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).

The Hydrating Effects of Hypertonic, Isotonic and Hypotonic Sports Drinks and Waters on Central Hydration During Continuous Exercise: A Systematic Meta-Analysis and Perspective

Background Body-fluid loss during prolonged continuous exercise can impair cardiovascular function, harming performance. Delta percent plasma volume (dPV) represents the change in central and circulatory body-water volume and therefore hydration during exercise; however, the effect of carbohydrate–electrolyte drinks and water on the dPV response is unclear. Objective To determine by meta-analysis the effects of ingested hypertonic (> 300 mOsmol kg−1), isotonic (275–300 mOsmol kg−1) and hypotonic (< 275 mOsmol kg−1) drinks containing carbohydrate and electrolyte ([Na+] < 50 mmol L−1), and non-carbohydrate drinks/water (< 40 mOsmol kg−1) on dPV during continuous exercise. Methods A systematic review produced 28 qualifying studies and 68 drink treatment effects. Random-effects meta-analyses with repeated measures provided estimates of effects and probability of superiority (p+) during 0–180 min of exercise, adjusted for drink osmolality, ingestion rate, metabolic rate and a weakly informative Bayesian prior. Results Mean drink effects on dPV were: hypertonic − 7.4% [90% compatibility limits (CL) − 8.5, − 6.3], isotonic − 8.7% (90% CL − 10.1, − 7.4), hypotonic − 6.3% (90% CL − 7.4, − 5.3) and water − 7.5% (90% CL − 8.5, − 6.4). Posterior contrast estimates relative to the smallest important effect (dPV = 0.75%) were: hypertonic-isotonic 1.2% (90% CL − 0.1, 2.6; p+ = 0.74), hypotonic-isotonic 2.3% (90% CL 1.1, 3.5; p+ = 0.984), water-isotonic 1.3% (90% CL 0.0, 2.5; p+ = 0.76), hypotonic-hypertonic 1.1% (90% CL 0.1, 2.1; p+ = 0.71), hypertonic-water 0.1% (90% CL − 0.8, 1.0; p+ = 0.12) and hypotonic-water 1.1% (90% CL 0.1, 2.0; p+ = 0.72). Thus, hypotonic drinks were very likely superior to isotonic and likely superior to hypertonic and water. Metabolic rate, ingestion rate, carbohydrate characteristics and electrolyte concentration were generally substantial modifiers of dPV. Conclusion Hypotonic carbohydrate–electrolyte drinks ingested continuously during exercise provide the greatest benefit to hydration. Graphical abstract

Interindividual Variation Refuses to Go Away: A Bayesian Computer Model of Language Change in Communicative Networks

Treating the speech communities as homogeneous entities is not an accurate representation of reality, as it misses some of the complexities of linguistic interactions. Inter-individual variation and multiple types of biases are ubiquitous in speech communities, regardless of their size. This variation is often neglected due to the assumption that “majority rules,” and that the emerging language of the community will override any such biases by forcing the individuals to overcome their own biases, or risk having their use of language being treated as “idiosyncratic” or outright “pathological.” In this paper, we use computer simulations of Bayesian linguistic agents embedded in communicative networks to investigate how biased individuals, representing a minority of the population, interact with the unbiased majority, how a shared language emerges, and the dynamics of these biases across time. We tested different network sizes (from very small to very large) and types (random, scale-free, and small-world), along with different strengths and types of bias (modeled through the Bayesian prior distribution of the agents and the mechanism used for generating utterances: either sampling from the posterior distribution [“sampler”] or picking the value with the maximum probability [“MAP”]). The results show that, while the biased agents, even when being in the minority, do adapt their language by going against their a priori preferences, they are far from being swamped by the majority, and instead the emergent shared language of the whole community is influenced by their bias.

Astrobiologists are rational but not Bayesian

The search for biosignatures is likely to generate controversial results, with no single biosignature being clear proof of the presence of life. Bayesian statistical frameworks have been suggested as a tool for testing the effect that a new observation has on our belief in the presence of life on another planet. We test this approach here using the tentative discovery of phosphine on Venus as an example of a possible detection of a biosignature on an otherwise well-characterized planet. We report on a survey of astrobiologists' views on the likelihood of life on Enceladus, Europa, Mars, Titan and Venus before the announcement of the detection of phosphine in Venus' atmosphere (the Bayesian Prior Probability) and after the announcement (the Posterior Probability). Survey results show that respondents have a general view on the likelihood of life on any world, independent of the relative ranking of specific bodies, and that there is a distinct ‘fans of icy moons’ sub-community. The announcement of the potential presence of phosphine on Venus resulted in the community showing a small but significant increase in its confidence that there was life on Venus; nevertheless the community still considers Venus to be the least likely abode of life among the five targets considered, last after Titan. We derive a Bayesian formulation that explicitly includes both the uncertainty in the interpretation of the signal as well as uncertainty in whether phosphine on Venus could have been produced by life. We show that although the community has shown rational restraint about a highly unexpected and still tentative detection, their changing expectations do not fit a Bayesian model.

A partial graphical model with a structural prior on the direct links between predictors and responses

This paper is devoted to the estimation of a partial graphical model with a structural Bayesian penalization. Precisely, we are interested in the linear regression setting where the estimation is made through the direct links between potentially high-dimensional predictors and multiple responses, since it is known that Gaussian graphical models enable to exhibit direct links only, whereas coefficients in linear regressions contain both direct and indirect relations (due \textit {e.g.} to strong correlations among the variables). A smooth penalty reflecting a generalized Gaussian Bayesian prior on the covariates is added, either enforcing patterns (like row structures) in the direct links or regulating the joint influence of predictors. We give a theoretical guarantee for our method, taking the form of an upper bound on the estimation error arising with high probability, provided that the model is suitably regularized. Empirical studies on synthetic data and a real dataset are conducted.

How predictability affects habituation to novelty

One becomes accustomed to repeated exposures, even for a novel event. In the present study, we investigated how predictability affects habituation to novelty by applying a mathematical model of arousal that we previously developed, and through the use of psychophysiological experiments to test the model’s prediction. We formalized habituation to novelty as a decrement in Kullback-Leibler divergence from Bayesian prior to posterior (i.e., information gain) representing arousal evoked from a novel event through Bayesian update. The model predicted an interaction effect between initial uncertainty and initial prediction error (i.e., predictability) on habituation to novelty: the greater the initial uncertainty, the faster the decrease in information gain (i.e., the sooner habituation occurs). This prediction was supported by experimental results using subjective reports of surprise and event-related potential (P300) evoked by visual-auditory incongruity. Our findings suggest that in highly uncertain situations, repeated exposure to stimuli can enhance habituation to novel stimuli.

Spontaneous and evoked activity patterns diverge over development

The immature brain is highly spontaneously active. Over development this activity must be integrated with emerging patterns of stimulus-evoked activity, but little is known about how this occurs. Here we investigated this question by recording spontaneous and evoked neural activity in the larval zebrafish tectum from 4 to 15 days post fertilisation. Correlations within spontaneous and evoked activity epochs were comparable over development, and their neural assemblies properties refined in similar ways. However both the similarity between evoked and spontaneous assemblies, and also the geometric distance between spontaneous and evoked patterns, decreased over development. At all stages of development evoked activity was of higher dimension than spontaneous activity. Thus spontaneous and evoked activity do not converge over development in this system, and these results do not support the hypothesis that spontaneous activity evolves to form a Bayesian prior for evoked activity.

Prior Elicitation for Use in Clinical Trial Design and Analysis: A Literature Review

Bayesian inference is increasingly popular in clinical trial design and analysis. The subjective knowledge derived from an expert elicitation procedure may be useful to define a prior probability distribution when no or limited data is available. This work aims to investigate the state-of-the-art Bayesian prior elicitation methods with a focus on clinical trial research. A literature search on the Current Index to Statistics (CIS), PubMed, and Web of Science (WOS) databases, considering “prior elicitation” as a search string, was run on 1 November 2020. Summary statistics and trend of publications over time were reported. Finally, a Latent Dirichlet Allocation (LDA) model was developed to recognise latent topics in the pertinent papers retrieved. A total of 460 documents pertinent to the Bayesian prior elicitation were identified. Of these, 213 (45.4%) were published in the “Probability and Statistics” area. A total of 42 articles pertain to clinical trial and the majority of them (81%) reports parametric techniques as elicitation method. The last decade has seen an increased interest in prior elicitation and the gap between theory and application getting narrower and narrower. Given the promising flexibility of non-parametric approaches to the experts’ elicitation, more efforts are needed to ensure their diffusion also in applied settings.