Bayesian Hypothesis Testing Research Articles

Subclinically Anxious Adolescents Do Not Display Attention Biases When Processing Emotional Faces - An Eye-Tracking Study.

Recent research suggests that early difficulties with emotion regulation go along with an increased risk for developing psychiatric disorders, such as anxiety disorders for example. Adolescent anxiety is often referred to as a gateway disorder, due to its high predictability for lifelong persistent mental health problems. It has been shown that clinically anxious adolescents exhibit attention biases toward negative stimuli, yet whether these biases can also be found in the subclinical range of subclinically anxious adolescents is currently unclear. In this study, we set out to investigate this question by combining an emotional Go-Nogo task with eye-tracking techniques to assess attention biases for emotional faces in a subclinical sample of 23 subclinically anxious adolescent girls. This combined approach allowed us to look at both, behavioral and covert attention biases. Using both traditional and Bayesian hypothesis testing, we found no evidence for a bias toward negative, threat-relevant stimuli in the behavioral level or eye-tracking data. We believe that the results can help close a gap in the current literature by showing that like low-anxious adolescents, subclinically anxious adolescents do not exhibit attention biases when viewing de-contextualized emotional stimuli in the Overlap task. Together with previous research findings in clinically anxious participants which have reported high levels of attention biases, our results seem to suggest that attention biases do no increase linearly as a function of individual anxiety level. Future research is now needed to explore the contribution of additional factors, such as depression for example.

Uniformly most powerful Bayesian interval design for phase I dose-finding trials.

Interval designs have recently attracted much attention in phase I clinical trials because of their simplicity and desirable finite-sample performance. However, existing interval designs typically cannot converge to the optimal dose level since their intervals do not shrink to the target toxicity probability as the sample size increases. The uniformly most powerful Bayesian test (UMPBT) is an objective Bayesian hypothesis testing procedure, which results in the largest probability that the Bayes factor against null hypothesis exceeds the evidence threshold for all possible values of the data generating parameter. On the basis of the rejection region of UMPBT, we develop the uniformly most powerful Bayesian interval (UMPBI) design for phase I dose-finding trials. The proposed UMPBI design enjoys convergence properties because the induced interval indeed shrinks to the toxicity target and the recommended dose converges to the true maximum tolerated dose as the sample size increases. Moreover, it possesses an optimality property that the probability of incorrect decisions is minimized. We conduct simulation studies to demonstrate the competitive finite-sample operating characteristics of the UMPBI in comparison with other existing interval designs. As an illustration, we apply the UMPBI design to a panitumumab and standard gemcitabine-based chemoradiation combination trial.

Education Does Not Affect Cognitive Decline in Aging: A Bayesian Assessment of the Association Between Education and Change in Cognitive Performance.

Education is positively associated with level of cognitive function but the association between education and rate of cognitive decline remains unresolved, partly for methodological reasons. In this article, we address this issue using linear mixed models and Bayesian hypothesis testing, using data from the Betula cohort-sequential longitudinal study. Our results support the null hypothesis that education does not alter the rate of cognitive decline for visuospatial ability, semantic knowledge, and episodic memory. We propose that education is only a relevant variable for understanding cognitive performance in older age because of the association between performance and education that is formed in early development.

Studying human eating behaviour in the laboratory: Theoretical considerations and practical suggestions

Robinson and colleagues (2018) make important first steps in highlighting the shortcomings of laboratory studies of human eating behaviour, and providing some general suggestions to increase methodological and reporting quality. In this commentary, we present additional important theoretical considerations and practical suggestions. First, we discuss the role of situational cues in eating behaviour and highlight the implications for designing ecologically valid laboratory experiments. Next, we discuss food intake in laboratory settings in the context of the distinction between implicit and explicit measures used widely in social psychology, and provide practical recommendations to keep intake a relatively implicit measure. Finally, we recognise that designing optimal experiments requires significant resources so we present a practical procedure to recruit the smallest informative sample via Bayesian sequential hypothesis testing.

Human odor and forensics: Towards Bayesian suspect identification using GC × GC–MS characterization of hand odor

A new method for identifying people by their odor is proposed. In this approach, subjects are characterized by a GC × GC–MS chromatogram of a sample of their hand odor. The method is based on the definition of a distance between odor chromatograms and the application of Bayesian hypothesis testing. Using a calibration panel of subjects for whom several odor chromatograms are available, the densities of the distance between chromatograms of the same person, and between chromatograms of different persons are estimated. Given the distance between a reference and a query chromatogram, the Bayesian framework provides an estimate of the probability that the corresponding two odor samples come from the same person. We tested the method on a panel that is fully independent from the calibration panel, with promising results for forensic applications.

Bayesian alternatives for common null-hypothesis significance tests in psychiatry: a non-technical guide using JASP

BackgroundDespite its popularity as an inferential framework, classical null hypothesis significance testing (NHST) has several restrictions. Bayesian analysis can be used to complement NHST, however, this approach has been underutilized largely due to a dearth of accessible software options. JASP is a recently developed open-source statistical package that facilitates both Bayesian and NHST analysis using a graphical interface. This article provides an applied introduction to Bayesian inference with Bayes factors using JASP.MethodsWe use JASP to compare and contrast Bayesian alternatives for several common classical null hypothesis significance tests: correlations, frequency distributions, t-tests, ANCOVAs, and ANOVAs. These examples are also used to illustrate the strengths and limitations of both NHST and Bayesian hypothesis testing.ResultsA comparison of NHST and Bayesian inferential frameworks demonstrates that Bayes factors can complement p-values by providing additional information for hypothesis testing. Namely, Bayes factors can quantify relative evidence for both alternative and null hypotheses. Moreover, the magnitude of this evidence can be presented as an easy-to-interpret odds ratio.ConclusionsWhile Bayesian analysis is by no means a new method, this type of statistical inference has been largely inaccessible for most psychiatry researchers. JASP provides a straightforward means of performing reproducible Bayesian hypothesis tests using a graphical “point and click” environment that will be familiar to researchers conversant with other graphical statistical packages, such as SPSS.

On f-Divergences: Integral Representations, Local Behavior, and Inequalities.

This paper is focused on f-divergences, consisting of three main contributions. The first one introduces integral representations of a general f-divergence by means of the relative information spectrum. The second part provides a new approach for the derivation of f-divergence inequalities, and it exemplifies their utility in the setup of Bayesian binary hypothesis testing. The last part of this paper further studies the local behavior of f-divergences.

Bayesian reanalysis of null results reported in medicine: Strong yet variable evidence for the absence of treatment effects.

Efficient medical progress requires that we know when a treatment effect is absent. We considered all 207 Original Articles published in the 2015 volume of the New England Journal of Medicine and found that 45 (21.7%) reported a null result for at least one of the primary outcome measures. Unfortunately, standard statistical analyses are unable to quantify the degree to which these null results actually support the null hypothesis. Such quantification is possible, however, by conducting a Bayesian hypothesis test. Here we reanalyzed a subset of 43 null results from 36 articles using a default Bayesian test for contingency tables. This Bayesian reanalysis revealed that, on average, the reported null results provided strong evidence for the absence of an effect. However, the degree of this evidence is variable and cannot be reliably predicted from the p-value. For null results, sample size is a better (albeit imperfect) predictor for the strength of evidence in favor of the null hypothesis. Together, our findings suggest that (a) the reported null results generally correspond to strong evidence in favor of the null hypothesis; (b) a Bayesian hypothesis test can provide additional information to assist the interpretation of null results.

Bayesian clinical trial design using historical data that inform the treatment effect.

We consider the problem of Bayesian sample size determination for a clinical trial in the presence of historical data that inform the treatment effect. Our broadly applicable, simulation-based methodology provides a framework for calibrating the informativeness of a prior while simultaneously identifying the minimum sample size required for a new trial such that the overall design has appropriate power to detect a non-null treatment effect and reasonable type I error control. We develop a comprehensive strategy for eliciting null and alternative sampling prior distributions which are used to define Bayesian generalizations of the traditional notions of type I error control and power. Bayesian type I error control requires that a weighted-average type I error rate not exceed a prespecified threshold. We develop a procedure for generating an appropriately sized Bayesian hypothesis test using a simple partial-borrowing power prior which summarizes the fraction of information borrowed from the historical trial. We present results from simulation studies that demonstrate that a hypothesis test procedure based on this simple power prior is as efficient as those based on more complicated meta-analytic priors, such as normalized power priors or robust mixture priors, when all are held to precise type I error control requirements. We demonstrate our methodology using a real data set to design a follow-up clinical trial with time-to-event endpoint for an investigational treatment in high-risk melanoma.

Long-term bridge health monitoring and performance assessment based on a Bayesian approach

This study presents a damage detection approach for the long-term health monitoring of bridge structures. The Bayesian approach comprising both Bayesian regression and Bayesian hypothesis testing is proposed to detect the structural changes in an in-service seven-span steel plate girder bridge with Gerber system. Both temperature and vehicle weight effects are accounted in the analysis. The acceleration responses at four points of the bridge span are utilised in this investigation. The data covering three different time periods are used in the bridge health monitoring (BHM). Regression analyses showed that the autoregressive exogenous model considering both temperature and vehicle weight effects has the best performance. The Bayesian factor is found to be a sensitive damage indicator in the BHM. The Bayesian approach can provide updated information in the real-time monitoring of bridge structures. The information provided from the Bayesian approach is convenient and easy to handle compared to the traditional approaches. The applicability of this approach is also validated in a case study where artificially generated damage data is added to the observation data.

ABrox-A user-friendly Python module for approximate Bayesian computation with a focus on model comparison.

We give an overview of the basic principles of approximate Bayesian computation (ABC), a class of stochastic methods that enable flexible and likelihood-free model comparison and parameter estimation. Our new open-source software called ABrox is used to illustrate ABC for model comparison on two prominent statistical tests, the two-sample t-test and the Levene-Test. We further highlight the flexibility of ABC compared to classical Bayesian hypothesis testing by computing an approximate Bayes factor for two multinomial processing tree models. Last but not least, throughout the paper, we introduce ABrox using the accompanied graphical user interface.

On Estimating Non-standard Discrete Distributions Using Adaptive MCMC Methods

In this paper, we compare empirically the performance of some adaptive MCMC methods, that is, Adaptive Metropolis (AM) algorithm, Single Component Adaptive Metropolis (SCAM) algorithm and Delayed Rejection Adaptive Metropolis (DRAM) algorithm. The context is the simulation of non-standard discrete distributions. The performance criterion used is the precision of the frequency estimator. An application to a Bayesian hypothesis testing problem shows the superiority of the DRAM algorithm over the other considered sampling schemes.

A novel hepatitis B virus species discovered in capuchin monkeys sheds new light on the evolution of primate hepadnaviruses

All known hepatitis B virus (HBV) genotypes occur in humans and hominoid Old World non-human primates (NHPs). The divergent woolly monkey HBV (WMHBV) forms another orthohepadnavirus species. The evolutionary origins of HBV are unclear. We analysed sera from 124 Brazilian monkeys collected during 2012-2016 for hepadnaviruses using molecular and serological tools, and conducted evolutionary analyses. We identified a novel orthohepadnavirus species in capuchin monkeys (capuchin monkey hepatitis B virus [CMHBV]). We found CMHBV-specific antibodies in five animals and high CMHBV concentrations in one animal. Non-inflammatory, probably chronic infection was consistent with an intact preCore domain, low genetic variability, core deletions in deep sequencing, and no elevated liver enzymes. Cross-reactivity of antisera against surface antigens suggested antigenic relatedness of HBV, CMHBV, and WMHBV. Infection-determining CMHBV surface peptides bound to the human HBV receptor (human sodium taurocholate co-transporting polypeptide), but preferentially interacted with the capuchin monkey receptor homologue. CMHBV and WMHBV pseudotypes infected human hepatoma cells via the human sodium taurocholate co-transporting polypeptide, and were poorly neutralised by HBV vaccine-derived antibodies, suggesting that cross-species infections may be possible. Ancestral state reconstructions and sequence distance comparisons associated HBV with humans, whereas primate hepadnaviruses as a whole were projected to NHP ancestors. Co-phylogenetic analyses yielded evidence for co-speciation of hepadnaviruses and New World NHP. Bayesian hypothesis testing yielded strong support for an association of the HBV stem lineage with hominoid ancestors. Neither CMHBV nor WMHBV was likely the ancestor of the divergent human HBV genotypes F/H found in American natives. Our data suggest ancestral co-speciation of hepadnaviruses and NHP, and an Old World origin of the divergent HBV genotypes F/H. The identification of a novel primate hepadnavirus offers new perspectives for urgently needed animal models of chronic hepatitis B. The origins of HBV are unclear. The new orthohepadnavirus species from Brazilian capuchin monkeys resembled HBV in elicited infection patterns and could infect human liver cells using the same receptor as HBV. Evolutionary analyses suggested that primate HBV-related viruses might have emerged in African ancestors of New World monkeys millions of years ago. HBV was associated with hominoid primates, including humans and apes, suggesting evolutionary origins of HBV before the formation of modern humans. HBV genotypes found in American natives were divergent from those found in American monkeys, and likely introduced along prehistoric human migration. Our results elucidate the evolutionary origins and dispersal of primate HBV, identify a new orthohepadnavirus reservoir, and enable new perspectives for animal models of hepatitis B.

A Pragmatic Approach to Statistical Testing and Estimation (PASTE)

The p-value has dominated research in education and related fields and a statistically non-significant p-value is quite commonly interpreted as ‘confirming’ the null hypothesis (H0) of ‘equivalence’. This is unfortunate, because p-values are not fit for that purpose. This paper discusses three alternatives to the traditional p-value that unfortunately have remained underused but can provide evidence in favor of ‘equivalence’ relative to ‘non-equivalence’: two one-sided tests (TOST) equivalence testing, Bayesian hypothesis testing, and information criteria. TOST equivalence testing and p-values both rely on concepts of statistical significance testing and can both be done with confidence intervals, but treat H0 and the alternative hypothesis (H1) differently. Bayesian hypothesis testing and the Bayesian credible interval aka posterior interval provide Bayesian alternatives to traditional p-values, TOST equivalence testing, and confidence intervals. However, under conditions outlined in this paper, confidence intervals and posterior intervals may yield very similar interval estimates. Moreover, Bayesian hypothesis testing and information criteria provide fairly easy to use alternatives to statistical significance testing when multiple competing models can be compared. Based on these considerations, this paper outlines a pragmatic approach to statistical testing and estimation (PASTE) for research in education and related fields. In a nutshell, PASTE states that all of the alternatives to p-values discussed in this paper are better than p-values, that confidence intervals and posterior intervals may both provide useful interval estimates, and that Bayesian hypothesis testing and information criteria should be used when the comparison of multiple models is concerned.

Power transformer dissolved gas analysis through Bayesian networks and hypothesis testing

Accurate diagnosis of power transformers is critical for the reliable and cost-effective operation of the power grid. Presently there are a range of methods and analytical models for transformer fault diagnosis based on dissolved gas analysis. However, these methods give conflicting results and they are not able to generate uncertainty information associated with the diagnostics outcome. In this situation it is not always clear which model is the most accurate. This paper presents a novel multiclass probabilistic diagnosis framework for dissolved gas analysis based on Bayesian networks and hypothesis testing. Bayesian network models embed expert knowledge, learn patterns from data and infer the uncertainty associated with the diagnostics outcome, and hypothesis testing aids in the data selection process. The effectiveness of the proposed framework is validated using the IEC TC 10 dataset and is shown to have a maximum diagnosis accuracy of 88.9%.

Bayesian hypothesis testing detector for one bit diffusion LMS with blind missing samples

This paper proposes a sparse distributed estimation algorithm when missing data occurs in the measurements over adaptive networks. Two classes of measurement models are considered. First, the traditional linear regression model is investigated and second the sign of the linear regression model is studied. The latter is referred to as one-bit model. We utilize the diffusion LMS strategy, in the proposed methods, where a set of nodes cooperates with each other to estimate a vector model parameter. In both models, it is shown that replacing the missing sample with a simple estimate is equivalent to removing the missing sample from the distributed diffusion algorithm. We consider two cases, where in the first case the positions of missing samples are known (non-blind) and in the second case the positions of missing samples are unknown (blind). In the linear regression model scenario, a Bayesian hypothesis testing (BHT) is used for detection of the missing samples. In the one-bit model, in addition to BHT detector, a simple heuristic detector, based on mean square error (MSE), is also suggested. Simulation results show the effectiveness of the proposed detector-assisted distributed algorithms.

Objective Bayesian hypothesis testing and estimation for the intraclass model

ABSTRACTThe intraclass correlation coefficient (ICC) plays an important role in various fields of study as a coefficient of reliability. In this paper, we consider objective Bayesian analysis for the ICC in the context of normal linear regression model. We first derive two objective priors for the unknown parameters and show that both result in proper posterior distributions. Within a Bayesian decision-theoretic framework, we then propose an objective Bayesian solution to the problems of hypothesis testing and point estimation of the ICC based on a combined use of the intrinsic discrepancy loss function and objective priors. The proposed solution has an appealing invariance property under one-to-one reparametrisation of the quantity of interest. Simulation studies are conducted to investigate the performance the proposed solution. Finally, a real data application is provided for illustrative purposes.

No evidence for systematic white matter correlates of dyslexia and dyscalculia.

Learning disabilities such as dyslexia, dyscalculia and their comorbid manifestation are prevalent, affecting as much as 15% of the population. Structural neuroimaging studies have indicated that these disorders can be related to differences in white matter integrity, although findings remain disparate. In this study, we used a unique design composed of individuals with dyslexia, dyscalculia, both disorders and controls, to systematically explore differences in fractional anisotropy across groups using diffusion tensor imaging. Specifically, we focused on the corona radiata and the arcuate fasciculus, two tracts associated with reading and mathematics in a number of previous studies. Using Bayesian hypothesis testing, we show that the present data favor the null model of no differences between groups for these particular tracts—a finding that seems to go against the current view but might be representative of the disparities within this field of research. Together, these findings suggest that structural differences associated with dyslexia and dyscalculia might not be as reliable as previously thought, with potential ramifications in terms of remediation.

Evidential Model Validation under Epistemic Uncertainty

This paper proposes evidence theory based methods to both quantify the epistemic uncertainty and validate computational model. Three types of epistemic uncertainty concerning input model data, that is, sparse points, intervals, and probability distributions with uncertain parameters, are considered. Through the proposed methods, the given data will be described as corresponding probability distributions for uncertainty propagation in the computational model, thus, for the model validation. The proposed evidential model validation method is inspired by the idea of Bayesian hypothesis testing and Bayes factor, which compares the model predictions with the observed experimental data so as to assess the predictive capability of the model and help the decision making of model acceptance. Developed by the idea of Bayes factor, the frame of discernment of Dempster-Shafer evidence theory is constituted and the basic probability assignment (BPA) is determined. Because the proposed validation method is evidence based, the robustness of the result can be guaranteed, and the most evidence-supported hypothesis about the model testing will be favored by the BPA. The validity of proposed methods is illustrated through a numerical example.

Bayesian Hypothesis Testing of Two Normal Samples using Bootstrap Prior Technique

Bayesian Hypothesis Testing of Two Normal Samples using Bootstrap Prior Technique