A novel multi-stage precision reliability assessment method for mechanical system by Bayesian fusion

Accounting for the failure sample size decreasing along with stages for large complex systems, a multi-stage Bayesian evaluation method of system reliability growth is proposed, which considers available information transfer across the stages. First, a reliability growth model for a stage of single subsystem is established by the non-homogeneous Poisson process. Its growth information is obtained by an improved means of equivalent transformation in this paper, and then prior expectations of parameters in this stage are gained by predicting failure rate of the post stage. Second, prior distribution of parameters is gained by the maximum entropy method and the moment equivalence method. Then, based on the prior distribution and a likelihood function of fewer failure samples, its posterior distribution and posterior Bayesian inference results can be achieved for the sake of evaluation of reliability growth of the whole system. Finally, a case study is illustrated that the information transfer across the stages of complex systems contributes to correct and economical evaluation of system reliability growth. The findings reveal that the proposed method is suitable for evaluation of reliability growth for large complex systems with small sample size, and has high value of popularization.

Local Bayesian fusion approaches aim to reduce high storage and computational costs of Bayesian fusion which is separated from fixed modeling assumptions. Using the small world formalism, we argue why this proceeding is conform with Bayesian theory. Then, we concentrate on the realization of local Bayesian fusion by focussing the fusion process solely on local regions that are task relevant with a high probability. The resulting local models correspond then to restricted versions of the original one. In a previous publication, we used bounds for the probability of misleading evidence to show the validity of the pre-evaluation of task specific knowledge and prior information which we perform to build local models. In this paper, we prove the validity of this proceeding using information theoretic arguments. For additional efficiency, local Bayesian fusion can be realized in a distributed manner. Here, several local Bayesian fusion tasks are evaluated and unified after the actual fusion process. For the practical realization of distributed local Bayesian fusion, software agents are predestinated. There is a natural analogy between the resulting agent based architecture and criminal investigations in real life. We show how this analogy can be used to improve the efficiency of distributed local Bayesian fusion additionally. Using a landscape model, we present an experimental study of distributed local Bayesian fusion in the field of reconnaissance, which highlights its high potential.

Sample size estimation is a fundamental element of a clinical trial, and a binomial experiment is the most common situation faced in clinical trial design. A Bayesian method to determine sample size is an alternative solution to a frequentist design, especially for studies conducted on small sample sizes. The Bayesian approach uses the available knowledge, which is translated into a prior distribution, instead of a point estimate, to perform the final inference. This procedure takes the uncertainty in data prediction entirely into account. When objective data, historical information, and literature data are not available, it may be indispensable to use expert opinion to derive the prior distribution by performing an elicitation process. Expert elicitation is the process of translating expert opinion into a prior probability distribution. We investigated the estimation of a binomial sample size providing a generalized version of the average length, coverage criteria, and worst outcome criterion. The original method was proposed by Joseph and is defined in a parametric framework based on a Beta-Binomial model. We propose a more flexible approach for binary data sample size estimation in this theoretical setting by considering parametric approaches (Beta priors) and semiparametric priors based on B-splines.

Efficient high-dimensional performance modeling of analog/RF circuits over multiple corners is an important-yet-challenging task. In this article, we propose a novel performance modeling approach for analog/RF circuits, referred to as correlated Bayesian model fusion (C-BMF). The key idea is to encode the correlation information for both model template and coefficient magnitude among different corners by using a unified prior distribution. Next, the prior distribution is combined with a few simulation samples via Bayesian inference to efficiently determine the unknown model coefficients. Two circuit examples designed in a commercial 40-nm CMOS process demonstrate that C-BMF achieves about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\times $ </tex-math></inline-formula> cost reduction over the traditional state-of-the-art modeling technique without surrendering any accuracy.

When Bayesian estimation is used to analyze Structural Equation Models (SEMs), prior distributions need to be specified for all parameters in the model. Many popular software programs offer default prior distributions, which is helpful for novel users and makes Bayesian SEM accessible for a broad audience. However, when the sample size is small, those prior distributions are not always suitable and can lead to untrustworthy results. In this tutorial, we provide a non-technical discussion of the risks associated with the use of default priors in small sample contexts. We discuss how default priors can unintentionally behave as highly informative priors when samples are small. Also, we demonstrate an online educational Shiny app, in which users can explore the impact of varying prior distributions and sample sizes on model results. We discuss how the Shiny app can be used in teaching; provide a reading list with literature on how to specify suitable prior distributions; and discuss guidelines on how to recognize (mis)behaving priors. It is our hope that this tutorial helps to spread awareness of the importance of specifying suitable priors when Bayesian SEM is used with small samples.

Bayesian piecewise growth models (PGMs) are useful tools to capture nonlinear trends comprised of distinct developmental phases. An important parameter in Bayesian PGMs is the knot location – the time at which transitions arise between phases. While researchers can specify knot locations when they are known a priori, a more flexible approach is to estimate knot locations based on data. The Bayesian estimation of knot locations is largely affected by prior distributions and missing data; however, little is known about the impact of these two factors in recovering knot placements. In the current article, we conducted a Monte Carlo simulation study to examine the impact of different prior specifications and the presence of missing data on the recovery of knot placements in Bayesian PGMs. Simulation results indicated that in small sample sizes, knot location estimates were dictated by prior distributions. Even with larger sample sizes, the estimates remained sensitive to informative and inaccurate prior specifications. The presence of missing data complicated the recovery linked to certain priors. While negative consequences, such as bias in parameter estimates, were caused by a larger amount of missing data, this could be alleviated by informative and accurate priors. These findings emphasize the critical role and intertwined influence of prior distributions and missing data in reaching conclusions about changepoints. We present an illustrative example using real data with missing values to demonstrate the Bayesian estimation of knot locations under realistic scenarios. Recommendations for applied researchers are discussed.

An innovative Bayesian sequential censored sampling inspection method and application to test design

The brain represents the state of the world around us based upon a stream of ambiguous sensory data. This requires the integration of different sources of information, including information received from different sense modalities, and information drawn from past experience. Bayesian theories of perception provide an approach to characterising how systematic differences in the probabilistic integration of information in the brain may underlie the differences that occur between individuals in their perceptual experience. The present thesis explores how perceptual, motor and social aspects of autism spectrum disorder (ASD) may emerge from variation in the neurocognitive processes described by Bayesian theories. A focus is on the predictive processing model of brain function, which links Bayesian theories of perception to neural mechanisms. The thesis includes empirical studies that examine perceptual, sensorimotor and cognitive aspects of ASD. ASD and nonclinical autistic traits are first examined in the context of body perception; concerning, specifically, how the brain represents the state of the limbs based on visual, tactile and proprioceptive information, and how this sensory information is integrated with prior expectations regarding the body. These processes are investigated using a multisensory perceptual illusion: the rubber hand illusion. ASD is associated with a largely typical perceptual experience of this illusion, indicating intact multisensory integration in the context of body representation. A reduced influence of the illusion on motor function, however, supports a difference in ASD in the integration of expectations for limb position (influenced by the illusion) with conflicting sensory (proprioceptive) signals. The integration of incoming information with existing expectations about the environment is also examined in the context of statistical learning. A computerised task is developed to assess the integration of iterative feedback with prior information as participants predict the location of a noisy set of visual markers. The hypothesis tested is that features of ASD are associated with a persistently higher weighting of incoming information in driving inference, at the expense of expectations developed from recent experience; in this more cognitive context, these data provide evidence against this hypothesis, suggesting that a more context-dependent atypicality in information processing in ASD is more likely than that initially hypothesised. The thesis also develops theoretical and philosophically-relevant treatments of how the symptoms of ASD may emerge from differences in brain function characterised within a Bayesian framework. This includes drawing on recent theoretical developments regarding the role of volatility processing and action in maintaining optimal inference on the environment. In addition, models of Bayesian inference in the brain can be extended to the social domain. For instance, the process of representing the mental states of other people (i.e., theory of mind) can be cast in terms of implicit inference on the external causes of sensory signals. In light of these expanded models of predictive processing, the differences in information processing hypothesised to occur in ASD have implications not just for perception, but also for motor behaviours, social cognition and social interaction. The overall view that emerges is that diverse aspects of ASD may be captured in terms of how incoming sensory signals are integrated, in a probabilistic manner, with the brain’s hierarchical and multimodal model of its environment. A promising direction for this field is in developing this idea in the context of action (i.e., active inference) and more recent models of how the brain estimates the optimal weighting of sensory information. This area of research has the potential to provide a nuanced perspective on the neurocognitive basis of ASD and the relationship between sensory mechanisms and autistic behaviours.

Resident Perspectives 56-5

Given the first n successive occurence times from a non-homogeneous Poisson process with a power-law intensity function, Bayes prediction intervals for future observations are derived. A Bayesian approach is compared, via Monte Carlo simulation, with a classical one, taking into account several factors, such as prior information, sample size and true values of process parameters. It is found that the Bayesian procedure generally attains sensibly better performances even when there is little prior information available.

We have completed a major Wide Field Upgrade (WFU) of the Hobby-Eberly Telescope (HET) and reentered scheduled queue science operations in mid-2016. This paper assesses the performance of the various mechanical systems which were upgraded, or added to HET, including the Telescope Structure, the star Tracker (aka, WFU Tracker), Prime Focus Instrument Package (PFIP), and VIRUS Support Structure (VSS). The upgrades were required to increase the field of view of HET, from 4 arc-minutes, to 22 arc-minutes, increasing the observed area of sky by 30 times the original FoV. In the process, the total weight of the system increased from 100 tons, to 153 tons, requiring a complete overhaul of most of the mechanical, servo, and control systems. The new 13-axis Tracker and control system was tested extensively prior to shipping and installation, and followed up with laser tracker measurements, which brought the tracking system to within 1 arc-minute RMS pointing, and followed up with on-sky derived mount-models, which has improved the pointing and guiding to within 12 arc-seconds RMS, and 0.1 arc-seconds, respectively. A completely new structural support system was implemented to house and connect a total of 156 VIRUS spectrographs, plus 4 new Low-Resolution Spectrographs (LRS2). The VIRUS units are arrayed in two large enclosures mounted to either side of the telescope. Each enclosure is approximately 1.3m deep x 6.7m wide x 6.2m tall and weighs 38 tons fully loaded. This structure is attached to HET in a way that allows it to be positioned by, but stand independent of, the HET during observation. As commissioning has transitioned to phased-science/engineering operations, and subsequently, to science operation, the tracking software and mechanical performance of the Tracker and VSS have been improved to meet specification. Performance data and lessons learned are provided.

Marine ecologists commonly use discriminant function analysis (DFA) to evaluate the similarity of distinct populations and to classify individuals of unknown origin to known populations. However, investigators using DFA must account for (1) the possibility of correct classification due to chance alone, and (2) the influence of prior probabilities of group membership on classification results. A search of the recent otolith chemistry literature showed that these two concerns are some- times ignored, so we used simulated data sets to explore the potential pitfalls of such oversights. We found that when estimating reclassification success for a training data set, small sample sizes or unbalanced sampling designs can produce remarkably high reclassification success rates by chance alone, especially when prior probabilities are estimated from sample size. When using a training data set to classify unknown individuals, maximum likelihood estimation of mixture proportions and group membership afforded up to 20% improvement over DFA with uninformative priors when groups contributed to the sample unequally. Given these results, we recommend the use of (1) ran- domization tests to estimate the probability that reclassification success is better than random, and (2) maximum likelihood estimation of mixture proportions in place of uninformative priors.

ObjectiveTo show how a simple Bayesian analysis method can be used to improve the evidence base in patient populations where recruitment and retention are challenging.MethodsA Bayesian conjugate analysis method was...

In testing, item response theory models are widely used in order to estimate item parameters and individual abilities. However, even unidimensional models require a considerable sample size so that all parameters can be estimated precisely. The introduction of empirical prior information about candidates and items might reduce the number of candidates needed for parameter estimation. Using data for IQ measurement, this work shows how empirical information about items can be used effectively for item calibration and in adaptive testing. First, we propose multivariate regression trees to predict the item parameters based on a set of covariates related to the item-solving process. Afterwards, we compare the item parameter estimation when tree-fitted values are included in the estimation or when they are ignored. Model estimation is fully Bayesian, and is conducted via Markov chain Monte Carlo methods. The results are two-fold: (a) in item calibration, it is shown that the introduction of prior information is effective with short test lengths and small sample sizes and (b) in adaptive testing, it is demonstrated that the use of the tree-fitted values instead of the estimated parameters leads to a moderate increase in the test length, but provides a considerable saving of resources.

BackgroundFamilial Alzheimer's disease research necessitates innovative methodologies to disentangle the intricate relationships between genetic factors and neuroimaging measures. Traditional frequentist approaches, often hampered by small sample sizes in this population and challenges in incorporating prior knowledge transparently, may limit the robustness of findings.MethodsWe analyzed neuroimaging data of preclinical PSNE1 single mutation carriers, utilizing the software JASP to test effects of carrier status on measures of basal forebrain functional connectivity using both frequentist and Bayesian approach. Bayesian Analysis of Covariance was first implemented to test the hypothesis of a basal forebrain functional connectivity reduction in mutation carriers compared to non‐mutation carriers. To get more precise information, Informative priors, derived from the existing literature on preclinical sporadic Alzheimer's disease, were integrated into post‐hoc Independent samples t‐tests. Student t‐tests were utilized for parameter estimation, using an Informed Cauchy specification of prior's location (‐0.7) and scale (0.707) allowing the derivation of posterior distributions.ResultsOur findings demonstrated that preclinical mutation carriers exhibited no significant alterations in basal forebrain functional connectivity compared to non‐carriers. However, the Bayesian analysis revealed distinct advantages over the traditional frequentist approach (anterior basal forebrain: t=‐1.126 (213), p= 0.131, Cohen's d = ‐0.165, 95 % CI for Cohen's d: [‐Inf., 0.077]; posterior basal forebrain: t=‐1.337 (213), p= 0.091, Cohen's d = ‐0.196, 95 % CI for Cohen's d: [‐Inf., 0.046]. Incorporating informative priors significantly improved the precision of parameter estimates, allowing us to reject our hypothesis with a relatively high degree of confidence, from anecdotal (anterior basal forebrain: BF10 = 1.167, δ = ‐ 0.319, 95 % CI: [‐0.599, ‐0.061]) to strong evidence (posterior basal forebrain: BF10 = 0.033, δ = ‐0.067, 95 % CI: [‐0.260, ‐0.003]).DiscussionOur results underscore the importance of adopting Bayesian frameworks in familial Alzheimer's disease research. The explicit integration of prior knowledge, as facilitated by Bayesian analysis, enhances the reliability of conclusions drawn from neuroimaging data. These methodological advantages are crucial in advancing the field and encouraging replication efforts.