SEARCH · Search PubMed

Results for “Bayes factor”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3Linked to original sources

PubMed2004

Bayesian phylogenetic model selection using reversible jump Markov chain Monte Carlo.

A common problem in molecular phylogenetics is choosing a model of DNA substitution that does a good job of explaining the DNA sequence alignment without introducing superfluous parameters. A number of methods have been used to choose among a small set of candidate substitution models, such as the likelihood ratio test, the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and Bayes factors. Current implementations of any of these criteria suffer from the limitation that only a small set of models are examined, or that the test does not allow easy comparison of non-nested models. In this article, we expand the pool of candidate substitution models to include all possible time-reversible models. This set includes seven models that have already been described. We show how Bayes factors can be calculated for these models using reversible jump Markov chain Monte Carlo, and apply the method to 16 DNA sequence alignments. For each data set, we compare the model with the best Bayes factor to the best models chosen using AIC and BIC. We find that the best model under any of these criteria is not necessarily the most complicated one; models with an intermediate number of substitution types typically do best. Moreover, almost all of the models that are chosen as best do not constrain a transition rate to be the same as a transversion rate, suggesting that it is the transition/transversion rate bias that plays the largest role in determining which models are selected. Importantly, the reversible jump Markov chain Monte Carlo algorithm described here allows estimation of phylogeny (and other phylogenetic model parameters) to be performed while accounting for uncertainty in the model of DNA substitution.

Algorithms↗

PubMed2004

Comparing dynamic causal models.

This article describes the use of Bayes factors for comparing dynamic causal models (DCMs). DCMs are used to make inferences about effective connectivity from functional magnetic resonance imaging (fMRI) data. These inferences, however, are contingent upon assumptions about model structure, that is, the connectivity pattern between the regions included in the model. Given the current lack of detailed knowledge on anatomical connectivity in the human brain, there are often considerable degrees of freedom when defining the connectional structure of DCMs. In addition, many plausible scientific hypotheses may exist about which connections are changed by experimental manipulation, and a formal procedure for directly comparing these competing hypotheses is highly desirable. In this article, we show how Bayes factors can be used to guide choices about model structure, both concerning the intrinsic connectivity pattern and the contextual modulation of individual connections. The combined use of Bayes factors and DCM thus allows one to evaluate competing scientific theories about the architecture of large-scale neural networks and the neuronal interactions that mediate perception and cognition.

Attention↗

PubMed2006

Model weights and the foundations of multimodel inference.

Statistical thinking in wildlife biology and ecology has been profoundly influenced by the introduction of AIC (Akaike's information criterion) as a tool for model selection and as a basis for model averaging. In this paper, we advocate the Bayesian paradigm as a broader framework for multimodel inference, one in which model averaging and model selection are naturally linked, and in which the performance of AIC-based tools is naturally evaluated. Prior model weights implicitly associated with the use of AIC are seen to highly favor complex models: in some cases, all but the most highly parameterized models in the model set are virtually ignored a priori. We suggest the usefulness of the weighted BIC (Bayesian information criterion) as a computationally simple alternative to AIC, based on explicit selection of prior model probabilities rather than acceptance of default priors associated with AIC. We note, however, that both procedures are only approximate to the use of exact Bayes factors. We discuss and illustrate technical difficulties associated with Bayes factors, and suggest approaches to avoiding these difficulties in the context of model selection for a logistic regression. Our example highlights the predisposition of AIC weighting to favor complex models and suggests a need for caution in using the BIC for computing approximate posterior model weights.

Animals↗

PubMed2026

Skeletal Muscles Do Not Compete for Growth: Activating Additional Muscle Mass Does Not Compromise Changes in Muscle Size.

Kataoka, R, Yamada, Y, Hammert, WB, Sallberg, RW, Kang, A, Song, JS, Kassiano, W, Metcalf, EE, and Loenneke, JP. Skeletal muscles do not compete for growth: Activating additional muscle mass does not compromise changes in muscle size. J Strength Cond Res 40(9): 1043-1049, 2026-This study investigated whether the magnitude of muscle size and strength differed based on the amount of muscle recruited during training sessions. One hundred five untrained individuals were randomly assigned to 1 of 3 groups: low-load unilateral elbow flexion exercise (a) to failure (LL-Failure, n = 36), (b) to failure and low-load knee extension exercise to failure (LL-Failure + Legs, n = 33), or (c) a time-matched nonexercise control (CON, n = 36). Training groups completed 18 supervised sessions over 6 weeks (2 sets at 30% 1 repetition maximum [1RM] to failure). LL-Failure + Legs group performed 4 additional sets of knee extension exercise in each leg (20-30 RM). Muscle thickness on the anterior upper arm (60 and 70% sites) and elbow flexor 1RM strength of the trained arm were measured at pretesting and posttesting. Changes were compared using the ANCOVA function of Bayes Factors for Informative Hypotheses (prevalues as the covariate). Specific hypotheses were evaluated by comparing Bayes factors and the posterior probabilities between models. Six weeks of training led to increases in muscle size and strength. However, performing additional leg exercise did not attenuate the muscle growth in the anterior upper arm (0.19 cm) compared with performing only arm exercise to failure (0.18 cm). Changes in 1RM strength also did not differ between training groups (0.32 and 0.25 kg for LL-Failure and LL-Failure + Legs, respectively). Overall, there was no evidence for competition of adaptations in muscle size and strength under uncontrolled nutritional conditions. Whether greater training volume or limited nutrient intake induces a competition for resources warrants further investigation.

Humans↗

PubMed2004

Bayesian model comparison of nonlinear structural equation models with missing continuous and ordinal categorical data.

Missing data are very common in behavioural and psychological research. In this paper, we develop a Bayesian approach in the context of a general nonlinear structural equation model with missing continuous and ordinal categorical data. In the development, the missing data are treated as latent quantities, and provision for the incompleteness of the data is made by a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm. We show by means of a simulation study that the Bayesian estimates are accurate. A Bayesian model comparison procedure based on the Bayes factor and path sampling is proposed. The required observations from the posterior distribution for computing the Bayes factor are simulated by the hybrid algorithm in Bayesian estimation. Our simulation results indicate that the correct model is selected more frequently when the incomplete records are used in the analysis than when they are ignored. The methodology is further illustrated with a real data set from a study concerned with an AIDS preventative intervention for Filipina sex workers.

Algorithms↗

PubMed2004

Random regression test-day models with residuals following a Student's-t distribution.

First-lactation milk yield test-day records of Canadian Holsteins were analyzed by single-trait random regression test-day models that assumed normal or Student's-t distribution for residuals. Objectives were to test the performance of the robust statistical models that use heavy-tailed distributions for the residual effect. Models fitted were: Gaussian, Student's-t, and Student's-t with fixed number of degrees of freedom (equal to 5, 15, 30, 100 or 1000) for the t distribution. Bayesian methods with Gibbs sampling were used to make inferences about overall model plausibility through Bayes factors, posterior means for covariance components, estimated breeding values for regression coefficients, solutions for permanent environmental regressions, and residuals of the models. Bayes factors favored Student's-t model with the posterior mean of degrees of freedom equal to 2.4 over all other models, indicating very strong departure from normality. Number of outliers in Student's-t model was reduced by 35% in comparison with the Gaussian model. Differences in covariance components for regression coefficients between models were small, and rankings of animals based on additive genetic merit for the first two regression coefficients (total yield and persistency) were similar. Results from the Gaussian and Student's-t models with fixed degrees of freedom become more alike (smaller departures from normality for Student's-t models) with increasing number of degrees of freedom for the t-distributions. For any pair of Student's-t models, the one with the smaller number of degrees of freedom for the t-distribution was shown to be superior. Similarly, number of outliers increased with increasing degrees of freedom for the t distribution.

Animals↗

PubMed1998

Understanding and testing for heterogeneity across 2 x 2 tables: application to meta-analysis.

A question of interest in a meta-analysis is whether the studies considered are homogeneous. This paper addresses two forms of heterogeneity. Additive heterogeneity occurs when a particular treatment performs differently in different studies. Interactive heterogeneity occurs when the relative performance of two treatments varies with the study. This paper discusses the use and calculation of Bayes factors to test for both forms of heterogeneity. I consider three hierarchical models. One exhibits both forms of heterogeneity, a second exhibits only additive heterogeneity, and the third model has neither form of heterogeneity. I use a method based on bridge sampling for calculating the Bayes factors between the models. I consider two examples: in one both forms of heterogeneity seem to be present and in the other there seems to be additive heterogeneity but not interactive heterogeneity.

Antineoplastic Agents, Hormonal↗

PubMed1997

Bayesian analysis for a single 2 x 2 table.

The simple comparison of two binomial populations is frequently of interest in epidemiology when the domains are large. For small domains, however, there are no exact methods except Fisher's exact test. A basic problem, therefore, is to compare two populations by assessing the difference between the proportions of individuals who possess a characteristic in the first and second populations. When there is prior information, we take the proportions to have independent conjugate beta distributions with known parameters, thereby facilitating a Bayesian analysis. We consider Bayesian inference on functions of the proportions, and the three most common scalar measures used in epidemiology and health services research, namely relative risk, odds ratio and attributable risk. We develop the highest density regions (both exact and approximate) for relative risk, odds ratio and attributable risk. In addition, we consider the Bayes factor for testing whether the model with a common proportion holds rather than one with distinct proportions. Using data from the population-based Worcester Heart Attack Study, we apply our methodology to study gender differences in the therapeutic management of patients with acute myocardial infarction (AMI) by selected demographic and clinical characteristics. The Bayes factor, the approximate and exact intervals generally suggest that there are no substantial differences in the pharmacologic management of males and females hospitalized with AMI.

Adult↗

PubMed2000

Bayesian information criterion for censored survival models.

We investigate the Bayesian Information Criterion (BIC) for variable selection in models for censored survival data. Kass and Wasserman (1995, Journal of the American Statistical Association 90, 928-934) showed that BIC provides a close approximation to the Bayes factor when a unit-information prior on the parameter space is used. We propose a revision of the penalty term in BIC so that it is defined in terms of the number of uncensored events instead of the number of observations. For a simple censored data model, this revision results in a better approximation to the exact Bayes factor based on a conjugate unit-information prior. In the Cox proportional hazards regression model, we propose defining BIC in terms of the maximized partial likelihood. Using the number of deaths rather than the number of individuals in the BIC penalty term corresponds to a more realistic prior on the parameter space and is shown to improve predictive performance for assessing stroke risk in the Cardiovascular Health Study.

Aged↗

PubMed2026

A single session of high-definition transcranial direct current stimulation does not modulate effects of knee two-point discrimination training or sensorimotor function in healthy adults: Double-blind randomised controlled trial.

BACKGROUND: Benefits of sensory-training interventions on sensorimotor outcomes are inconsistent, and it is unclear whether transcranial direct current stimulation (tDCS) can enhance proprioception, which is fundamental to neuromuscular control. Existing evidence is dominated by upper-limb studies, so transferability to the knee is unclear. This study investigated whether a single session of anodal high-definition (HD)-tDCS, alone or combined with brief two-point discrimination (TPD) training, enhances knee sensorimotor function and performance in healthy adults. METHODS: In a double-blind randomised-controlled trial, 57 healthy participants received (1) 20-min, 1 mA anodal HD-tDCS over the knee primary somatosensory (S1) map or sham stimulation, and (2) 15-min knee TPD training or no training. Knee somatosensory, sensorimotor, and functional performance measures were assessed pre- and immediately post-intervention. Three-way mixed-design ANOVAs, equivalence testing (smallest effect size of interest η2 = 0.02), Bayes factors, and linear mixed-effects models quantified effects. RESULTS: HD-tDCS, TPD training, and their sequential combination had no effect on any outcome measure (p ≥ 0.05; η2 ≤ 0.015). Confidence intervals spanned equivalence bounds, and equivalence testing results were non-significant (p ≥ 0.05). Bayes factors (<0.33) showed moderate evidence for the null (no effect). Mixed-effects modelling attributed ≤8% of total variance to intervention fixed effects, with the remainder captured by participant-level random effects. CONCLUSION: A single 20-minute session of 1 mA HD-tDCS, with or without brief TPD training, does not acutely modify knee somatosensory, sensorimotor, or functional performance in healthy adults. Existing evidence at the hand may not translate to the lower limb. Future work should investigate higher-dose, multi-session, task-concurrent, or network-targeted strategies in clinical populations.

Humans↗

PubMed2005

Functional form and risk adjustment of hospital costs: Bayesian analysis of a Box-Cox random coefficients model.

While risk-adjusted outcomes are often used to compare the performance of hospitals and physicians, the most appropriate functional form for the risk adjustment process is not always obvious for continuous outcomes such as costs. Semi-log models are used most often to correct skewness in cost data, but there has been limited research to determine whether the log transformation is sufficient or whether another transformation is more appropriate. This study explores the most appropriate functional form for risk-adjusting the cost of coronary artery bypass graft (CABG) surgery. Data included patients undergoing CABG surgery at four hospitals in the midwest and were fit to a Box-Cox model with random coefficients (BCRC) using Markov chain Monte Carlo methods. Marginal likelihoods and Bayes factors were computed to perform model comparison of alternative model specifications. Rankings of hospital performance were created from the simulation output and the rankings produced by Bayesian estimates were compared to rankings produced by standard models fit using classical methods. Results suggest that, for these data, the most appropriate functional form is not logarithmic, but corresponds to a Box-Cox transformation of -1. Furthermore, Bayes factors overwhelmingly rejected the natural log transformation. However, the hospital ranking induced by the BCRC model was not different from the ranking produced by maximum likelihood estimates of either the linear or semi-log model.

Bayes Theorem↗

PubMed1998

Testing simultaneous hypotheses in pharmaceutical trials: a Bayesian approach.

The purpose of this paper is to compare the Bayes factor and the likelihood ratio test in a pharmaceutical trial where the two treatments are a new drug and a control (a positive control or a placebo). The goal is to jointly answer the questions (1) is the new drug or the control toxic? (2) Is the new drug more effective and safer than the control? We consider a bivariate model where each treatment is characterized by a target effect (a continuous primary response y) and by a side effect (a continuous supplementary response xi). Using a Bayesian approach, we account for the uncertainty resulting from prediction of the side effect, by making use of the physician's prior inputs about the target-toxicity relationship and the maximum tolerated target effects that are considered to be safe. Finally, we consider an example about a sleeplessness drug, and we show that the Bayes factor provides a more flexible and informative tool than the likelihood ratio test in simultaneous testing. Advantages are greater when the number of experimental subjects is small.

Anti-Anxiety Agents↗

PubMed2005

Partitioned Bayesian analyses, partition choice, and the phylogenetic relationships of scincid lizards.

Partitioned Bayesian analyses of approximately 2.2 kb of nucleotide sequence data (mtDNA) were used to elucidate phylogenetic relationships among 30 scincid lizard genera. Few partitioned Bayesian analyses exist in the literature, resulting in a lack of methods to determine the appropriate number of and identity of partitions. Thus, a criterion, based on the Bayes factor, for selecting among competing partitioning strategies is proposed and tested. Improvements in both mean -lnL and estimated posterior probabilities were observed when specific models and parameter estimates were assumed for partitions of the total data set. This result is expected given that the 95% credible intervals of model parameter estimates for numerous partitions do not overlap and it reveals that different data partitions may evolve quite differently. We further demonstrate that how one partitions the data (by gene, codon position, etc.) is shown to be a greater concern than simply the overall number of partitions. Using the criterion of the 2 ln Bayes factor > 10, the phylogenetic analysis employing the largest number of partitions was decisively better than all other strategies. Strategies that partitioned the ND1 gene by codon position performed better than other partition strategies, regardless of the overall number of partitions. Scincidae, Acontinae, Lygosominae, east Asian and North American "Eumeces" + Neoseps; North African Eumeces, Scincus, and Scincopus, and a large group primarily from sub-Saharan Africa, Madagascar, and neighboring islands are monophyletic. Feylinia, a limbless group of previously uncertain relationships, is nested within a "scincine" clade from sub-Saharan Africa. We reject the hypothesis that the nearly limbless dibamids are derived from within the Scincidae, but cannot reject the hypothesis that they represent the sister taxon to skinks. Amphiglossus, Chalcides, the acontines Acontias and Typhlosaurus, and Scincinae are paraphyletic. The globally widespread "Eumeces" is polyphyletic and we make necessary taxonomic changes.

Animals↗

PubMed2006

A comparison between multivariate Slash, Student's t and probit threshold models for analysis of clinical mastitis in first lactation cows.

Robust threshold models with multivariate Student's t or multivariate Slash link functions were employed to infer genetic parameters of clinical mastitis at different stages of lactation, with each cow defining a cluster of records. The robust fits were compared with that from a multivariate probit model via a pseudo-Bayes factor and an analysis of residuals. Clinical mastitis records on 36 178 first-lactation Norwegian Red cows from 5286 herds, daughters of 245 sires, were analysed. The opportunity for infection interval, going from 30 days pre-calving to 300 days postpartum, was divided into four periods: (i) -30 to 0 days pre-calving; (ii) 1-30 days; (iii) 31-120 days; and (iv) 121-300 days of lactation. Within each period, absence or presence of clinical mastitis was scored as 0 or 1 respectively. Markov chain Monte Carlo methods were used to draw samples from posterior distributions of interest. Pseudo-Bayes factors strongly favoured the multivariate Slash and Student's t models over the probit model. The posterior mean of the degrees of freedom parameter for the Slash model was 2.2, indicating heavy tails of the liability distribution. The posterior mean of the degrees of freedom for the Student's t model was 8.5, also pointing away from a normal liability for clinical mastitis. A residual was the observed phenotype (0 or 1) minus the posterior mean of the probability of mastitis. The Slash and Student's t models tended to have smaller residuals than the probit model in cows that contracted mastitis. Heritability of liability to clinical mastitis was 0.13-0.14 before calving, and ranged from 0.05 to 0.08 after calving in the robust models. Genetic correlations were between 0.50 and 0.73, suggesting that clinical mastitis resistance is not the same trait across periods, corroborating earlier findings with probit models.

Animals↗

PubMed2006

A Bayesian semi-parametric model for colorectal cancer incidences.

A Bayesian semi-parametric model is proposed to capture the interaction among demographic effects (age and gender), spatial effects (county) and temporal effects of colorectal cancer incidences simultaneously. In particular, an extension of multivariate conditionally autoregressive (CAR) processes to a partially informative Gaussian demographic spatial temporal CAR (DSTCAR) process for a spatial-temporal setting is proposed. The precision matrix of the Gaussian DSTCAR process is the Kronecker product of several components. The spatial component is modelled with a CAR prior. A pth order intrinsic autoregressive prior (IAR(p)) is implemented for the temporal component to estimate a smoothed and non-parametric temporal trend. The demographic component is modelled with a Wishart prior. Data analysis shows significant spatial correlation only exists in the age group of 50-59. Males and females in their 50s and 60s show fairly strong correlation. The hypothesis testing based on Bayes factor suggests that gender correlation cannot be ignored in this model.

Adult↗

PubMed2000

[Correlation of photoplankton and its environmental factors in Rushan Bay].

The relationship between photoplankton and its environmental factors in Rushan Bay was studied from June to September, 1995. The result shows that there existed a negative correlation between the number of photoplankton and the content of inorganic nutrients. The correlation coefficients for inorganic nitrogen and phosphorus were -0.67 and -0.80, respectively. The dissolved oxygen and chlorophyll-a were positively correlated to photoplankton, and their correlation coefficients were 0.92 and 0.85 respectively. Based on N/P analysis, the content of inorganic nitrogen was relatively short to the reproductive growth of photoplankton during experimental months, except for the last ten days of August.

China↗

PubMed2001

Bayesian estimation and test for factor analysis model with continuous and polytomous data in several populations.

The main purpose of this paper is to develop a Bayesian approach for the multisample factor analysis model with continuous and polytomous variables. Joint Bayesian estimates of the thresholds, the factor scores and the structural parameters subjected to some simple constraints across groups are obtained simultaneously. The Gibbs sampler is used to produce the joint Bayesian estimates. It is shown that the conditional distributions involved in the implementation are the familiar uniform, gamma, normal, univariate truncated normal and Wishart distributions. The Bayes factor is introduced to test hypotheses involving constraints among the structural parameters of the factor analysis models across groups. Two procedures for computing the test statistics are developed, one based on the Schwarz criterion (or Bayesian information criterion), while the other computes the posterior densities and likelihood ratios by means of draws from the appropriate conditional distributions via the Gibbs sampler. The empirical performance of the proposed Bayesian procedure and its sensitivity to prior distributions are illustrated by some simulation results and two real-life examples.

Bayes Theorem↗

PubMed2006

Random regression models for male and female fertility evaluation using longitudinal binary data.

A longitudinal Bayesian threshold analysis of insemination outcomes was carried out using 2 random regression models with 3 (Model 1) and 5 (Model 2) parameters to model the additive genetic values at the liability scale. All insemination events of first-parity Holstein cows were used. The outcome of an insemination event was treated as a binary response of either a success (1) or a failure (0). Thus, all breeding information for a cow, including all service sires, was included, thereby allowing for a joint evaluation of male and female fertility. An edited data set of 369,353 insemination records from 210,373 first-lactation cows was used. On the liability scale, both models included the systematic effects of herd-year, month of insemination, technician, and regressions on age of service sire and milk yield during the first 100 d of lactation. The random effects in the model were the 3 or 5 random regression coefficients specific to each cow, the permanent effect of the cow, and the service sire effect. Using Model 1, the estimated heritability of an insemination outcome decreased from 0.035 at d 50 to 0.032 at d 140 and then increased continuously with DIM. The genetic correlations for insemination success at different time points ranged from 0.83 to 0.99, and their magnitude decreased with an increase in the interval between inseminations. A similar trend was observed for heritability and genetic correlations using Model 2. However, the average estimate of heritability was much higher (0.058) than those obtained using Model 1 or a repeatability model. In addition, the estimated genetic correlations followed the same trend as Model 1, but were lower and with a higher rate of decrease when the interval between inseminations increased. The posterior mean of service sire variance was 0.01 for both models, and permanent environmental variance was 0.05 and 0.02 for Models 1 and 2, respectively. Model comparison based on the Bayes factor indicated that Model 1 was more plausible, given the data.

Animals↗