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Motivated by the need for effectively summarising, modelling, and forecasting the distributional characteristics of intra-daily returns, as well as the recent work on forecasting histogram-valued time-series in the area of symbolic data analysis, we develop a time-series model for forecasting quantile-function-valued (QF-valued) daily summaries for intra-daily returns. We call this model the dynamic quantile function (DQF) model. Instead of a histogram, we propose to use a $g$-and-$h$ quantile function to summarise the distribution of intra-daily returns. We work with a Bayesian formulation of the DQF model in order to make statistical inference while accounting for parameter uncertainty; an efficient MCMC algorithm is developed for sampling-based posterior inference. Using ten international market indices and approximately 2,000 days of out-of-sample data from each market, the performance of the DQF model compares favourably, in terms of forecasting VaR of intra-daily returns, against the interval-valued and histogram-valued time-series models. Additionally, we demonstrate that the QF-valued forecasts can be used to forecast VaR measures at the daily timescale via a simple quantile regression model on daily returns (QR-DQF). In certain markets, the resulting QR-DQF model is able to provide competitive VaR forecasts for daily returns., Comment: MATLAB code: https://github.com/wilson-ye-chen/aqua

Much research on advice taking examines how people revise point estimates given input from others. This work has established that people often egocentrically discount advice. If they were to place more weight on advice, their point estimates would be more accurate. Yet the focus on point estimates and accuracy has resulted in a narrow conception of what it means to heed advice. We distinguish between revisions of point estimates and revisions of attendant probability distributions. Point estimates represent a single best guess; distributions represent the probabilities that people assign to all possible answers. A more complete picture of advice taking is provided by considering revisions of distributions, which reflect changes in both confidence and best guesses. We capture this using a new measure of advice utilization: the influence of advice. We observe that, when input from a high-quality advisor largely agrees with a person’s initial opinion, it engenders little change in one’s point estimate and, hence, little change in accuracy yet significantly increases confidence. This pattern suggests more advice taking than generally suspected. However, it is not necessarily beneficial. Because people are typically overconfident to begin with, receiving advice that agrees with their initial opinion can exacerbate overconfidence. In several experiments, we manipulate advisor quality and measure the extent to which advice agrees with a person’s initial opinion. The results allow us to pinpoint circumstances in which heeding advice is beneficial, improving accuracy or reducing overconfidence, as well as circumstances in which it is harmful, hurting accuracy or exacerbating overconfidence. This paper was accepted by Yuval Rottenstreich, judgment and decision making.

This article presents a framework to determine driving style and design a driver steering model considering driver characteristics. First, principal component analysis (PCA) and K-means clustering are utilized to classify 30 participants into cautious, moderate, and aggressive drivers. Subsequently, a generic steering model is established based on the model predictive control method. Thereafter, the maximum lateral acceleration is extracted as a crucial indicator to represent driver characteristics, and it is calibrated through probabilistic models using the dataset, which consists of the classified drivers. Besides, point estimation model and interval estimation model are leveraged to determine driving style and adjust constraints in the stochastic programming-based steering model. Finally, simulation experiments present the variations of actual output trajectories between the aggressive drivers and the cautious drivers.

Rail surface defect inspection based on machine vision faces challenges against the complex background with interference and severe data imbalance. To meet these challenges, we regard defect detection as a key-point estimation problem and present the attention neural network for rail surface defect detection via CASIoU-guided center-point estimation (CCEANN). CCEANN contains two crucial components. One is the stacked attention Hourglass backbone via cross-stage fusion of multi-scale features (CSFA-Hourglass), in which the convolutional block attention module with variable receptive fields (VRF-CBAM) is introduced, and a two-stage Hourglass structure balancing the network depth and feature fusion plays a key role. Furthermore, the CASIoU-guided center-point estimation head module (CASIoU-CEHM) integrating the delicate coordinate compensation mechanism regresses detection boxes flexibly to adapt to defects' large-scale variation, in which the proposed CASIoU loss, a loss regressing the consistency of Intersection-over-Union (IoU), central-point distance, area ratio, and scale ratio between the targeted defect and the predicted defect, achieves higher regression accuracy than state-of-the-art IoU-based losses. The experiments demonstrate that CCEANN outperforms competitive deep learning-based methods in four surface defect datasets.

Purpose Mokken scale analysis (MSA) is an attractive scaling procedure for ordinal data. MSA is frequently used in health-related quality of life research. Two of MSA's prime features are the scalability coefficients and the automated item selection procedure (AISP). The AISP partitions a (large) set of items into scales based on the observed item scores; the resulting scales can be used as measurement instruments. There exist two issues in MSA: First, point estimates, standard errors, and test statistics for scalability coefficients are inappropriate for clustered item scores, which are omnipresent in quality of life research data. Second, the AISP insufficiently takes sampling fluctuation of Mokken’s scalability coefficients into account. Methods We solved both issues by providing point estimates and standard errors for the scalability coefficients for clustered data and by implementing a Wald-based significance test in the AISP algorithm, resulting in a test-guided AISP (T-AISP), that is available for both nonclustered and clustered test scores. Results We integrated the T-AISP into a two-step, test-guided MSA for scale construction, to guide the analysis for nonclustered and clustered data. The first step is performing a T-AISP and select the final scale( s ). For clustered data, within-group dependency is investigated on the final scale(s). In the second step, the strength of the scale(s) is determined and further analyses are performed. The procedure was demonstrated on clustered item scores obtained from administering a questionnaire on quality of life in schools to 639 students nested in 30 classrooms. Conclusions We developed a two-step, test-guided MSA for scale construction that takes into account sample fluctuation of all scalability coefficients and that can be applied to item scores obtained by a nonclustered or clustered sampling design.

Phase II/III clinical trials are efficient two-stage designs that test multiple experimental treatments. In stage 1, patients are allocated to the control and all experimental treatments, with the data collected from them used to select experimental treatments to continue to stage 2. Patients recruited in stage 2 are allocated to the selected treatments and the control. Combined data of stage 1 and stage 2 are used for a confirmatory phase III analysis. Appropriate analysis needs to adjust for selection bias of the stage 1 data. Point estimators exist for normally distributed outcome data. Extending these estimators to time to event data is not straightforward because treatment selection is based on correlated treatment effects and stage 1 patients who do not get events in stage 1 are followed-up in stage 2. We have derived an approximately uniformly minimum variance conditional unbiased estimator (UMVCUE) and compared its biases and mean squared errors to existing bias adjusted estimators. In simulations, one existing bias adjusted estimator has similar properties as the practically unbiased UMVCUE while the others can have noticeable biases but they are less variable than the UMVCUE. For confirmatory phase II/III clinical trials where unbiased estimators are desired, we recommend the UMVCUE or the existing estimator with which it has similar properties.

The degree of uncertainty associated with the value of a company plays a relevant role in valuation analysis. We propose an original and robust methodology for company market valuation, which replaces the traditional point estimate of the conventional Discounted Cash Flow model with a probability distribution of fair values that convey information about both the expected value of the company and its intrinsic uncertainty. Our methodology depends on two main ingredients: an econometric model for company revenues and a set of firm-specific balance sheet relations that are estimated using historical data. We explore the effectiveness and scope of our methodology through a series of statistical exercises on publicly traded U.S. companies. At the firm level, we show that the fair value distribution derived with our methodology constitutes a reliable predictor of the company’s future abnormal returns. At the market level, we show that a long-short valuation (LSV) factor, built using buy-sell recommendations based on the fair value distribution, contains information not accessible through the traditional market factors. The LSV factor significantly increases the explanatory and the predictive power of factor models estimated on portfolios and individual stock returns.

When designing a clinical trial, one key aspect of the design is the sample size calculation. The sample size calculation tends to rely on a target or expected difference. The expected difference can be based on the observed data from previous studies, which results in bias. It has been reported that large treatment effects observed in trials are often not replicated in subsequent trials. If these values are used to design subsequent studies, the sample sizes may be biased which results in an unethical study. Regression to the mean (RTM) is one explanation for this. If only health technologies which meet a particular continuation criterion (such as p

In this paper, the interest is in estimating the Weibull products when the available data is obtained via generalized progressive hybrid censoring. The testing scheme conducts products of interest under a more flexible way and allows collecting failure data in efficient and adaptable experimental scenarios than traditional lifetime testing. When the latent lifetime of products follows Weibull distribution, classical and Bayesian inferences are considered for unknown parameters. The existence and uniqueness of maximum likelihood estimates are established, and approximate confidence intervals are also constructed via asymptotic theory. Bayes point estimates as well as the credible intervals of the parameters are obtained, and correspondingly, Monte Carlo sampling technique is also provided for complex posterior computation. Extensive numerical analysis is carried out, and the results show that the generalized progressive hybrid censoring is an adaptive procedure in practical lifetime experiment, both proposed classical and Bayesian inferential approaches perform satisfactorily, and the Bayesian results are superior to conventional likelihood estimates.

The limited sample size in multi-stress accelerated life testing makes the conventional large-sample-based inference methods inefficient. To overcome this problem, this paper develops a new statistical inference method based on random variable transformation for multi-stress accelerated life testing with Weibull distribution and progressive Type-II censoring. Firstly, a χ2 statistic is constructed using the random variable transformation method, and the exact point estimates of model parameters are derived based on the χ2 statistic. Subsequently, based on the χ2 statistic, the exact confidence interval of shape parameter is provided, while the generalized confidence intervals of the accelerated model parameters are calculated by constructing the new multivariate generalized pivotal quantities. Furthermore, the generalized confidence intervals of some commonly used reliability indexes are provided for better reliability management and decision making. Finally, a simulation study and a real case study are conducted to illustrate the implementation and effectiveness of the proposed method.

Funder: Biometrika Trust, Funder: Health and Care Research Wales; Id: http://dx.doi.org/10.13039/100012068, Recent FDA guidance on adaptive clinical trial designs defines bias as "a systematic tendency for the estimate of treatment effect to deviate from its true value," and states that it is desirable to obtain and report estimates of treatment effects that reduce or remove this bias. The conventional end-of-trial point estimates of the treatment effects are prone to bias in many adaptive designs, because they do not take into account the potential and realized trial adaptations. While much of the methodological developments on adaptive designs have tended to focus on control of type I error rates and power considerations, in contrast the question of biased estimation has received relatively less attention. This article is the first in a two-part series that studies the issue of potential bias in point estimation for adaptive trials. Part I provides a comprehensive review of the methods to remove or reduce the potential bias in point estimation of treatment effects for adaptive designs, while part II illustrates how to implement these in practice and proposes a set of guidelines for trial statisticians. The methods reviewed in this article can be broadly classified into unbiased and bias-reduced estimation, and we also provide a classification of estimators by the type of adaptive design. We compare the proposed methods, highlight available software and code, and discuss potential methodological gaps in the literature.

We consider the detection of multiple change-points for ρ-mixing sequence. A CUSUM-type method is proposed to estimate the multiple mean change-points and the strong consistency of the multiple mea...

To increase power or reduce the number of patients needed for a parallel groups design, the crossover design has been often used to study treatments for noncurable chronic diseases. However, in the presence of carry-over effect caused by treatments, the commonly-used estimator which ignores the carry-over effect leads to a biased estimator for estimating the treatment effect difference. A two-stage test approach aimed to address carry-over effect proposed was found to be potentially misleading. In this paper, we propose a weighted average of the commonly-used estimator and an unbiased estimator that uses only the first period of the data. We derive an optimal weight that minimizes the mean squared error (MSE) and its modified estimator. We apply Monte Carlo simulation to evaluate the performance of the proposed estimators in a variety of situations. In the simulations, we examine the estimated MSE (EMSE), percentile interval length, and coverage probability calculated from the percentile intervals among considered estimators. Simulation results show that our proposed weighted average estimator and its modified estimator lead to smaller EMSEs on average comparing to the two commonly used estimators. The coverage probabilities using our proposed estimators are reasonably close to the nominal confidence level and the interval lengths are shorter comparing to the use of the unbiased estimator that uses only the first period of the data. We apply an example that was to evaluate the efficacy of two type of bronchodilators for asthma treatment to demonstrate the use of the proposed estimators.

We examine the impact of geographic distance, economic size, and jurisdictional borders on Canadian interprovincial trade in services at the industry level. Using a gravity model, we find that the average elasticity of service trade with respect to distance is − 1.1, which coincides with the median estimate of average elasticity of merchandise trade with respect to distance. However, the point estimates of the elasticity of distance are significantly higher in magnitude in Arts and Health, while distance matters much less for Telecommunications and Information Technology. We also find that the elasticity of trade with respect to exporter and importer gross domestic product is highly industry specific. Our findings suggest that distance is still a key determinant of service trade and the income elasticity of demand is heterogeneous within the service sector. Supplementary Information The online version contains supplementary material available at 10.1007/s11079-021-09629-3.

1.AbstractPedigree inference from genotype data is a challenging problem, particularly when pedigrees are sparsely sampled and individuals may be distantly related to their closest genotyped relatives. We present a new method that infers small pedigrees of close relatives and then assembles them into larger pedigrees. To assemble large pedigrees, we introduce several new formulas and tools including a new likelihood for the degree separating two small pedigrees, a method for detecting individuals who share background identity-by-descent (IBD) that does not reflect recent common ancestry, and a method for identifying the ancestral branches through which distant relatives are connected. Our method also takes several new approaches that help to improve the accuracy and efficiency of pedigree inference. In particular, we incorporate age information directly into the likelihood rather than using ages only for consistency checks and we employ a heuristic branch-and-bound-like approach to more efficiently explore the space of possible pedigrees. Together, these approaches make it possible to construct large pedigrees that are challenging or intractable for current inference methods. The new method, Bonsai, is available at https://github.com/23andMe/bonsaitree.

Under partial shading conditions (PSCs), a series-connected photovoltaic (PV) string often shows multi-peak power-voltage (P-V) characteristics, which indicates a multi-modal distribution of maximum power points (MPPs). The phenomenon brings challenges to the maximum power point estimation (MPPE), since a single model usually cannot perform well in different modes. To address this problem, a real-time shading identification process is proposed to identify the shading information of the applied PV string. The measured data are divided into several fields according to the obtained number of peaks in the P-V curve. Multiple Gaussian process regression (M-GPR) models are then proposed to predict the MPP locus in a specific data field. Experiments are conducted to evaluate the accuracy of the proposed method. Simulation and experimental results show that the shading information enables the proposed M-GPR to obtain more accurate estimation performance compared to its single-model counterparts.

Stratification is commonly employed in clinical trials to reduce the chance covariate imbalances and increase the precision of the treatment effect estimate. We propose a general framework for constructing the confidence interval (CI) for a difference or ratio effect parameter under stratified sampling by the method of variance estimates recovery (MOVER). We consider the additive variance and additive CI approaches for the difference, in which either the CI for the weighted difference, or the CI for the weighted effect in each group, or the variance for the weighted difference is calculated as the weighted sum of the corresponding stratum-specific statistics. The CI for the ratio is derived by the Fieller and log-ratio methods. The weights can be random quantities under the assumption of a constant effect across strata, but this assumption is not needed for fixed weights. These methods can be easily applied to different endpoints in that they require only the point estimate, CI, and variance estimate for the measure of interest in each group across strata. The methods are illustrated with two real examples. In one example, we derive the MOVER CIs for the risk difference and risk ratio for binary outcomes. In the other example, we compare the restricted mean survival time and milestone survival in stratified analysis of time-to-event outcomes. Simulations show that the proposed MOVER CIs generally outperform the standard large sample CIs, and that the additive CI approach performs slightly better than the additive variance approach., Comment: 13 pages

Cost-effective threshold (CET) is essential for health technology assessment and decision-making based on health economic evaluations. Recently, it has been argued that the commonly used once and three times of gross domestic product (GDP) per capita CETs of a quality-adjusted life year (QALY) are not necessarily empirically supported in all countries. Therefore, we aimed to estimate the CET of a QALY as times of GDP per capita in China, of which the reimbursement coverage decisions are increasingly engaging economic evaluations. Estimates on the value of statistical life (VSL) in China were identified from several studies in the literature and converted to times of GDP per capita, the weighted average of which was used for subsequent calculation. By pooling data on population mortality, health utility, and age distribution, we estimated the value of a statistical QALY (VSQ) from VSL using an established mathematical process, which represented the theoretical upper bound of CET. The corresponding point estimate and theoretical lower bound were obtained using their numerical relationships with the upper bound. Scenarios analyses were also conducted. The estimated CET, its upper bound, and its lower bound were 1.45, 2.90, and 1.16 times of GDP per capita in China, respectively. In different scenarios, the estimated CET varied but was greater than once GDP per capita in most cases. As such, the CET of a QALY in China is close to 1.5 times of GDP per capita, which should be benchmarked for future ICER-based coverage decisions.

The literature review highlighted the impacts of drivers’ behavior on passengers’ attitudes in the choice of seatbelt usage. However, limited studies have been done to determine those impacts. Studying the passengers’ seatbelt use is especially needed to find out why passengers choose not to buckle up, and consequently it helps decision makers to target appropriate groups. So, this study was conducted to find drivers’ characteristics that might impact the passenger’s seatbelt use, in addition to other passengers’ characteristics themselves. While performing any analysis, it is important to use a right statistical model to achieve a less biased point estimate of the model parameters. The latent class multinomial logit model (LC-MNL) can be seen as an alternative to the mixed logit model, replacing the continuous with a discrete distribution, by capturing possible heterogeneity through membership in various clusters. In this study, instead of a response to the survey or crash observations, we employed a real-life observational data for the analysis. Results derived from the analysis reveal a clear indication of heterogeneity across individuals for almost all parameters. Various socio-demographic variables for class allocation and models with different latent numbers were considered and checked in terms of goodness of fit. The results indicated that a class membership with three factors based on vehicle type would result in a best fit. The results also highlighted the significant impacts of driver seatbelt status, time of a day, distance of traveling, vehicle type, and driver gender, instead of passenger gender, as some of the factors impacting the passengers’ choice of seatbelt usage. In addition, it was found that the belting status of passengers is positively associated with the belting condition of drivers, highlighting the psychological behavioral impact of drivers on passengers. Extensive discussion has been made regarding the implications of the findings.

Adaptation of a classifier to new domains is one of the challenging problems in machine learning. This has been addressed using many deep and non-deep learning based methods. Among the methodologies used, that of adversarial learning is widely applied to solve many deep learning problems along with domain adaptation. These methods are based on a discriminator that ensures source and target distributions are close. However, here we suggest that rather than using a point estimate obtaining by a single discriminator, it would be useful if a distribution based on ensembles of discriminators could be used to bridge this gap. This could be achieved using multiple classifiers or using traditional ensemble methods. In contrast, we suggest that a Monte Carlo dropout based ensemble discriminator could suffice to obtain the distribution based discriminator. Specifically, we propose a curriculum based dropout discriminator that gradually increases the variance of the sample based distribution and the corresponding reverse gradients are used to align the source and target feature representations. An ensemble of discriminators helps the model to learn the data distribution efficiently. It also provides a better gradient estimates to train the feature extractor. The detailed results and thorough ablation analysis show that our model outperforms state-of-the-art results., Comment: This work is an extension of our BMVC-2019 paper (arXiv:1907.10628)

The Bayesian approach, a non-classical estimation technique, is very widely used in statistical inference for real world situations. The parameter is considered to be a random variable, and knowledge of the prior distribution is used to update the parameter estimation. Herein, two Bayesian approaches for Poisson parameter estimation by deriving the posterior distribution under the squared error loss or quadratic loss functions are proposed. Their performances were compared with frequentist (maximum likelihood estimator) and Empirical Bayes approaches through Monte Carlo simulations. The mean square error was used as the test criterion for comparing the methods for point estimation; the smallest value indicates the best performing method with the estimated parameter value closest to the true parameter value. Coverage Probabilities (CPs) and average lengths (ALs) were obtained to evaluate the performances of the methods for constructing confidence intervals. The results reveal that the Bayesian approaches were excellent for point estimation when the true parameter value was small (0.5, 1 and 2). In the credible interval comparison, these methods obtained CP values close to the nominal 0.95 confidence level and the smallest ALs for large sample sizes (50 and 100), when the true parameter value was small (0.5, 1 and 2). Doi: 10.28991/esj-2021-01310 Full Text: PDF

Risk management is considered as a vital process contributing to the successful outcome of a complex construction project in terms of achieving the associated project objectives. The widely used industrial practice in managing construction project risks is to assign probability and impact values to each risk and to map risks on a risk matrix. The main criticism of this practice relates to ignoring complex interdependencies between risks and using point estimates for probability and impact values. Furthermore, risks mapped on a matrix are deemed to influence a specific objective and there is a challenge involved in aggregating the impact of risks across multiple (conflicting) project objectives. Utilizing a data-driven Bayesian Belief Network methodology, in this paper we introduce a new process where the risks mapped on a risk matrix corresponding to each project objective are aggregated and modeled as a risk network, and a holistic impact of each risk is captured across the network by means of new risk metrics. The proposed methodology is demonstrated through a real application. The results specific to the two ranking schemes (assuming independence/interdependence of risks) are found to be negatively correlated, which substantiates the importance of utilizing an interdependency-based risk management process.

In this paper, we consider Bayesian point estimation and predictive density estimation in the binomial case. After presenting preliminary results on these problems, we compare the risk functions of the Bayes estimators based on the truncated and untruncated beta priors and obtain dominance conditions when the probability parameter is less than or equal to a known constant. The case where there are both a lower bound restriction and an upper bound restriction is also treated. Then our problems are shown to be related to similar problems in the Poisson case. Finally, numerical studies are presented., 29 pages, 4 figures; Theorem 3.3 and Sections 4 and 6 have been added

The drill and blast method is the most prominent rock excavation method used in mining and civil engineering projects. The ground vibration is the most undesirable effect of the blasting and needs to be controlled. The blasts are designed so that ground vibration at nearby structures must remain under the prescribed limit. Various empirical blast vibration attenuation models have been presented to estimate the ground vibration for designing purposes. These models assume ground vibration as a function of distance and maximum charge per delay. United States Bureau of Mines (USBM) model is most commonly used for the blast design. However, the uncertainty associated with these models is seldom characterized, thus diminishing its reliability. The probabilistic Bayesian approach associated with the Monte Carlo method can easily quantify uncertainties associated with the model and its parameters. Thirty-three blast vibration observation data from a granite quarry in Kerala, India, is used to estimate the probability distribution of model parameters. Markov Chain Monte Carlo (MCMC) approach is used for sampling 12,000 samples for obtaining the posterior distribution of parameters. The uncertainty associated with model parameters is quantified from the posterior distribution, and this is further used to estimate the credible and prediction limits of the model. The point estimate of the most optimum value of the parameter is estimated using maximum-a-posteriori or MAP estimate. The model parameters are also obtained using the commonly used least-square error method, which is a maximum likelihood estimation or MLE approach. It has been observed that the accuracy of the model obtained using both MAP and MLE approach is almost equal. However, the MAP estimate as per Bayesian probabilistic analysis has the added advantage that it can estimate the uncertainty of parameters as well as the model, which is not possible using the MLE approach.

PurposeThe primary objective of this study is to propose a robust multiobjective solution search approach for a mean-variance multiple correlated quality characteristics optimisation problem, so-called “multiple response optimisation (MRO) problem”. The solution approach needs to consider response surface (RS) model parameter uncertainties, response uncertainties, process setting sensitivity and response correlation strength to derive the robust solutions iteratively.Design/methodology/approachThis study adopts a new multiobjective solution search approach to determine robust solutions for a typical mean-variance MRO formulation. A fine-tuned, non-dominated sorting genetic algorithm-II (NSGA-II) is used to derive efficient multiobjective solutions for varied mean-variance MRO problems. The iterative search considers RS model uncertainties, process setting uncertainties and response correlation structure to derive efficient fronts. The final solutions are ranked based on two different multi-criteria decision-making (MCDM) techniques.FindingsFive different mean-variance MRO cases are selected from the literature to verify the efficacy of the proposed solution approach. Results derived from the proposed solution approach are compared and contrasted with the best solution(s) derived from other approaches suggested in the literature. Comparative results indicate significant superiorities of the top-ranked predicted robust solutions in nondominated frequency, closeness-to-target and response variabilities.Research limitations/implicationsThe solution approach depends on RS modelling and considers continuous search space.Practical implicationsIn this study, promising robust solutions are expected to be more suitable for implementation than point estimate-based MOO solutions for a real-life MRO problem.Originality/valueNo evidence of earlier research demonstrates the superiority of a MOO-based iterative solution search approach for mean-variance MRO problems by simultaneously considering model uncertainties, response correlation and process setting sensitivity.

With the rise of the semiconductor industry, passive components have become a foundation of the electronics industry and propelled the development of peripheral equipment and industries. This paper focused on improving the lifetime performance of products to increase product value and achieve the green production goals of energy conservation and waste reduction. We first established a relative lifetime performance index for passive component capacitors. Next, we derived the cumulative distribution function and reliability function based on the probability density function of relative lifetime to investigate the properties of the relative lifetime performance index. The results indicated that the reliability increased with the index value and that the probability of the product lifetime exceeding the minimum requirement also increased with the index value. Due to the fact that the index contains unknown parameters, using point estimates to estimate product lifetime performance may lead to misjudgment caused by sampling errors. For this reason, we propose a uniformly minimum-variance unbiased estimator for the index and derived its probability density function. In addition, we establish a fuzzy testing model based on the confidence interval to determine whether the lifetime performance of a product reaches the required performance level. Finally, we present a numerical example of passive components to demonstrate application of the proposed model. This example further demonstrates how the proposed model improves product lifetime performance, which in turn increases product value and also achieves the green objectives of energy conservation and waste reduction.

Under constant-stress accelerated life test, the general progressive type-II censoring sample and the two parameters following the linear Arrhenius model, the point estimation and interval estimation of the two parameters log-normal distribution were discussed. The unknown parameters of the model as well as reliability and hazard rate functions are estimated by using Maximum likelihood (ML) and Bayesian methods. The maximum-likelihood estimates are derived by the Newton–Raphson method and the corresponding asymptotic variance is derived by the Fisher information matrix. Since the Bayesian estimates (BEs) of the unknown parameters cannot be expressed explicitly, the approximate BEs of the unknown parameters. The approximate highest posterior density confidence intervals are calculated. The practicality of the proposed method is illustrated by simulation study and real data application analysis.

Null hypothesis significance testing is the major statistical procedure in fMRI, but provides only a rather limited picture of the effects in a data set. When sample size and power is low relying only on strict significance testing may lead to a host of false negative findings. In contrast, with very large data sets virtually every voxel might become significant. It is thus desirable to complement significance testing with procedures like inferiority and equivalence tests that allow to formally compare effect sizes within and between data sets and offer novel approaches to obtain insight into fMRI data. The major component of these tests are estimates of standardized effect sizes and their confidence intervals. Here, we show how Hedges' g, the bias corrected version of Cohen's d, and its confidence interval can be obtained from SPM t maps. We then demonstrate how these values can be used to evaluate whether nonsignificant effects are really statistically smaller than significant effects to obtain “regions of undecidability” within a data set, and to test for the replicability and lateralization of effects. This method allows the analysis of fMRI data beyond point estimates enabling researchers to take measurement uncertainty into account when interpreting their findings., Inferiority and equivalence tests allow to compare effect sizes within and between data sets and are based on standardized effect sizes and their confidence intervals. We show how Hedges'g and its confidence interval can be obtained from SPM t maps and demonstrate how these can be used to obtain “regions of undecidability” within a data set, to test for the replicability, and for the lateralization of effects.

We describe the application of Bayesian hierarchical models to the analysis of data from long-term, environmental monitoring programs. The goal of these ongoing programs is to understand status and trend in natural resources. Data are usually collected using complex sampling designs including stratification, revisit schedules, finite populations, unequal probabilities of inclusion of sample units, and censored observations. Complex designs intentionally create data that are missing from the complete data that could theoretically be obtained. This “missingness” cannot be ignored in analysis. Data collected by monitoring programs have traditionally been analyzed using the design-based Horvitz–Thompson estimator to obtain point estimates of means and variances over time. However, Horvitz–Thompson point estimates are not capable of supporting inference on temporal trend or the predictor variables that might explain trend, which instead requires model-based inference. The key to applying model-based inference to data arising from complex designs is to include information about the sampling design in the analysis. The statistical concept of ignorability provides a theoretical foundation for meeting this requirement. We show how Bayesian hierarchical models provide a general framework supporting inference on status and trend using data from the National Park Service Inventory and Monitoring Program as examples. Supplemental Materials Code and data for implementing the analyses described here can be accessed here: https://doi.org/10.36967/code-2287025.

In many biomedical experiments, such as toxicology and pharmacological dose–response studies, one primary goal is to identify a threshold value such as the minimum effective dose. This paper applies Fisher’s fiducial idea to develop an inference method for these threshold values. In addition to providing point estimates, this method also offers confidence intervals. Another appealing feature of the proposed method is that it allows the use of multiple parametric relationships to model the underlying pattern of the data and hence, reduces the risk of model mis-specification. All these parametric relationships satisfy the qualitative assumption that the response and dosage relationship is monotonic after the threshold value. In practice, this assumption may not be valid but is commonly used in dose–response studies. The empirical performance of the proposed method is illustrated with synthetic experiments and real data applications. When comparing to existing methods in the literature, the proposed method produces superior results in most synthetic experiments and real data sets. Supplementary materials accompanying this paper appear on-line.

Objective To provide practical principles and examples to help GRADE users make optimal choices regarding their ratings of certainty of evidence using a minimally or partially contextualized approach. Study Design and Setting Based on the GRADE clarification of certainty of evidence in 2017, a project group within the GRADE Working Group conducted iterative discussions and presentations at GRADE Working Group meetings to refine this construct and produce practical guidance. Results Systematic review and health technology assessment authors need to clarify what it is in which they are rating their certainty of evidence (i.e., the target of their certainty rating). The decision depends on the degree of contextualization (partially or minimally contextualized), thresholds (null, small, moderate or large effect threshold), and where the point estimate lies in relation to the chosen threshold(s). When the 95% confidence interval crosses multiple possible thresholds (i.e., including both large benefit and large harm), it is not worthwhile for authors to determine the target of certainty rating. Conclusion GRADE provides practical principles to help systematic review and health technology assessment authors specify the target of their certainty of evidence rating.

A better understanding of regional differences in green development (GD) is crucial to achieving the sustainability goals in China's high-quality development stage. Data envelopment analysis–based productivity indexes, which link multiple inputs and multiple outputs, have been widely used to evaluate GD. However, most of these models do not take into account the imprecision of regional economic data due to over- or under-reporting by local governments. Here, to alleviate the GD calculation errors due to point estimation as far as possible, we propose a novel global Malmquist–Luenberger productivity index with the interval slacks-based measure to evaluate the provincial green total factor productivity (GTFP) in China from 2000 to 2018. The results showed that the overall GTFP in China during the study period exhibits an increasingly upward trend, accompanied by a declining and converging growth rate in recent years. Moreover, we found an emerging shift in the patterns of inter-regional GTFP from “East–Center–West” to “South–North”, as the differences in the GTFP between the eastern, central and western regions shrink while the gap between the southern and the northern regions expands. A further impact mechanism analysis based on dynamic spatial Durbin panel models revealed that the green development mode in the central, western and northern regions is more exogenously government-dependent, whereas that in the eastern and southern regions is more endogenously market-driven. These findings provide a new reference for optimizing the relationship between the market and government and coordinating the regional green development of China.