On Two Measure-Theoretic Aspects of the Full Bayesian Significance Test for Precise Bayesian Hypothesis Testing †

The Full Bayesian Significance Test (FBST) has been proposed as a convenient method to replace frequentist p-values for testing a precise hypothesis. Although the FBST enjoys various appealing properties, the purpose of this paper is to investigate two aspects of the FBST which are sometimes observed as measure-theoretic inconsistencies of the procedure and have not been discussed rigorously in the literature. First, the FBST uses the posterior density as a reference for judging the Bayesian statistical evidence against a precise hypothesis. However, under absolutely continuous prior distributions, the posterior density is defined only up to Lebesgue null sets which renders the reference criterion arbitrary. Second, the FBST statistical evidence seems to have no valid prior probability. It is shown that the former aspect can be circumvented by fixing a version of the posterior density before using the FBST, and the latter aspect is based on its measure-theoretic premises. An illustrative example demonstrates the two aspects and their solution. Together, the results in this paper show that both of the two aspects which are sometimes observed as measure-theoretic inconsistencies of the FBST are not tenable. The FBST thus provides a measure-theoretically coherent Bayesian alternative for testing a precise hypothesis.

Updating Knowledge in The Estimation of The Genetics Parameters Multi-trait and Multi-Environment Bayesian Analysis in Rice (Oryza Sativa L.)

Among the multi-trait models used to jointly study several traits and environments, the Bayesian framework has been a preferable tool for using a more complex and biologically realistic model. In most cases, the non-informative prior distributions are adopted in studies using the Bayesian approach. Still, the Bayesian approach tends to present more accurate estimates when it uses informative prior distributions. The present study was developed to evaluate the efficiency and applicability of multi-trait multi-environment (MTME) models under a Bayesian framework utilizing a strategy for eliciting informative prior distribution using previous data from rice. The study involved data pertained to rice genotypes in three environments and five agricultural years (2010/2011 until 2014/2015) for the following traits: grain yield (GY), flowering in days (FLOR) and plant height (PH). Variance components and genetic and non-genetic parameters were estimated by the Bayesian method. In general, the informative prior distribution in Bayesian MTME models provided higher estimates of heritability and variance components, as well as minor lengths for the highest probability density interval (HPD), compared to their respective non-informative prior distribution analyses. The use of more informative prior distributions makes it possible to detect genetic correlations between traits, which cannot be achieved with the use of non-informative prior distributions. Therefore, this mechanism presented for updating knowledge to the elicitation of an informative prior distribution can be efficiently applied in rice genetic selection.

Bayesian Processing of Data on Bursts of Pressure Vessels

Two alternative Bayesian approaches are proposed for the prediction of fragmentation of pressure vessels triggered off by accidental explosions (bursts) of these containment structures. It is shown how to carry out this prediction with post-mortem data on fragment numbers counted after past explosion accidents. Results of the prediction are estimates of probabilities of individual fragment numbers. These estimates are expressed by means of Bayesian prior or posterior distributions. It is demonstrated how to elicit the prior distributions from relatively scarce post-mortem data on vessel fragmentations. Specifically, it is suggested to develop priors with two Bayesian models known as compound Poisson-gamma and multinomial-Dirichlet probability distributions. The available data is used to specify non-informative prior for Poisson parameter that is subsequently transformed into priors of individual fragment number probabilities. Alternatively, the data is applied to a specification of Dirichlet concentration parameters. The latter priors directly express epistemic uncertainty in the fragment number probabilities. Example calculations presented in the study demonstrate that the suggested non-informative prior distributions are responsive to updates with scarce data on vessel explosions. It is shown that priors specified with Poisson-gamma and multinomial-Dirichlet models differ tangibly; however, this difference decreases with increasing amount of new data. For the sake of brevity and concreteness, the study was limited to fire induced vessel bursts known as boiling liquid expanding vapour explosions (BLEVEs).

FMixFN: A Fast Big Data-Oriented Genomic Selection Model Based on an Iterative Conditional Expectation algorithm

Genomic selection is an approach to select elite breeding stock based on the use of dense genetic markers and that has led to the development of various models to derive a predictive equation. However, the current genomic selection software faces several issues such as low prediction accuracy, low computational efficiency, or an inability to handle large-scale sample data. We report the development of a genomic prediction model named FMixFN with four zero-mean normal distributions as the prior distributions to optimize the predictive ability and computing efficiency. The variance of the prior distributions in our model is precisely determined based on an F2 population, and genomic estimated breeding values (GEBV) can be obtained accurately and quickly in combination with an iterative conditional expectation algorithm. We demonstrated that FMixFN improves computational efficiency and predictive ability compared to other methods, such as GBLUP, SSgblup, MIX, BayesR, BayesA, and BayesB. Most importantly, FMixFN may handle large-scale sample data, and thus should be able to meet the needs of large breeding companies or combined breeding schedules. Our study developed a Bayes genomic selection model called FMixFN, which combines stable predictive ability and high computational efficiency, and is a big data-oriented genomic selection model that has potential in the future. The FMixFN method can be freely accessed at https://zenodo.org/record/5560913 (DOI: 10.5281/zenodo.5560913).

Remote expert elicitation to determine the prior probability distribution for Bayesian sample size determination in international randomized controlled trials: Bronchiolitis in Infants Placebo Versus Epinephrine and Dexamethasone (BIPED) Study

BackgroundBayesian methods are increasing in popularity in clinical research. The design of Bayesian clinical trials requires a prior distribution, which can be elicited from experts. Current elicitation approaches either use face-to-face sessions or expert surveys. In diseases with international differences in management, the elicitation exercise should recruit internationally, requiring expensive face-to-face sessions or surveys, which suffer low response rates. To address this, we developed a remote, real-time elicitation exercise to construct prior distributions. These elicited distributions were then used to determine the sample size of the Bronchiolitis in Infants with Placebo Versus Epinephrine and Dexamethasone (BIPED) Study, an international randomized controlled trial trial in the Pediatric Emergency Research Network (PERN). The BIPED study aims to determine whether the combination of epinephrine and dexamethasone, compared to placebo, is effective in reducing hospital admission for infants presenting with bronchiolitis to the emergency department.MethodsWe developed a web-based tool to support the elicitation of the probability of hospitalization for infants with bronchiolitis. Experts participated in online workshops to specify their individual prior distributions, which were aggregated using the equal-weighted linear pooling method. The Average Length Criterion determined the BIPED sample size.ResultsFifteen paediatric emergency medicine clinicians from Canada, USA, Australia and New Zealand participated in three workshops to provide their elicitied prior distributions. The elicited probability of admission for infants with bronchiolitis was slightly lower for those receiving epinephrine and dexamethasone compared to supportive care in the aggregate distribution. There were substantial differences in the individual beliefs but limited differences between North America and Australaisia. From this aggregate distribution, a sample size of 410 patients per arm results in an average 95% credible interval length of less than 9% and a relative predictive power of 90%.ConclusionRemote expert elicitation is a feasible, useful and practical tool to determine a prior distribution for international randomized controlled trials. Bayesian methods can then determine the trial sample size using these elicited prior distributions. The ease and low cost of remote expert elicitation means that this approach is suitable for future international randomized controlled trials.Trial Registration: clinicaltrials.gov Identifier: NCT03567473

Adversarial flow-based model for unsupervised fault diagnosis of rolling element bearings

Nowadays, numerous supervised deep learning models have been applied to bearing fault diagnosis. However, labelling the health states of the bearing vibration data is a time-consuming work and dependent on expert experience. In order to tackle this problem, a novel unsupervised bearing fault diagnosis method named adversarial flow-based model is explored in this paper. Flow-based model is a type of generative models that is proved to be better than other types in many aspects. This paper introduces the flow-based model into the field of machinery fault diagnosis, and designs an appropriate model architecture so as to train the model in unsupervised and adversarial ways. The proposed model contains an autoencoder (AE), a flow-based model, and a classifier. Firstly, the AE maps the vibration data from signal space to latent vector space. Then, the flow-based model aligns the distributions of the latent vectors of different bearing states with specific prior distributions. Finally, the classifier tries to discriminate the aligned latent vectors from the vectors sampled from the prior distributions. With the help of distinguishable prior distributions and the adversarial training mechanism between the classifier and the flow-based model together with the AE, the bearing data with the same health states are clustered into the same areas. The good clustering performance of the adversarial flow-based model is verified by a dataset with 10 health states from a bearing test rig.

A Review of Probabilistic Genotyping Systems: EuroForMix, DNAStatistX and STRmix™

Probabilistic genotyping has become widespread. EuroForMix and DNAStatistX are both based upon maximum likelihood estimation using a γ model, whereas STRmix™ is a Bayesian approach that specifies prior distributions on the unknown model parameters. A general overview is provided of the historical development of probabilistic genotyping. Some general principles of interpretation are described, including: the application to investigative vs. evaluative reporting; detection of contamination events; inter and intra laboratory studies; numbers of contributors; proposition setting and validation of software and its performance. This is followed by details of the evolution, utility, practice and adoption of the software discussed.