the form of Gaussian Markov random fields) mitigating the necessity to smooth data prior to statistical analysis. For validation, we used simulated data and MRI data of 27 healthy controls (age: ; range, ). We first observed robust segmentation of both simulated T2-hypointensities and gray-matter regions known to be T2-hypointense. Second, simulated data and images of segmented T2-hypointensity were analyzed. We found not only robust identification of simulated effects but also a biologically plausible age-related increase of T2-hypointensity primarily within the dentate nucleus but also within the globus pallidus, substantia nigra, and red nucleus. Our results indicate that fully Bayesian inference can successfully be applied for preprocessing and statistical analysis of structural MRI data.     

A Primer on Bayesian Inference for Biophysical Systems

Bayesian inference is a powerful statistical paradigm that has gained popularity in many fields of science, but adoption has been somewhat slower in biophysics. Here, I provide an accessible tutorial on the use of Bayesian methods by focusing on example applications that will be familiar to biophysicists. I first discuss the goals of Bayesian inference and show simple examples of posterior inference using conjugate priors. I then describe Markov chain Monte Carlo sampling and, in particular, discuss Gibbs sampling and Metropolis random walk algorithms with reference to detailed examples. These Bayesian methods (with the aid of Markov chain Monte Carlo sampling) provide a generalizable way of rigorously addressing parameter inference and identifiability for arbitrarily complicated models.     

A Full Bayesian Approach for Boolean Genetic Network Inference

Boolean networks are a simple but efficient model for describing gene regulatory systems. A number of algorithms have been proposed to infer Boolean networks. However, these methods do not take full consideration of the effects of noise and model uncertainty. In this paper, we propose a full Bayesian approach to infer Boolean genetic networks. Markov chain Monte Carlo algorithms are used to obtain the posterior samples of both the network structure and the related parameters. In addition to regular link addition and removal moves, which can guarantee the irreducibility of the Markov chain for traversing the whole network space, carefully constructed mixture proposals are used to improve the Markov chain Monte Carlo convergence. Both simulations and a real application on cell-cycle data show that our method is more powerful than existing methods for the inference of both the topology and logic relations of the Boolean network from observed data.     

BiomeNet: A Bayesian Model for Inference of Metabolic Divergence among Microbial Communities

Metagenomics yields enormous numbers of microbial sequences that can be assigned a metabolic function. Using such data to infer community-level metabolic divergence is hindered by the lack of a suitable statistical framework. Here, we describe a novel hierarchical Bayesian model, called BiomeNet (Bayesian inference of metabolic networks), for inferring differential prevalence of metabolic subnetworks among microbial communities. To infer the structure of community-level metabolic interactions, BiomeNet applies a mixed-membership modelling framework to enzyme abundance information. The basic idea is that the mixture components of the model (metabolic reactions, subnetworks, and networks) are shared across all groups (microbiome samples), but the mixture proportions vary from group to group. Through this framework, the model can capture nested structures within the data. BiomeNet is unique in modeling each metagenome sample as a mixture of complex metabolic systems (metabosystems). The metabosystems are composed of mixtures of tightly connected metabolic subnetworks. BiomeNet differs from other unsupervised methods by allowing researchers to discriminate groups of samples through the metabolic patterns it discovers in the data, and by providing a framework for interpreting them. We describe a collapsed Gibbs sampler for inference of the mixture weights under BiomeNet, and we use simulation to validate the inference algorithm. Application of BiomeNet to human gut metagenomes revealed a metabosystem with greater prevalence among inflammatory bowel disease (IBD) patients. Based on the discriminatory subnetworks for this metabosystem, we inferred that the community is likely to be closely associated with the human gut epithelium, resistant to dietary interventions, and interfere with human uptake of an antioxidant connected to IBD. Because this metabosystem has a greater capacity to exploit host-associated glycans, we speculate that IBD-associated communities might arise from opportunist growth of bacteria that can circumvent the host''s nutrient-based mechanism for bacterial partner selection.     

Simultaneous Statistical Inference for Epigenetic Data

Epigenetic research leads to complex data structures. Since parametric model assumptions for the distribution of epigenetic data are hard to verify we introduce in the present work a nonparametric statistical framework for two-group comparisons. Furthermore, epigenetic analyses are often performed at various genetic loci simultaneously. Hence, in order to be able to draw valid conclusions for specific loci, an appropriate multiple testing correction is necessary. Finally, with technologies available for the simultaneous assessment of many interrelated biological parameters (such as gene arrays), statistical approaches also need to deal with a possibly unknown dependency structure in the data. Our statistical approach to the nonparametric comparison of two samples with independent multivariate observables is based on recently developed multivariate multiple permutation tests. We adapt their theory in order to cope with families of hypotheses regarding relative effects. Our results indicate that the multivariate multiple permutation test keeps the pre-assigned type I error level for the global null hypothesis. In combination with the closure principle, the family-wise error rate for the simultaneous test of the corresponding locus/parameter-specific null hypotheses can be controlled. In applications we demonstrate that group differences in epigenetic data can be detected reliably with our methodology.     

A Mixture of Delta-Rules Approximation to Bayesian Inference in Change-Point Problems

Error-driven learning rules have received considerable attention because of their close relationships to both optimal theory and neurobiological mechanisms. However, basic forms of these rules are effective under only a restricted set of conditions in which the environment is stable. Recent studies have defined optimal solutions to learning problems in more general, potentially unstable, environments, but the relevance of these complex mathematical solutions to how the brain solves these problems remains unclear. Here, we show that one such Bayesian solution can be approximated by a computationally straightforward mixture of simple error-driven ‘Delta’ rules. This simpler model can make effective inferences in a dynamic environment and matches human performance on a predictive-inference task using a mixture of a small number of Delta rules. This model represents an important conceptual advance in our understanding of how the brain can use relatively simple computations to make nearly optimal inferences in a dynamic world.     

Statistical Inference Methods for Two Crossing Survival Curves: A Comparison of Methods

A common problem that is encountered in medical applications is the overall homogeneity of survival distributions when two survival curves cross each other. A survey demonstrated that under this condition, which was an obvious violation of the assumption of proportional hazard rates, the log-rank test was still used in 70% of studies. Several statistical methods have been proposed to solve this problem. However, in many applications, it is difficult to specify the types of survival differences and choose an appropriate method prior to analysis. Thus, we conducted an extensive series of Monte Carlo simulations to investigate the power and type I error rate of these procedures under various patterns of crossing survival curves with different censoring rates and distribution parameters. Our objective was to evaluate the strengths and weaknesses of tests in different situations and for various censoring rates and to recommend an appropriate test that will not fail for a wide range of applications. Simulation studies demonstrated that adaptive Neyman’s smooth tests and the two-stage procedure offer higher power and greater stability than other methods when the survival distributions cross at early, middle or late times. Even for proportional hazards, both methods maintain acceptable power compared with the log-rank test. In terms of the type I error rate, Renyi and Cramér—von Mises tests are relatively conservative, whereas the statistics of the Lin-Xu test exhibit apparent inflation as the censoring rate increases. Other tests produce results close to the nominal 0.05 level. In conclusion, adaptive Neyman’s smooth tests and the two-stage procedure are found to be the most stable and feasible approaches for a variety of situations and censoring rates. Therefore, they are applicable to a wider spectrum of alternatives compared with other tests.     

Back to basics for Bayesian model building in genomic selection

Numerous Bayesian methods of phenotype prediction and genomic breeding value estimation based on multilocus association models have been proposed. Computationally the methods have been based either on Markov chain Monte Carlo or on faster maximum a posteriori estimation. The demand for more accurate and more efficient estimation has led to the rapid emergence of workable methods, unfortunately at the expense of well-defined principles for Bayesian model building. In this article we go back to the basics and build a Bayesian multilocus association model for quantitative and binary traits with carefully defined hierarchical parameterization of Student's t and Laplace priors. In this treatment we consider alternative model structures, using indicator variables and polygenic terms. We make the most of the conjugate analysis, enabled by the hierarchical formulation of the prior densities, by deriving the fully conditional posterior densities of the parameters and using the acquired known distributions in building fast generalized expectation-maximization estimation algorithms.     

Bayesian Inference for Gene Expression and Proteomics.

A text that has a systematic account of Bayesian analysis incomputational biology has been needed for a long time. Thisbook is a timely publication entirely devoted to cutting-edgeBayesian methods in genomics and proteomics research and manyof its contributors are leading authorities in the field. Itis thus an indispensable reference for researchers who are interestedin applying Bayesian techniques in their own biological research.Moreover, the book calls for more methodological and theoreticalresearch to     

A Bayesian Inference Framework to Reconstruct Transmission Trees Using Epidemiological and Genetic Data

The accurate identification of the route of transmission taken by an infectious agent through a host population is critical to understanding its epidemiology and informing measures for its control. However, reconstruction of transmission routes during an epidemic is often an underdetermined problem: data about the location and timings of infections can be incomplete, inaccurate, and compatible with a large number of different transmission scenarios. For fast-evolving pathogens like RNA viruses, inference can be strengthened by using genetic data, nowadays easily and affordably generated. However, significant statistical challenges remain to be overcome in the full integration of these different data types if transmission trees are to be reliably estimated. We present here a framework leading to a bayesian inference scheme that combines genetic and epidemiological data, able to reconstruct most likely transmission patterns and infection dates. After testing our approach with simulated data, we apply the method to two UK epidemics of Foot-and-Mouth Disease Virus (FMDV): the 2007 outbreak, and a subset of the large 2001 epidemic. In the first case, we are able to confirm the role of a specific premise as the link between the two phases of the epidemics, while transmissions more densely clustered in space and time remain harder to resolve. When we consider data collected from the 2001 epidemic during a time of national emergency, our inference scheme robustly infers transmission chains, and uncovers the presence of undetected premises, thus providing a useful tool for epidemiological studies in real time. The generation of genetic data is becoming routine in epidemiological investigations, but the development of analytical tools maximizing the value of these data remains a priority. Our method, while applied here in the context of FMDV, is general and with slight modification can be used in any situation where both spatiotemporal and genetic data are available.     

Bayesian Framework for Causal Inference with Principal Stratification and Clusters

Statistics in Biosciences - In observational studies, principal stratification is a well-established method in causal analysis to adjust the treatment effect estimation for post-treatment...     

StochPy: A Comprehensive,User-Friendly Tool for Simulating Stochastic Biological Processes

Single-cell and single-molecule measurements indicate the importance of stochastic phenomena in cell biology. Stochasticity creates spontaneous differences in the copy numbers of key macromolecules and the timing of reaction events between genetically-identical cells. Mathematical models are indispensable for the study of phenotypic stochasticity in cellular decision-making and cell survival. There is a demand for versatile, stochastic modeling environments with extensive, preprogrammed statistics functions and plotting capabilities that hide the mathematics from the novice users and offers low-level programming access to the experienced user. Here we present StochPy (Stochastic modeling in Python), which is a flexible software tool for stochastic simulation in cell biology. It provides various stochastic simulation algorithms, SBML support, analyses of the probability distributions of molecule copy numbers and event waiting times, analyses of stochastic time series, and a range of additional statistical functions and plotting facilities for stochastic simulations. We illustrate the functionality of StochPy with stochastic models of gene expression, cell division, and single-molecule enzyme kinetics. StochPy has been successfully tested against the SBML stochastic test suite, passing all tests. StochPy is a comprehensive software package for stochastic simulation of the molecular control networks of living cells. It allows novice and experienced users to study stochastic phenomena in cell biology. The integration with other Python software makes StochPy both a user-friendly and easily extendible simulation tool.     

DivStat: A User-Friendly Tool for Single Nucleotide Polymorphism Analysis of Genomic Diversity

Recent developments have led to an enormous increase of publicly available large genomic data, including complete genomes. The 1000 Genomes Project was a major contributor, releasing the results of sequencing a large number of individual genomes, and allowing for a myriad of large scale studies on human genetic variation. However, the tools currently available are insufficient when the goal concerns some analyses of data sets encompassing more than hundreds of base pairs and when considering haplotype sequences of single nucleotide polymorphisms (SNPs). Here, we present a new and potent tool to deal with large data sets allowing the computation of a variety of summary statistics of population genetic data, increasing the speed of data analysis.