Bayesian Hypothesis Testing Research Articles

Bayesian hierarchical hypothesis testing in large-scale genome-wide association analysis.

Variable selection and large-scale hypothesis testing are techniques commonly used to analyze high-dimensional genomic data. Despite recent advances in theory and methodology, variable selection and inference with highly collinear features remain challenging. For instance, collinearity poses a great challenge in genome-wide association studies involving millions of variants, many of which may be in high linkage disequilibrium. In such settings, collinearity can significantly reduce the power of variable selection methods to identify individual variants associated with an outcome. To address such challenges, we developed a Bayesian hierarchical hypothesis testing (BHHT)-a novel multiresolution testing procedure that offers high power with adequate error control and fine-mapping resolution. We demonstrate through simulations that the proposed methodology has a power-FDR performance that is competitive with (and in many scenarios better than) state-of-the-art methods. Finally, we demonstrate the feasibility of using BHHT with large sample size (n∼ 300,000) and ultra dimensional genotypes (∼ 15 million single-nucleotide polymorphisms or SNPs) by applying it to eight complex traits using data from the UK-Biobank. Our results show that the proposed methodology leads to many more discoveries than those obtained using traditional SNP-centered inference procedures. The article is accompanied by open-source software that implements the methods described in this study using algorithms that scale to biobank-size ultra-high-dimensional data.

Exploring Estimation Procedures for Reducing Dimensionality in Psychological Network Modeling.

To understand psychological data, it is crucial to examine the structure and dimensions of variables. In this study, we examined alternative estimation algorithms to the conventional GLASSO-based exploratory graph analysis (EGA) in network psychometric models to assess the dimensionality structure of the data. The study applied Bayesian conjugate or Jeffreys' priors to estimate the graphical structure and then used the Louvain community detection algorithm to partition and identify groups of nodes, which allowed the detection of the multi- and unidimensional factor structures. Monte Carlo simulations suggested that the two alternative Bayesian estimation algorithms had comparable or better performance when compared with the GLASSO-based EGA and conventional parallel analysis (PA). When estimating the multidimensional factor structure, the analytically based method (i.e., EGA.analytical) showed the best balance between accuracy and mean biased/absolute errors, with the highest accuracy tied with EGA but with the smallest errors. The sampling-based approach (EGA.sampling) yielded higher accuracy and smaller errors than PA; lower accuracy but also lower errors than EGA. Techniques from the two algorithms had more stable performance than EGA and PA across different data conditions. When estimating the unidimensional structure, the PA technique performed the best, followed closely by EGA, and then EGA.analytical and EGA.sampling. Furthermore, the study explored four full Bayesian techniques to assess dimensionality in network psychometrics. The results demonstrated superior performance when using Bayesian hypothesis testing or deriving posterior samples of graph structures under small sample sizes. The study recommends using the EGA.analytical technique as an alternative tool for assessing dimensionality and advocates for the usefulness of the EGA.sampling method as a valuable alternate technique. The findings also indicated encouraging results for extending the regularization-based network modeling EGA method to the Bayesian framework and discussed future directions in this line of work. The study illustrated the practical application of the techniques to two empirical examples in R.

A Bayesian hypothesis testing model for quality control of mass customized cabinet manufacturing process

The demand for customization of cabinets and homes has increased, and customized product components are cumbersome in size and time-consuming. In order to realize the mass production of customized cabinet furniture, research from the custom design, optimization of factory machine production process and quality inspection, as well as the flow of the way, is to realize the fundamental method of large-scale production of cabinet furniture. Based on modern intelligent information processing functions instead of manual ordering, order splitting, and unit parts for reasonable division of classification, optimize the topology of the production line, to achieve modern intelligent production of panels. However, in the production process, there is a lack of on-line inspection of some links, and the yield of the product is affected. This thesis establishes a Bayesian hypothesis testing model based on the topological model of the production line process, and through the actual production data, the defective nodes of the manufacturing process are retraced to achieve the purpose of optimizing the customized production.

A Bayesian flexible model for testing Granger causality

A new Bayesian hypothesis testing procedure for evaluating the Granger causality between two or more time series is proposed. The test is based on a flexible model for the joint evolution of multiple series, where a latent binary matrix indicates whether there is a Granger-causal relationship between such time series. The model is specified through a dependent Geometric stick-breaking process that generalizes the standard parametric Gaussian vector autoregression model, whereas the prior distribution of the latent matrix ensures a multiple testing correction. A Monte Carlo simulation study is provided for comparing the robustness of the proposed hypothesis test with state-of-the-art alternatives. The results show that this proposal performs better than competing approaches. Finally, the new test is applied to real economic data.

Bayesian non-parametric modeling by mixture of Kibble-Pólya tree to detect Low-Activity uranium contamination

Accurate detection of low-level radioactivity is critical for decommissioning projects in nuclear facilities, particularly in the design of radiation monitoring systems with a low false alarm rate. Utilizing a non-parametric Bayesian continuous probability distribution enables reliable mapping of potential contamination. Our method introduces a statistical test based on a Pólya tree prior, applied to radiation detection. The detection efficiency of this proposed Bayesian test is quantified using receiver-operating characteristic (ROC) curves and compared to a Bayesian test based on the Kibble bivariate gamma distribution developed for the same purpose. The results demonstrate that the new Bayesian test generally outperforms the previous method in terms of detection performance under very low signal-to-noise ratios, with improvements ranging from 3% to 28% against both stationary and non-stationary radiological backgrounds, respectively. This superiority is further reaffirmed through comparisons with alternative Bayesian and frequentist hypothesis tests, with gains estimated at 52% and 4%, respectively.

Comparing researchers' degree of dichotomous thinking using frequentist versus Bayesian null hypothesis testing.

A large amount of scientific literature in social and behavioural sciences bases their conclusions on one or more hypothesis tests. As such, it is important to obtain more knowledge about how researchers in social and behavioural sciences interpret quantities that result from hypothesis test metrics, such as p-values and Bayes factors. In the present study, we explored the relationship between obtained statistical evidence and the degree of belief or confidence that there is a positive effect in the population of interest. In particular, we were interested in the existence of a so-called cliff effect: A qualitative drop in the degree of belief that there is a positive effect around certain threshold values of statistical evidence (e.g., at p = 0.05). We compared this relationship for p-values to the relationship for corresponding degrees of evidence quantified through Bayes factors, and we examined whether this relationship was affected by two different modes of presentation (in one mode the functional form of the relationship across values was implicit to the participant, whereas in the other mode it was explicit). We found evidence for a higher proportion of cliff effects in p-value conditions than in BF conditions (N = 139), but we did not get a clear indication whether presentation mode had an effect on the proportion of cliff effects. PROTOCOL REGISTRATION: The stage 1 protocol for this Registered Report was accepted in principle on 2 June 2023. The protocol, as accepted by the journal, can be found at: https://doi.org/10.17605/OSF.IO/5CW6P .

Detecting mediation effects with the Bayes factor: Performance evaluation and tools for sample size determination.

Testing the presence of mediation effects is important in social science research. Recently, Bayesian hypothesis testing with Bayes factors (BFs) has become increasingly popular. However, the use of BFs for testing mediation effects is still under-studied, despite the growing literature on Bayesian mediation analysis. In this study, we systematically examine the performance of the BF for testing the presence versus absence of a mediation effect. Our results showed that the false and/or true positive rates of detecting mediation with the BF can be impacted by the prior specification, including the prior odds of the presence of each path (treatment-mediator path or mediator-outcome path) used in the design stage for data generation and in the analysis stage for calculating the BF of the mediation effect. Based on our examination, we developed an R function and a web application to determine sample sizes for testing mediation effects with the BF. Our study provides insights on the performance of the BF for testing mediation effects and adds to researchers' toolbox of sample size determination for mediation studies. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

The Calibrated Bayesian Hypothesis Test for Directional Hypotheses of the Odds Ratio in $$2\times 2$$ Contingency Tables

AbstractThe $$\chi ^{2}$$ χ 2 test is among the most widely used statistical hypothesis tests in medical research. Often, the statistical analysis deals with the test of row-column independence in a $$2\times 2$$ 2 × 2 contingency table, and the statistical parameter of interest is the odds ratio. A novel Bayesian analogue to the frequentist $$\chi ^{2}$$ χ 2 test is introduced. The test is based on a Dirichlet-multinomial model under a joint sampling scheme and works with balanced and unbalanced randomization. The test focusses on the quantity of interest in a variety of medical research, the odds ratio in a $$2\times 2$$ 2 × 2 contingency table. A computational implementation of the test is developed and R code is provided to apply the test. To meet the demands of regulatory agencies, a calibration of the Bayesian test is introduced which allows to calibrate the false-positive rate and power. The latter provides a Bayes-frequentist compromise which ensures control over the long-term error rates of the test. Illustrative examples using clinical trial data and simulations show how to use the test in practice. In contrast to existing Bayesian tests for $$2\times 2$$ 2 × 2 tables, calibration of the acceptance threshold for the hypothesis of interest allows to achieve a bound on the false-positive rate and minimum power for a prespecified odds ratio of interest. The novel Bayesian test provides an attractive choice for Bayesian biostatisticians who face the demands of regulatory agencies which usually require formal control over false-positive errors and power under the alternative. As such, it constitutes an easy-to-apply addition to the arsenal of already existing Bayesian tests.

Insights into Medieval Grape Cultivation in Al-Andalus: Morphometric, Domestication, and Multivariate Analysis of Vitis vinifera Seed Types

Understanding the origins and evolution of modern grapevine varieties in the Iberian Peninsula and western Europe necessitates an examination of the proportions of Vitis vinifera cultivars, their relationships with wild grapevine populations, and the utilization of seedless cultivars in al-Andalus. Employing morphometric studies, domestication indices, multivariate analysis, and Bayesian hypothesis testing, this study investigates several distinct seed types identified in materials from Roman and medieval deposits. These seeds exhibit a spectrum from highly domesticated to purely wild. Our findings reveal the predominance of Proles Occidentalis Negrul, and the presence of feral-like grapevines associated with Proles Euphratica. Additionally, we observe the continuous presence of wild grapevines related to Vitis sylvestris CC Gmelin throughout the studied period. Seeds exhibiting intermediate characteristics are documented, alongside the identification of “stenosperms”, suggesting anomalies in seed formation. Notably, the presence of Vitis vinifera raisins “stenospermocarpics” of the sultana type is suggested, potentially elucidating the absence of table grapes and raisins of the Proles Orientalis Negrul in the archaeological record, despite frequent mentions by medieval agronomy writers from al-Andalus.

Bayesian modeling of binomial experiments in sociology: problem analysis

The article is devoted to Bayesian modeling of simple comparative binomial experiments with binary data sets (of “hit” and “miss” format) in sociology and other social sciences. The main methodological foundations of application of Bayesian approach in statistics are briefly reviewed: the use of priors in analysis, features of Bayesian statistical inference, differences in frequency and Bayesian confidence intervals, features of hypothesis testing in Bayesian statistics. A Bayesian model of a comparative binomial experiment has been constructed. It supports comparison of independent and dependent samples of binomial variables, and also allows for differences in sizes of the compared samples. The capabilities of the model, as well as the principles of the Bayesian hypothesis testing, were demonstrated on test data using PyMC and ArviZ, contemporary free packages of the Bayesian modeling and analysis. The use of these tools allows implementing direct tensor operations with the obtained posterior distributions and provides the researcher with an effective way to calculate the effect size when comparing two binomial samples without having to resort to complicated forms of calculating this parameter. The possibilities and limitations of the Bayesian approach are shown in the context of comparative analysis of the results of binomial experiments in social sciences by estimating the probability of hypotheses via finding and comparing the area of intervals of posterior distributions

Efficient alternatives for Bayesian hypothesis tests in psychology.

Bayesian hypothesis testing procedures have gained increased acceptance in recent years. A key advantage that Bayesian tests have over classical testing procedures is their potential to quantify information in support of true null hypotheses. Ironically, default implementations of Bayesian tests prevent the accumulation of strong evidence in favor of true null hypotheses because associated default alternative hypotheses assign a high probability to data that are most consistent with a null effect. We propose the use of "nonlocal" alternative hypotheses to resolve this paradox. The resulting class of Bayesian hypothesis tests permits more rapid accumulation of evidence in favor of both true null hypotheses and alternative hypotheses that are compatible with standardized effect sizes of most interest in psychology. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Comparative analysis of glymphatic system alterations in multiple sclerosis and neuromyelitis optica spectrum disorder using MRI indices from diffusion tensor imaging.

The glymphatic system is a glial-based perivascular network that promotes brain metabolic waste clearance. Glymphatic system dysfunction has been observed in both multiple sclerosis (MS) and neuromyelitis optica spectrum disorder (NMOSD), indicating the role of neuroinflammation in the glymphatic system. However, little is known about how the two diseases differently affect the human glymphatic system. The present study aims to evaluate the diffusion MRI-based measures of the glymphatic system by contrasting MS and NMOSD. This prospective study included 63 patients with NMOSD (n = 21) and MS (n = 42) who underwent DTI. The fractional volume of extracellular-free water (FW) and an index of diffusion tensor imaging (DTI) along the perivascular space (DTI-ALPS) were used as indirect indicators of water diffusivity in the interstitial extracellular and perivenous spaces of white matter, respectively. Age and EDSS scores were adjusted. Using Bayesian hypothesis testing, we show that the present data substantially favor the null model of no differences between MS and NMOSD for the diffusion MRI-based measures of the glymphatic system. The inclusion Bayes factor (BF10) of model-averaged probabilities of the group (MS, NMOSD) was 0.280 for FW and 0.236 for the ALPS index. Together, these findings suggest that glymphatic alteration associated with MS and NMOSD might be similar and common as an eventual result, albeit the disease etiologies differ. Previous literature indicates important glymphatic system alteration in MS and NMOSD. We explore the difference between MS and NMOSD using diffusion MRI-based measures of the glymphatic system. We show support for the null hypothesis of no difference between MS and NMOSD. This suggests that glymphatic alteration associated with MS and NMOSD might be similar and common etiology.

Bayesian hypothesis tests with diffuse priors: Can we have our cake and eat it too?

SummaryWe propose a new class of priors for Bayesian hypothesis testing, which we name ‘cake priors’. These priors circumvent the Jeffreys–Lindley paradox (also called Bartlett's paradox) a problem associated with the use of diffuse priors leading to nonsensical statistical inferences. Cake priors allow the use of diffuse priors (having one's cake) while achieving theoretically justified inferences (eating it too). We demonstrate this methodology for Bayesian hypotheses tests for various common scenarios. The resulting Bayesian test statistic takes the form of a penalised likelihood ratio test statistic. Under typical regularity conditions, we show that Bayesian hypothesis tests based on cake priors are Chernoff consistent, that is, achieve zero type I and II error probabilities asymptotically. We also discuss Lindley's paradox and argue that the paradox occurs with small and vanishing probability as sample size increases.

Cognitive control adjustments are dependent on the level of conflict

The congruency sequence effect (CSE) is one of the most investigated effects in the cognitive control literature. The conflict monitoring theory suggests that the CSE is the result of adjustments in cognitive control based on perceived conflict. A recent paper by Zhang and colleagues, has investigated whether the manipulation of conflict level by changing distractor incompatibility in a flanker task affects the amount of adjustments in cognitive control. Their study produced mixed findings, somewhat supporting the original conflict monitoring theory, but also suggesting other explanations, such as the repetition expectancy account. We replicated the experimental design in a multisite online study (N = 347), with Hungarian, Italian, and Singaporean participants. Our results supported the prediction that changes in the level of conflict trigger conflict adaptation, revealing that increasing conflict levels induced stronger adaptive control. Bayesian hypothesis testing indicated a monotonic reduction in congruency effects as a function of previous conflict strength. This finding is in line with the extension of the traditional conflict monitoring theory, as well as other theories like affective signaling and expected value of control, implying that the relationship between conflict and interference effects is gradual, rather than a binary function.

The flaw of averages: Bayes factors as posterior means of the likelihood ratio.

As an alternative to the Frequentist p-value, the Bayes factor (or ratio of marginal likelihoods) has been regarded as one of the primary tools for Bayesian hypothesis testing. In recent years, several researchers have begun to re-analyze results from prominent medical journals, as well as from trials for FDA-approved drugs, to show that Bayes factors often give divergent conclusions from those of p-values. In this paper, we investigate the claim that Bayes factors are straightforward to interpret as directly quantifying the relative strength of evidence. In particular, we show that for nested hypotheses with consistent priors, the Bayes factor for the null over the alternative hypothesis is the posterior mean of the likelihood ratio. By re-analyzing 39 results previously published in the New England Journal of Medicine, we demonstrate how the posterior distribution of the likelihood ratio can be computed and visualized, providing useful information beyond the posterior mean alone.

The effect of a dermoscopy training programme on diagnostic accuracy and management decisions regarding pigmented skin lesions: a comparison between dermal therapists and general practitioners.

Dermoscopy is known to increase the diagnostic accuracy of pigmented skin lesions (PSLs) when used by trained professionals. The effect of dermoscopy training on the diagnostic ability of dermal therapists (DTs) has not been studied so far. This study aimed to investigate whether DTs, in comparison with general practitioners (GPs), benefited from a training programme including dermoscopy, in both their ability to differentiate between different forms of PSL and to assign the correct therapeutic strategy. In total, 24 DTs and 96 GPs attended a training programme on PSLs. Diagnostic skills as well as therapeutic strategy were assessed, prior to the training (pretest) and after the training (post-test) using clinical images alone, as well as after the addition of dermatoscopic images (integrated post-test). Bayesian hypothesis testing was used to determine statistical significance of differences between pretest, post-test and integrated post-test scores. Both the DTs and the GPs demonstrated benefit from the training: at the integrated post-test, the median proportion of correctly diagnosed PSLs was 73% (range 30-90) for GPs and 63% (range 27-80) for DTs. A statistically significant difference between pretest results and integrated test results was seen, with a Bayes factor > 100. At 12 percentage points higher, the GPs outperformed DTs in the accuracy of detecting PSLs. The study shows that a training programme focusing on PSLs while including dermoscopy positively impacts detection of PSLs by DTs and GPs. This training programme could form an integral part of the training of DTs in screening procedures, although additional research is needed.

Assessing background contamination of sample tubes used in human biomonitoring by non-targeted liquid chromatography–high resolution mass spectrometry

Controlling and minimising background contamination is crucial for maintaining a high quality of samples in human biomonitoring targeting organic chemicals. We assessed the contamination of three previous types and one newly introduced medical-grade type of sample tubes used for storing human body fluids at the German Environmental Specimen Bank. Aqueous extracts from these tubes were analysed by non-targeted liquid chromatography-high resolution mass spectrometry (LC-HRMS) before and after a dedicated cleaning procedure. After peak detection using MZmine, Bayesian hypothesis testing was used to group peaks into those originating either from instrumental and laboratory background contamination, or actual tube contaminants, based on if their peak height was reduced, increased or not affected by the cleaning procedure. For all four tube types 80–90% of the 2475 peaks (1549 in positive and 926 in negative mode) were assigned to laboratory/instrumental background, which we have to consider as potential sample tube contaminants. Among the tube contaminants, results suggest a considerable difference in the contaminant peak inventory and the absolute level of contamination among the different sample tube types. The cleaning procedure did not affect the largest fraction of peaks (50–70%). For the medical grade tubes, the removal of contaminants by the cleaning procedure was strongest compared to the previous tubes, but in all cases a small fraction increased in intensity after cleaning, probably due to a release of oligomers or additives. The identified laboratory background contaminants were mainly semi-volatile polymer additives such as phthalates and phosphate esters. A few compounds could be assigned solely as tube-specific contaminants, such as N,N-dibutylformamide and several constituents of the oligomeric light stabiliser Tinuvin-622. A cleaning procedure before use is an effective way to standardise the used sample tubes and minimises the background contamination, and therefore increases sample quality and therewith analytical results.

The Application of Artificial Intelligence to The Bayesian Model Algorithm for Combining Genome Data

The combination of bioinformatics and artificial intelligence (AI) has made significant progress in the current phase. AI technology, especially deep learning, has been widely used in biology, resulting in many innovations. Currently, AI plays a key role in genomics, proteomics, and drug discovery. Deep learning models are used to predict protein structures, discover potential drug compounds, interpret genomic sequences, analyze medical images, and make personalized medical recommendations. In addition, AI can also help accelerate the processing and interpretation of biological big data, helping biologists to understand complex problems in the life sciences more deeply. Compared to traditional genetic data analysis methods, AI combined with bioinformatics methods are often faster and more accurate, and are capable of processing large-scale, high-dimensional biological data, opening up unprecedented opportunities for life science research. In this paper, the whole genome data and biomedical imaging data are used from the perspective of Bayesian hypothesis testing. Genome-wide association analysis, led by large-scale multiple tests, is a very popular tool for identifying genetic variation points in new complex diseases. In genome-wide association analysis, tens of thousands of SNPS need to be tested simultaneously to find out some SNPS related to traits. These tests are related due to factors such as linkage imbalances in the genetic process, and the test questions are set against the background of high-dimensional data (p >=n).

The Rationale of Physical Education and Aesthetics in the Context of Big Data and the Value and Significance of its Implementation in Colleges and Universities

Abstract This paper first takes the deep learning theory as the basis of the thesis of sports and aesthetic education, constructs the flipped classroom teaching model of sports and aesthetic education based on the theory, and introduces the Bayesian estimation theory and the structural equation model to apply it to sports and aesthetic education. Secondly, the research object and method are selected for the flipped classroom teaching model of physical education and aesthetic education, and the teaching process of the flipped classroom experiment and the assumptions related to students’ learning satisfaction are given. Finally, the application value of physical education and aesthetics in colleges and universities is analyzed through the convergence of path coefficients in Bayesian structural equation modeling and hypothesis testing. When the number of iterations reaches 100*103 times, the H6-H11 path coefficient convergence value interval is [-22.5, 14.2]. The convergence interval fluctuates a lot and shows a more unstable trend than the H1-H5 path coefficient. Students learning satisfaction will have a direct effect on their aesthetic ability and improve their aesthetic awareness, and the path coefficients are 0.629 and 0.524, respectively. Deep learning theory based on sports and aesthetics in colleges and universities under the background of big data can improve students’ learning satisfaction and then promote the enhancement of students’ aesthetic ability and aesthetic awareness.

A Bayesian change-point detection approach to the economic evaluation of risky projects: an application to healthcare technology assessment

Abstract We propose a Bayesian hypothesis testing framework that allows for the assessment of evidence collected during a clinical trial about the cost-effectiveness of a healthcare technology. The model exploits a Bayesian updating rule that makes the link between the evidence collected in clinical research and the expected payoffs of adoption to the healthcare system. The framework takes into account the cost of decision errors in the payoff function, allowing the decision maker to compute the cost of taking a decision when evidence is far from the optimal decision triggers. We show, using a real-world cost-effectiveness study based on clinical trial evidence, how rules derived from a sequential adaptive design approach can lead to quicker decisions when compared to the value of information decision framework. Our application shows that a sequential approach has the potential to lead to quicker decisions, higher payoffs, and better health outcomes.