Bayes Factor Test Research Articles

A New Migration Map of HIV-1 CRF07_BC in China: Analysis of Sequences from 12 Provinces over a Decade

BackgroundAs one of prevalence HIV-1 strains in IDUs in Asia, the origination and full transmission map of CRF07_BC is of great interested and remains unclear. In the study, we collected 769 CRF07_BC derived sequences (including 45 sequences generated in our laboratory) from 12 provinces in China for reconstructing transmission map. Meanwhile, ample historic epidemic evidences were also reviewed to assist sequences analysis.Methodology/Principal FindingsIn the study, we collected 769 CRF07_BC derived sequences and identified 138 independent sequences from 12 provinces in China for subsequent phylogeographic tree analysis, Bayes Factor test and the estimation of state tMRCA. The analyses demonstrated that CRF07_BC was originated in 1993 in IDU in Yunnan province and then initially spread to Guangxi (eastern neighbor to Yunnan) in 1994, to Xinjiang (northwest) in 1995 and to Sichuan (northern neighbor to Yunnan) in 1996. The subsequent transmissions occurred from Yunnan to Liaoning (northeast) in 1997 and to Jiangsu in 1998. Interestingly, after the early introduction of CRF07_BC into Guangxi, Xinjiang and Sichuan, these three regions served as secondary epicenters for further spreading into Gansu, Ningxia, Qinghai, Beijing and Hunan during 1999–2001. These analyzed results are in accordance with early epidemic investigations.Conclusions/SignificanceOur data not just reconstructed the migration map of CRF07_BC, but also firstly revealed the active roles of these secondary epicenters in the dynamic migration of CRF07_BC in China.

Phylogeny and classification of whirligig beetles (Coleoptera: Gyrinidae): relaxed‐clock model outperforms parsimony and time‐free Bayesian analyses

Phylogenetic relationships among members of the family Gyrinidae (Coleoptera: Adephaga) were inferred from analysis of 42 morphological characters and DNA sequence data from the genes 12S rRNA, cytochrome c oxidase I and II, elongation factor 1 alpha (2 different copies) and histone III. Eighty‐nine species of Gyrinidae were included representing all known subfamilies, tribes and genera. Outgroups include species from Noteridae, Paelobiidae and Dytiscidae. Analyses include parsimony analysis, and partitioned time‐free and relaxed‐clock Bayesian analyses of the combined data using reversible‐jump MCMC to simultaneously integrate over all possible 4 × 4 nucleotide substitution models. Analyses resulted in conflicting topologies between the combined parsimony and Bayesian analyses on the one hand, and the relaxed‐clock analysis on the other. The marginal likelihoods of competing models were calculated with stepping‐stone sampling and used in a Bayes factor test, which, along with arguments from morphology, supported the topology generated by the relaxed‐clock analysis. This phylogenetic hypothesis is adopted to revise the higher classification of Gyrinidae. Major taxonomic conclusions include: (i) monophyletic Gyrinidae, (ii) the Nearctic Spanglerogyrinae Folkerts (with one species, Spanglerogyrus albiventris Folkerts) sister to all other Gyrinidae, (iii) the Madagascar endemic Heterogyrinae Brinck stat. n. (with one species, Heterogyrus milloti Legros) sister to all Gyrinidae except Spanglerogyrinae, (iv) monophyletic Gyrininae Latreille including three monophyletic tribes with the following relationship: Orectochilini Régimbart + (Gyrinini Latreille + Enhydrini Régimbart), (v) monophyletic Orectochilini comprising four monophyletic genera with the following relationships: (Gyretes Brullé + Patrus Aubéstat. n.) + (Orectogyrus Régimbart + Orectochilus Dejean), (vi) monophyletic Gyrinini comprising three genera with the following relationships: Gyrinus Geoffroy + (Metagyrinus Brinck + Aulonogyrus Motschulsky), each monophyletic except Metagyrinus with only one included species and not tested for monophyly, and (vii) monophyletic Enhydrini comprising five genera with the following relationships: (Porrorhynchus Laporte + Dineutus MacLeay) + (Enhydrus Laporte + (Andogyrus Ochs + Macrogyrus Régimbart)), each monophyletic except Porrorhynchus, Enhydrus and Andogyrus each with one included species and untested for monophyly. Each subfamily, tribe and genus is diagnosed and discussed. The female reproductive tract of each group is presented, illustrated and discussed with respect to the phylogenetic conclusions.

Default Bayes factors for ANOVA designs

Bayes factors have been advocated as superior to p-values for assessing statistical evidence in data. Despite the advantages of Bayes factors and the drawbacks of p-values, inference by p-values is still nearly ubiquitous. One impediment to the adoption of Bayes factors is a lack of practical development, particularly a lack of ready-to-use formulas and algorithms. In this paper, we discuss and expand a set of default Bayes factor tests for ANOVA designs. These tests are based on multivariate generalizations of Cauchy priors on standardized effects, and have the desirable properties of being invariant with respect to linear transformations of measurement units. Moreover, these Bayes factors are computationally convenient, and straightforward sampling algorithms are provided. We cover models with fixed, random, and mixed effects, including random interactions, and do so for within-subject, between-subject, and mixed designs. We extend the discussion to regression models with continuous covariates. We also discuss how these Bayes factors may be applied in nonlinear settings, and show how they are useful in differentiating between the power law and the exponential law of skill acquisition. In sum, the current development makes the computation of Bayes factors straightforward for the vast majority of designs in experimental psychology.

Phylodynamics of HIV-1 unique recombinant forms in China–Myanmar border: Implication for HIV-1 transmission to Myanmar from Dehong, China

China–Myanmar border plays a crucial role in HIV-1 transmission in Asia. Here, we performed Bayesian phylodynamics analyses on p17 gene using BEAST to investigate HIV-1 transmission in this region. Maximum clade credibility trees of subtype C and CRF01_AE show that majority of unique recombinant forms (URFs) and pure subtype strains from Dehong and Myanmar cluster together, forming large clades with ancestral geographical states of Dehong. Bayes factor tests support the statistically significant geographic diffusion link between Dehong and Myanmar. The estimated time to the most recent common ancestor of Myanmar URFs_BC (1999.2) was later than that of Dehong URFs_BC (1998.0), but earlier than that of Myanmar URFs_01BC (2004.3). Since 1998, HIV-1 recombination between subtypes B, C and CRF01_AE has been continuously occurring in China–Myanmar border region. These results suggest that HIV-1 subtypes B, C and CRF01_AE were most likely transmitted from Dehong to Myanmar, and predict that URFs_01BC should be also prevalent in Dehong, Yunnan.

Identifying the sister group to the bees: a molecular phylogeny of Aculeata with an emphasis on the superfamily Apoidea

Debevec, AH., Cardinal, S & Danforth, BN. Identifying the sister group to the bees: a molecular phylogeny of Aculeata with an emphasis on the superfamily Apoidea. —Zoologica Scripta, 41, 527–535.The hymenopteran superfamily Apoidea includes the bees (Anthophila) as well as four predatory wasp families (Heterogynaidae, Ampulicidae, Sphecidae and Crabronidae) collectively referred to as the “sphecoid” or “apoid” wasps. The most widely cited studies suggest that bees are sister to the wasp family Crabronidae, but alternative hypotheses have been proposed based on both morphological and molecular data. We combined DNA sequence data from previously published studies and newly generated data for four nuclear genes (28S, long‐wavelength rhodopsin, elongation factor‐1α and wingless) to identify the likely sister group to the bees. Analysis of our four‐gene data set by maximum likelihood and Bayesian methods indicates that bees most likely arise from within a paraphyletic Crabronidae. Possible sister groups to the bees include Philanthinae, Pemphredoninae or Philanthinae + Pemphredoninae. We used Bayesian methods to explore the robustness of our results. Bayes Factor tests strongly rejected the hypotheses of crabronid monophyly as well as placement of Heterogynaidae within Crabronidae. Our results were also stable to alternative rootings of the bees. These findings provide additional support for the hypothesis that bees arise from within Crabronidae, rather than being sister to Crabronidae, thus altering our understanding of bee ancestry and evolutionary history.

MrBayes 3.2: efficient Bayesian phylogenetic inference and model choice across a large model space.

Since its introduction in 2001, MrBayes has grown in popularity as a software package for Bayesian phylogenetic inference using Markov chain Monte Carlo (MCMC) methods. With this note, we announce the release of version 3.2, a major upgrade to the latest official release presented in 2003. The new version provides convergence diagnostics and allows multiple analyses to be run in parallel with convergence progress monitored on the fly. The introduction of new proposals and automatic optimization of tuning parameters has improved convergence for many problems. The new version also sports significantly faster likelihood calculations through streaming single-instruction-multiple-data extensions (SSE) and support of the BEAGLE library, allowing likelihood calculations to be delegated to graphics processing units (GPUs) on compatible hardware. Speedup factors range from around 2 with SSE code to more than 50 with BEAGLE for codon problems. Checkpointing across all models allows long runs to be completed even when an analysis is prematurely terminated. New models include relaxed clocks, dating, model averaging across time-reversible substitution models, and support for hard, negative, and partial (backbone) tree constraints. Inference of species trees from gene trees is supported by full incorporation of the Bayesian estimation of species trees (BEST) algorithms. Marginal model likelihoods for Bayes factor tests can be estimated accurately across the entire model space using the stepping stone method. The new version provides more output options than previously, including samples of ancestral states, site rates, site dN/dS rations, branch rates, and node dates. A wide range of statistics on tree parameters can also be output for visualization in FigTree and compatible software.

Bayes factor approaches for testing interval null hypotheses.

Psychological theories are statements of constraint. The role of hypothesis testing in psychology is to test whether specific theoretical constraints hold in data. Bayesian statistics is well suited to the task of finding supporting evidence for constraint, because it allows for comparing evidence for 2 hypotheses against each another. One issue in hypothesis testing is that constraints may hold only approximately rather than exactly, and the reason for small deviations may be trivial or uninteresting. In the large-sample limit, these uninteresting, small deviations lead to the rejection of a useful constraint. In this article, we develop several Bayes factor 1-sample tests for the assessment of approximate equality and ordinal constraints. In these tests, the null hypothesis covers a small interval of non-0 but negligible effect sizes around 0. These Bayes factors are alternatives to previously developed Bayes factors, which do not allow for interval null hypotheses, and may especially prove useful to researchers who use statistical equivalence testing. To facilitate adoption of these Bayes factor tests, we provide easy-to-use software.

Phylogeographic Analyses Reveal a Crucial Role of Xinjiang in HIV-1 CRF07_BC and HCV 3a Transmissions in Asia

BackgroundChina faces an increasing prevalence of two HIV-1 circulating recombinant forms (CRFs) 07_BC and 08_BC. Both CRFs_BC were previously demonstrated to originate in Yunnan and spread to Liaoning from Yunnan via injection drug use (IDU) in China. Supposing it is true, we are unable to answer why only CRF07_BC, rather than both CRFs_BC together, was transmitted to Xinjiang.Methodology/Principal FindingsWe investigated the phylogeography of CRF07_BC and CRF08_BC using multiple HIV-1 genomic regions with Bayesian phylogeography method. Phylogenetic reconstructions showed that all CRF07_BC sequences were divided into two clades, Yunnan and Xinjiang, and all strains from other regions of mainland China clustered within the Xinjiang clade. Significant geographic diffusion links of Xinjiang with other regions (including Liaoning, Beijing, Jiangsu and Guangdong) were supported by Bayes factor tests. The temporal dynamics analyses showed that CRF07_BC spread from Xinjiang to Liaoning in 1996.10, and to Jiangsu in 2000.9. The analyses of CRF08_BC not only confirmed the previous conclusion on temporal and spatial dynamics of CRF08_BC, but also indicated that the CRF08_BC strains from Guangdong and Shanghai originated from Yunnan. The analyses of HCV 3a showed that it was introduced into Xinjiang in the early 1980s, and spread from Xinjiang to Yunnan in 1990.10 and to Jiangsu in 1999.2, and further from Yunnan to Guangxi in 1995.3. The temporal and spatial dynamics of HCV 3a were similar to some extent to that of HIV-1 CRF07_BC and/or CRF08_BC, suggesting a possible association in migration patterns between HCV and HIV-1 through IDU. In addition, HCV 3a spread from Xinjiang to Pakistan, implying a drug trafficking route linking them.Conclusions/SignificanceXinjiang, as the most important transfer station for drug trafficking from Golden Crescent to other regions of China, plays a very crucial role in the transmission of viruses (e.g., HIV-1 and HCV) through IDU in Asia.

Reconstructing the initial global spread of a human influenza pandemicA Bayesian spatial-temporal model for the global spread of H1N1pdm

Here, we present an analysis of the H1N1pdm genetic data sampled over the initial stages in the epidemic. To infer phylodynamic spread in time and space we employ a recently developed Bayesian statistical inference framework (Lemey et al., in press). We model spatial diffusion as a continuous-time Markov chain process along time-measured genealogies. In this analysis, we consider 40 locations for which sequence data were available on 06-Aug-2009. The sampling time interval of the 242 sequences spans from 30-Mar-2009 to 12-Jul-2009. The Bayesian inference typically results in a posterior distribution of phylogenetic trees, each having an estimate of the epidemic locations at the ancestral nodes in the tree. We summarize these trees using the most representative clustering pattern and annotate these clusters with the most probable location states. We can visualize this information as tree that grows over time, seeding locations each time an ancestral node is inferred to exist at a different location. A Bayes factor test provides statistical support for epidemiological linkage throughout the evolutionary history. We demonstrate how our full probabilistic approach efficiently tracks an epidemic based on viral genetic data as it unfolds across the globe.

A phylogeny of anisopterous dragonflies (Insecta, Odonata) using mtRNA genes and mixed nucleotide/doublet models

The application of mixed nucleotide/doublet substitution models has recently received attention in RNA-based phylogenetics. Within a Bayesian approach, it was shown that mixed models outperformed analyses relying on simple nucleotide models. We analysed an mt RNA data set of dragonflies representing all major lineages of Anisoptera plus outgroups, using a mixed model in a Bayesian and parsimony (MP) approach. We used a published mt 16S rRNA secondary consensus structure model and inferred consensus models for the mt 12S rRNA and tRNA valine. Secondary structure information was used to set data partitions for paired and unpaired sites on which doublet or nucleotide models were applied, respectively. Several different doublet models are currently available of which we chose the most appropriate one by a Bayes factor test. The MP reconstructions relied on recoded data for paired sites in order to account for character covariance and an application of the ratchet strategy to find most parsimonious trees. Bayesian and parsimony reconstructions are partly differently resolved, indicating sensitivity of the reconstructions to model specification. Our analyses depict a tree in which the damselfly family Lestidae is sister group to a monophyletic clade Epiophlebia + Anisoptera, contradicting recent morphological and molecular work. In Bayesian analyses, we found a deep split between Libelluloidea and a clade ‘Aeshnoidea’ within Anisoptera largely congruent with Tillyard’s early ideas of anisopteran evolution, which had been based on evidently plesiomorphic character states. However, parsimony analysis did not support a clade ‘Aeshnoidea’, but instead, placed Gomphidae as sister taxon to Libelluloidea. Monophyly of Libelluloidea is only modestly supported, and many inter-family relationships within Libelluloidea do not receive substantial support in Bayesian and parsimony analyses. We checked whether high Bayesian node support was inflated owing to either: (i) wrong secondary consensus structures; (ii) under-sampling of the MCMC process, thereby missing other local maxima; or (iii) unrealistic prior assumptions on topologies or branch lengths. We found that different consensus structure models exert strong influence on the reconstruction, which demonstrates the importance of taxon-specific realistic secondary structure models in RNA phylogenetics.

A reassessment of apheloriine millipede phylogeny: additional taxa, Bayesian inference, and direct optimization (Polydesmida: Xystodesmidae)

Millipedes in the tribe Apheloriini occur throughout the eastern United States, predominately in the deciduous forests of the Appalachian Mountains. Herein we present a reassessment of apheloriine millipede phylogeny using mitochondrial DNA sequences and an additional 29 exemplar taxa (including 15 undescribed species and all of the species in the genus Brachoria, except one). In this study, first we check the results of the previous phylogeny of the tribe (Marek and Bond, 2006) with different alignment and phylogenetic techniques (direct optimization and maximum likelihood), and second reconstruct a new phylogeny evaluating it in the same way with Bayesian, maximum likelihood, and direct optimization. Using this updated and expanded phylogeny, we tested historical classifications with Bayes factor and Shimodaira-Hasegawa hypothesis testing, consistently finding very strong evidence against their implied phylogenetic hypotheses. Lastly, using the new phylogeny as a foundation, we make taxonomic modifications and provide an updated species list of Apheloriini (106 species/17 genera).

Modelling unobserved heterogeneity in contingent valuation of health risks

Human preferences for alternative levels of health risks can be heterogeneous. In this paper a flexible distribution approach to model health values elicited with the dichotomous choice contingent valuation method is considered. Rigid parametric structures cannot model sample heterogeneity while imposing strong assumptions on the error distribution. A mixture of normal distributions is considered which can approximate arbitrary well any empirical distributions as the number of mixtures increases. The model is applied to data on willingness to pay for reducing the individual risk of an episode of respiratory illness. The mixture distribution model is compared with the rigid probit model using a Bayes factor test. The results show that the mixture modelling approach improves performance while allowing for the consideration of alternative groups of individuals with different preferences for health risks.

A Bayesian Approach for Discriminating Among Alternative Inheritance Hypotheses in Plant Polyploids: The Allotetraploid Origin of Genus Borderea (Dioscoreaceae)

Polyploidy is a common phenomenon occurring in a vast number of land plants. Investigations of patterns of inheritance and the origins of plants (i.e., autopolyploidy vs. allopolyploidy) usually involve cytogenetic and molecular studies of chromosome pairing, chromosome mapping, and marker segregation analysis through experimental crosses and progeny tests. Such studies are missing for most wild species, for which artificial crosses are difficult, not feasible, or unaffordable. We report here a Bayesian method to discriminate between alternative inheritance patterns in the two extant, tetraploid species of the monocot genus Borderea (Dioscoreaceae), which does not involve progeny array tests. Our approach is based on the screening of a large number of SSR genotypes, which were obtained from successful amplifications of 17 microsatellite regions in individuals of both B. chouardii and B. pyrenaica. We tested for tetrasomic vs. disomic modes of inheritance, using the Bayes factor test. Assignment of genotypes under both alternatives could be unequivocally done for 14 and 11 of the 17 studied microsatellite regions in B. chouardii and B. pyrenaica, respectively, totaling 9502 analyzed genotypes. The comparison of posterior probabilities for the two competing hypotheses across the surveyed loci clearly favored a disomic inheritance pattern. Linkage tests indicated that none of the studied SSR loci were in linkage disequilibrium, thus representing independent samples of the Borderea genome. These results, along with previous allozyme data, support the allotetraploid origin of this paleoendemic genus and reveal the lowest reported chromosome base number for the family of the yams.

Single or double bounded contingent valuation? A Bayesian test

AbstractThis paper evaluates the performance of asymptotic approximations of the Bayes factor to appraise the relative likelihoods of the bivariate and the restricted double bounded models for contingent valuation. The performance of the Bayes factor test is studied by Monte Carlo simulation showing that it correctly chooses the bivariate model when appropriate, but tends to over predict the double bounded model when the correlation coefficient is not estimated accurately. However, the quadratic error in estimating willingness to pay is reduced if the model preferred by the test is chosen. In addition, we consider the effect of averaging the estimates of WTP from both models, weighting each model with its posterior probability. The results show that ‘model averaging’ across the competing hypothesis further reduces the squared error. The applications with two data sets on National Parks show that the test rejects the restricted double bounded hypotheses against the bivariate model.

Oh brother, where art thou? A Bayes factor test for recombination with uncertain heritage.

Current methods to identify recombination between subtypes of human immunodeficiency virus 1 (HIV-1) fall into a sequential testing trap, in which significance is assessed conditional on parental representative sequences and crossover points (COPs) that maximize the same test statistic. We overcame this shortfall by testing for recombination while inferring parental heritage and COPs using an extended Bayesian multiple change-point model. The model assumes that aligned molecular sequence data consist of an unknown number of contiguous segments that may support alternative topologies or varying evolutionary pressures. We allowed for heterogeneity in the substitution process and specifically tested for intersubtype recombination using Bayes factors. We also developed a new class of priors to assess significance across a wide range of support for recombination in the data. We applied our method to three putative gag gene recombinants. HIV-1 isolate RW024 decisively supported recombination with an inferred parental heritage of AD and a COP 95% Bayesian credible interval of (1,152, 1,178) using the HXB2 numbering scheme. HIV-1 isolate VI557 barely supported recombination. HIV-1 isolate RF decisively rejected recombination as expected, given that the sequence is commonly used as a reference sequence for subtype B. We employed scaled regeneration quantile plots to assess convergence and found this approach convenient to use even for our variable dimensional model parameter space.

Empirical Evaluation of Prior Beliefs about Frequencies: Methodology and a Case Study in Congenital Heart Disease

Abstract We consider the problem of critiquing prior beliefs concerning the distribution of a discrete random variable in the light of a sequentially obtained sample. A topical application concerns a probabilistic expert system for the diagnosis of congenital heart disease, which requires specification of a large number of conditional probabilities that are initially imprecisely estimated by a suitable “expert.” These prior beliefs may be formally updated as data become available, but it would seem essential to contrast the original expert assessments with the data obtained to quickly identify inappropriate subjective inputs. We consider both Bayes factor and significance testing techniques for such a prior/data comparison, both in nonsequential and sequential forms. The common basis as alternative standardizations of the logarithm of the predictive ordinate of the observed data is emphasised, and a Bayesian discrepancy statistic with a variety of interpretations provides a formal means of discounting the...

Algorithm. 45. Bayes factor test. An algorithm giving tables for a non-parametric two-sample test of the Bayesian discrimination power of an observed factor

Algorithm. 45. Bayes factor test. An algorithm giving tables for a non-parametric two-sample test of the Bayesian discrimination power of an observed factor