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At least 19 recordsLinked to original sources

PubMed2005

Models for estimating bayes factors with applications to phylogeny and tests of monophyly.

Bayes factors comparing two or more competing hypotheses are often estimated by constructing a Markov chain Monte Carlo (MCMC) sampler to explore the joint space of the hypotheses. To obtain efficient Bayes factor estimates, Carlin and Chib (1995, Journal of the Royal Statistical Society, Series B57, 473-484) suggest adjusting the prior odds of the competing hypotheses so that the posterior odds are approximately one, then estimating the Bayes factor by simple division. A byproduct is that one often produces several independent MCMC chains, only one of which is actually used for estimation. We extend this approach to incorporate output from multiple chains by proposing three statistical models. The first assumes independent sampler draws and models the hypothesis indicator function using logistic regression for various choices of the prior odds. The two more complex models relax the independence assumption by allowing for higher-lag dependence within the MCMC output. These models allow us to estimate the uncertainty in our Bayes factor calculation and to fully use several different MCMC chains even when the prior odds of the hypotheses vary from chain to chain. We apply these methods to calculate Bayes factors for tests of monophyly in two phylogenetic examples. The first example explores the relationship of an unknown pathogen to a set of known pathogens. Identification of the unknown's monophyletic relationship may affect antibiotic choice in a clinical setting. The second example focuses on HIV recombination detection. For potential clinical application, these types of analyses must be completed as efficiently as possible.

Bayes Theorem↗

PubMed2006

Impact of prior choice on local Bayes factors for cluster detection.

In this paper, we evaluate the usefulness of local Bayes factors as a tool for spatial cluster detection. In particular, we consider whether local Bayes factors from models with a fixed, but overly large number of clusters can consistently identify the evidence for clustering for a variety of prior specifications for the cluster locations. We also investigate the robustness of the local Bayes factor to the number of clusters included in the model. We explore the impacts of prior choice for cluster location and the number of clusters on posterior inference for disease rates. We conduct the comparison by analysing data on 1990 breast cancer incidence in Wisconsin.

Bayes Theorem↗

PubMedDate not supplied

Bayes factors for detection of quantitative trait loci.

A fundamental issue in quantitative trait locus (QTL) mapping is to determine the plausibility of the presence of a QTL at a given genome location. Bayesian analysis offers an attractive way of testing alternative models (here, QTL vs. no-QTL) via the Bayes factor. There have been several numerical approaches to computing the Bayes factor, mostly based on Markov Chain Monte Carlo (MCMC), but these strategies are subject to numerical or stability problems. We propose a simple and stable approach to calculating the Bayes factor between nested models. The procedure is based on a reparameterization of a variance component model in terms of intra-class correlation. The Bayes factor can then be easily calculated from the output of a MCMC scheme by averaging conditional densities at the null intra-class correlation. We studied the performance of the method using simulation. We applied this approach to QTL analysis in an outbred population. We also compared it with the Likelihood Ratio Test and we analyzed its stability. Simulation results were very similar to the simulated parameters. The posterior probability of the QTL model increases as the QTL effect does. The location of the QTL was also correctly obtained. The use of meta-analysis is suggested from the properties of the Bayes factor.

Algorithms↗

PubMed2004

Derivation of a Bayes factor to distinguish between linked or pleiotropic quantitative trait loci.

A simple procedure to calculate the Bayes factor between linked and pleiotropic QTL models is presented. The Bayes factor is calculated from the marginal prior and posterior densities of the locations of the QTL under a linkage and a pleiotropy model. The procedure is computed with a Gibbs sampler, and it can be easily applied to any model including the location of the QTL as a variable. The procedure was compared with a multivariate least-squares method. The proposed procedure showed better results in terms of power of detection of linkage when low information is available. As information increases, the performance of both procedures becomes similar. An example using data provided by an Iberian by Landrace pig intercross is presented. The results showed that three different QTL segregate in SSC6: a pleiotropic QTL affects myristic, palmitic, and eicosadienoic fatty acids; another pleiotropic QTL affects palmitoleic, stearic, and vaccenic fatty acids; and a third QTL affects the percentage of linoleic acid. In the example, the Bayes factor approach was more powerful than the multivariate least-squares approach.

Animals↗

PubMed1999

Toward evidence-based medical statistics. 2: The Bayes factor.

Bayesian inference is usually presented as a method for determining how scientific belief should be modified by data. Although Bayesian methodology has been one of the most active areas of statistical development in the past 20 years, medical researchers have been reluctant to embrace what they perceive as a subjective approach to data analysis. It is little understood that Bayesian methods have a data-based core, which can be used as a calculus of evidence. This core is the Bayes factor, which in its simplest form is also called a likelihood ratio. The minimum Bayes factor is objective and can be used in lieu of the P value as a measure of the evidential strength. Unlike P values, Bayes factors have a sound theoretical foundation and an interpretation that allows their use in both inference and decision making. Bayes factors show that P values greatly overstate the evidence against the null hypothesis. Most important, Bayes factors require the addition of background knowledge to be transformed into inferences--probabilities that a given conclusion is right or wrong. They make the distinction clear between experimental evidence and inferential conclusions while providing a framework in which to combine prior with current evidence.

Bayes Theorem↗

PubMed2004

A new mixture model approach to analyzing allelic-loss data using Bayes factors.

BACKGROUND: Allelic-loss studies record data on the loss of genetic material in tumor tissue relative to normal tissue at various loci along the genome. As the deletion of a tumor suppressor gene can lead to tumor development, one objective of these studies is to determine which, if any, chromosome arms harbor tumor suppressor genes. RESULTS: We propose a large class of mixture models for describing the data, and we suggest using Bayes factors to select a reasonable model from the class in order to classify the chromosome arms. Bayes factors are especially useful in the case of testing that the number of components in a mixture model is n0 versus n1. In these cases, frequentist test statistics based on the likelihood ratio statistic have unknown distributions and are therefore not applicable. Our simulation study shows that Bayes factors favor the right model most of the time when tumor suppressor genes are present. When no tumor suppressor genes are present and background allelic-loss varies, the Bayes factors are often inconclusive, although this results in a markedly reduced false-positive rate compared to that of standard frequentist approaches. Application of our methods to three data sets of esophageal adenocarcinomas yields interesting differences from those results previously published. CONCLUSIONS: Our results indicate that Bayes factors are useful for analyzing allelic-loss data.

Adenocarcinoma↗

PubMed2007

Bayes factor for testing between different structures of random genetic groups: a case study using weaning weight in Bruna dels Pirineus beef cattle.

The implementation of genetic groups in BLUP evaluations accounts for different expectations of breeding values in base animals. Notwithstanding, many feasible structures of genetic groups exist and there are no analytical tools described to compare them easily. In this sense, the recent development of a simple and stable procedure to calculate the Bayes factor between nested competing models allowed us to develop a new approach of that method focused on compared models with different structures of random genetic groups. The procedure is based on a reparameterization of the model in terms of intraclass correlation of genetic groups. The Bayes factor can be easily calculated from the output of a Markov chain Monte Carlo sampling by averaging conditional densities at the null intraclass correlation. It compares two nested models, a model with a given structure of genetic groups against a model without genetic groups. The calculation of the Bayes factor between different structures of genetic groups can be quickly and easily obtained from the Bayes factor between the nested models. We applied this approach to a weaning weight data set of the Bruna dels Pirineus beef cattle, comparing several structures of genetic groups, and the final results showed that the preferable structure was an only group for unknown dams and different groups for unknown sires for each year of calving.

Animals↗

PubMed2004

Phylogenetic relationships of typical antbirds (Thamnophilidae) and test of incongruence based on Bayes factors.

BACKGROUND: The typical antbirds (Thamnophilidae) form a monophyletic and diverse family of suboscine passerines that inhabit neotropical forests. However, the phylogenetic relationships within this assemblage are poorly understood. Herein, we present a hypothesis of the generic relationships of this group based on Bayesian inference analyses of two nuclear introns and the mitochondrial cytochrome b gene. The level of phylogenetic congruence between the individual genes has been investigated utilizing Bayes factors. We also explore how changes in the substitution models affected the observed incongruence between partitions of our data set. RESULTS: The phylogenetic analysis supports both novel relationships, as well as traditional groupings. Among the more interesting novel relationship suggested is that the Terenura antwrens, the wing-banded antbird (Myrmornis torquata), the spot-winged antshrike (Pygiptila stellaris) and the russet antshrike (Thamnistes anabatinus) are sisters to all other typical antbirds. The remaining genera fall into two major clades. The first includes antshrikes, antvireos and the Herpsilochmus antwrens, while the second clade consists of most antwren genera, the Myrmeciza antbirds, the "professional" ant-following antbirds, and allied species. Our results also support previously suggested polyphyly of Myrmotherula antwrens and Myrmeciza antbirds. The tests of phylogenetic incongruence, using Bayes factors, clearly suggests that allowing the gene partitions to have separate topology parameters clearly increased the model likelihood. However, changing a component of the nucleotide substitution model had much higher impact on the model likelihood. CONCLUSIONS: The phylogenetic results are in broad agreement with traditional classification of the typical antbirds, but some relationships are unexpected based on external morphology. In these cases their true affinities may have been obscured by convergent evolution and morphological adaptations to new habitats or food sources, and genera like Myrmeciza antbirds and the Myrmotherula antwrens obviously need taxonomic revisions. Although, Bayes factors seem promising for evaluating the relative contribution of components to an evolutionary model, the results suggests that even if strong evidence for a model allowing separate topology parameters is found, this might not mean strong evidence for separate gene phylogenies, as long as vital components of the substitution model are still missing.

Animals↗

PubMed2006

Computing Bayes factors using thermodynamic integration.

In the Bayesian paradigm, a common method for comparing two models is to compute the Bayes factor, defined as the ratio of their respective marginal likelihoods. In recent phylogenetic works, the numerical evaluation of marginal likelihoods has often been performed using the harmonic mean estimation procedure. In the present article, we propose to employ another method, based on an analogy with statistical physics, called thermodynamic integration. We describe the method, propose an implementation, and show on two analytical examples that this numerical method yields reliable estimates. In contrast, the harmonic mean estimator leads to a strong overestimation of the marginal likelihood, which is all the more pronounced as the model is higher dimensional. As a result, the harmonic mean estimator systematically favors more parameter-rich models, an artefact that might explain some recent puzzling observations, based on harmonic mean estimates, suggesting that Bayes factors tend to overscore complex models. Finally, we apply our method to the comparison of several alternative models of amino-acid replacement. We confirm our previous observations, indicating that modeling pattern heterogeneity across sites tends to yield better models than standard empirical matrices.

Amino Acid Sequence↗

PubMed2025

Navigating Sampling Bias in Discrete Phylogeographic Analysis: Assessing the Performance of an Adjusted Bayes Factor.

Bayesian phylogeographic inference is widely used in molecular epidemiological studies to reconstruct the dispersal history of pathogens. Discrete phylogeographic analysis treats geographic locations as discrete traits and infers lineage transition events among them, and is typically followed by a Bayes factor (BF) test to assess the statistical support. In the standard BF (BFstd) test, the relative abundance of the involved trait states is not considered, which can be problematic in the case of unbalanced sampling. Existing methods to correct sampling bias in discrete phylogeographic analyses using continuous-time Markov chain (CTMC) model, often require additional epidemiological information to balance the sampling effort among locations. As such data is not necessarily available, alternative approaches that rely solely on available genomic data are needed. In this perspective, we assess the performance of a modification of the BFstd, the adjusted Bayes factor (BFadj), which incorporates information on the relative abundance of samples by location when inferring support for transition events and root location inference without requiring additional data. Using a simulation framework, we assess the statistical performance of BFstd and BFadj under varying levels of sampling bias, estimating their type I and type II error rates. Our results show that BFadj complements the BFstd by reducing type I errors at the cost increasing type II errors for inferred transition events, while improving type I and type II errors in root location inference. Our findings provide guidelines for implementing the complementary BFadj to detect and mitigate sampling bias in discrete phylogeographic inference using CTMC modeling.

Bayes Theorem↗

PubMed1999

Criticism of a hierarchical model using Bayes factors.

This paper analyses a data file of heart transplant surgeries performed in the United States over a two-year period. A Poisson/gamma exchangeable model is used to learn about the underlying death rates for 94 hospitals. There are concerns about the suitability of this hierarchical model, including the need for a hierarchical structure, the existence of outliers, the choice of prior hyperparameters, the need for a covariate in the model, and the manner in which exchangeability was modelled. Each concern motivates the construction of alternative models and Bayes factors are used to compare the existing model with the alternative models. Graphical displays are used to check the sensitivity of the posterior analysis with respect to model perturbations and plots of Bayes factors are used to criticize these perturbations.

Bayes Theorem↗

PubMed2001

An unconditional exact test for the Hardy-Weinberg equilibrium law: sample-space ordering using the Bayes factor.

Much forensic inference based upon DNA evidence is made assuming that the Hardy-Weinberg equilibrium (HWE) is valid for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, each having advantages and limitations. The limitations become more obvious when testing for deviation within multiallelic DNA loci is attempted. Here we present an exact test for HWE in the biallelic case, based on the ratio of weighted likelihoods under the null and alternative hypotheses, the Bayes factor. This test does not depend on asymptotic results and minimizes a linear combination of type I and type II errors. By ordering the sample space using the Bayes factor, we also define a significance (evidence) index, P value, using the weighted likelihood under the null hypothesis. We compare it to the conditional exact test for the case of sample size n = 10. Using the idea under the method of chi(2) partition, the test is used sequentially to test equilibrium in the multiple allele case and then applied to two short tandem repeat loci, using a real Caucasian data bank, showing its usefulness.

Alleles↗

PubMed2006

Bayes factor for testing the genetic background of quantitative threshold traits.

The recent development of the Bayes factor methodology to test between nested competing models has allowed to evaluate the genetic component of continuous traits through a methodology based on the reparameterization of a variance component model in terms of intra-class correlation. In this study, we present a modification of that procedure to compare between threshold models that only differ in a bounded variable. An extra data-augmentation step is required to sample liability, an underlying continuous variable related with phenotypic records through an adequate number of thresholds. In this context, we describe a procedure to sample from a truncated multivariate normal distribution with non-null covariances between records, taking as starting point the Cholesky factorization and the inclusion of linear restrictions. The method was tested by computer simulations with satisfactory results.

Animals↗

PubMed2005

Bayes factor analysis for the genetic background of physiological and vitality variables of F2 Iberian x Meishan newborn piglets.

The Bayes factor (BF) procedure was applied to examine the additive genetic component of several physiological and vitality variables for newborn pigs. Nine variables were studied: heart rate, arterial oxygen saturation, rectal temperature (all at birth and 60 min later), birth weight, interval between birth and first teats contact, and interval between birth and first colostrum intake. The available numbers of data ranged from 288 (heart rate at 60 min) to 839 records (birth weight) from F(2) Iberian x Meishan newborn pigs. We compared a model with zero heritability (nonheritable) with the one where the additive genetic background was included. The BF was used to discriminate between both candidate models. Very strong evidence of genetic background was detected for heart rate 60 min after birth (BF = 48.90), and strong evidence was detected for rectal temperature at birth (BF = 13.82). Posterior modes (means) of heritabilities were 0.29 (0.32) and 0.40 (0.39), respectively. In addition, substantial evidence of absence of genetic background was detected for arterial oxygen saturation at birth.

Animals↗

PubMed2003

Bayesian approach to average bioequivalence using Bayes' factor.

In recent years, bioavailability studies for assessment of bioequivalence between two or more drug formulations have become very popular in drug development. However the current practice for the assessment of bioequivalence suffers from certain serious drawbacks. For example, sometimes these tests fail to control the consumer's risk. In this article a new methodology based on the application of Bayes' factor for solving the average bioequivalence problem is proposed. We compare our approach with the existing methods by using real data sets from the Food and Drug Administration (FDA). Results are further explored using simulation studies.

Bayes Theorem↗

PubMed1997

Predictive model selection for repeated measures random effects models using Bayes factors.

The random effects model fit to repeated measures data is an extremely common model and data structure in current biostatistical practice. Modern data analysis often involves the selection of models within broad classes of prespecified models, but for models beyond the generalized linear model, few model-selection tools have been actively studied. In a Bayesian analysis, Bayes factors are the natural tool to use to explore these classes of models. In this paper, we develop a predictive approach for specifying the priors of a repeated measures random effects model with emphasis on selecting the fixed effects. The advantage of the predictive approach is that a single predictive specification is used to specify priors for all models considered. The methodology is applied to a pediatric pain data analysis.

Bayes Theorem↗

PubMed2002

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.

Algorithms↗

PubMed2001

Bayes factor of model selection validates FLMP.

The fuzzy logical model of perception (FLMP; Massaro, 1998) has been extremely successful at describing performance across a wide range of ecological domains as well as for a broad spectrum of individuals. An important issue is whether this descriptive ability is theoretically informative or whether it simply reflects the model's ability to describe a wider range of possible outcomes. Previous tests and contrasts of this model with others have been adjudicated on the basis of both a root mean square deviation (RMSD) for goodness-of-fit and an observed RMSD relative to a benchmark RMSD if the model was indeed correct. We extend the model evaluation by another technique called Bayes factor (Kass & Raftery, 1995; Myung & Pitt, 1997). The FLMP maintains its significant descriptive advantage with this new criterion. In a series of simulations, the RMSD also accurately recovers the correct model under actual experimental conditions. When additional variability was added to the results, the models continued to be recoverable. In addition to its descriptive accuracy, RMSD should not be ignored in model testing because it can be justified theoretically and provides a direct and meaningful index of goodness-of-fit. We also make the case for the necessity of free parameters in model testing. Finally, using Newton's law of universal gravitation as an analogy, we argue that it might not be valid to expect a model's fit to be invariant across the whole range of possible parameter values for the model. We advocate that model selection should be analogous to perceptual judgment, which is characterized by the optimal use of multiple sources of information (e.g., the FLMP). Conclusions about models should be based on several selection criteria.

Bayes Theorem↗