Improving Bayesian credibility intervals for classifier error rates using maximum entropy empirical priors

The data used for the analysis were collected from multiple regions or years. Evaluating each region or year separately may be insufficient for drawing comprehensive inferences and may fail to reveal statistically significant differences. To ensure the reliability of the analysis and to enable overall conclusions, it is necessary to apply a statistical method known as simultaneous confidence intervals. This technique enables the simultaneous construction of confidence intervals for multiple parameters. Therefore, we proposed and evaluated methods for constructing simultaneous confidence intervals for all pairwise differences between the coefficients of variation in zero-inflated Birnbaum-Saunders distributions. The methods utilized for constructing simultaneous confidence intervals comprise the generalized confidence interval (GCI), the bootstrap confidence interval (BCI), the method of variance estimates recovery (MOVER), the MOVER based on GCI, the MOVER based on BCI, the Bayesian credible interval, and the highest posterior density interval (HPD). Monte Carlo simulations were employed to evaluate the performance of each method, which involved the assessment of coverage probabilities and average widths under a set of parameter configurations and sample sizes. The generalized confidence interval method was the most efficient overall, as indicated by the simulation results. Finally, all proposed methods were applied to real-world wind speed data to examine their practical applicability and to demonstrate the consistency of the results between the simulation study and real-world applications.

Under progressive type II censoring, the credible interval estimation and the credible region for parameters of two-parameter exponential distribution based on the Bayesian approach are presented in this paper. Two methods of Bayesian credible region are proposed under a given confidence level. We also presented the predictive interval of the future observation under this type of censoring. In order to compare the performance of our proposed Bayesian credible interval and region with the existing non-Bayesian methods, we conduct a simulation study by the Monte Carlo method to find the corresponding coverage probabilities. This research is related to the topic of asymmetrical probability distributions and applications across disciplines. Finally, one engineering example is used to demonstrate the Bayesian credible interval estimation methods proposed in this paper.

Bayesian assessment of three serological tests for the screening of Trypanosoma cruzi in hunting dogs of Virginia and West Virginia, USA.

Striped skunks are one of the most important terrestrial reservoirs of rabies virus in North America, and yet the prevalence of rabies among this host is only passively monitored and the disease among this host remains largely unmanaged. Oral vaccination campaigns have not efficiently targeted striped skunks, while periodic spillovers of striped skunk variant viruses to other animals, including some domestic animals, are routinely recorded. In this study we evaluated the spatial and spatio-temporal patterns of infection status among striped skunk cases submitted for rabies testing in the North Central Plains of US in a Bayesian hierarchical framework, and also evaluated potential eco-climatological drivers of such patterns. Two Bayesian hierarchical models were fitted to point-referenced striped skunk rabies cases [n = 656 (negative), and n = 310 (positive)] received at a leading rabies diagnostic facility between the years 2007–2013. The first model included only spatial and temporal terms and a second covariate model included additional covariates representing eco-climatic conditions within a 4km2 home-range area for striped skunks. The better performing covariate model indicated the presence of significant spatial and temporal trends in the dataset and identified higher amounts of land covered by low-intensity developed areas [Odds ratio (OR) = 3.41; 95% Bayesian Credible Intervals (CrI) = 2.08, 3.85], higher level of patch fragmentation (OR = 1.70; 95% CrI = 1.25, 2.89), and diurnal temperature range (OR = 0.54; 95% CrI = 0.27, 0.91) to be important drivers of striped skunk rabies incidence in the study area. Model validation statistics indicated satisfactory performance for both models; however, the covariate model fared better. The findings of this study are important in the context of rabies management among striped skunks in North America, and the relevance of physical and climatological factors as risk factors for skunk to human rabies transmission and the space-time patterns of striped skunk rabies are discussed.

We investigate the estimation of multi-stress strength reliability under progressively first failure censoring for the generalized inverted exponential distribution using classical and Bayesian approaches. Classical estimation employs maximum likelihood estimators with the Expectation-Maximization algorithm to handle incomplete data. Bayesian estimation utilizes Markov Chain Monte Carlo (MCMC) techniques and Tierney-Kadane's approximation to approximate the posterior distribution. Furthermore, A generalized entropy loss function is employed to measure estimation accuracy. Finally, Validation is provided through Monte Carlo simulations and real-world applications. Findings highlight the robustness and accuracy of Bayesian methods, particularly with informative priors, and underscore the strengths of MCMC techniques and Bayesian Credible Intervals in specific aspects of estimation.

Bayesian designs are increasingly used to conduct phase II clinical trials. However, stopping boundaries in most Bayesian designs are defined from posterior credible intervals. The use of designs based on posterior credible intervals results in a loss of efficiency when compared to formal stopping rules based on Bayesian hypothesis tests. Such designs also introduce an unnecessary element of subjectivity in the interpretation of trial results. We derive a new class of Bayesian designs based on formal hypothesis tests. The prior densities used to define the alternative hypotheses in these tests assign no mass to parameter values that are consistent with the null hypotheses and are called nonlocal alternative prior densities. We show that Bayesian designs based on hypothesis tests and nonlocal alternative prior densities are more efficient than common Bayesian designs based on posterior credible intervals and common frequentist designs. In contrast to trial designs based on Bayesian credible intervals, we demonstrate that the mis-specification of the prior densities used to describe the anticipated effect of the experimental treatment in designs based on hypothesis tests cannot increase the expected weight of evidence in favor of the trial agent. Extension of test-based designs to phase I-II designs and randomized phase II designs remains an open research question. Phase II single-arm trials designed using Bayesian hypothesis tests with nonlocal alternatives provide better operating characteristics, use fewer patients per correct decision, and provide more directly interpretable results than other commonly used Bayesian and frequentist designs. Because the mis-specification of the prior density on the effect of the experimental agent decreases the expected weight of evidence that is collected in favor of the experimental treatment, the use of Bayesian hypothesis tests to design clinical trials also eliminates a potential source of bias often associated with trials designed using posterior credible intervals.

Conventional methods for assessing the impacts of climate change on crop production are often unable to account for the impacts of extreme weather events and therefore underestimate the impacts of climate change. Risk assessment allows for the inclusion of inconsistent impact assessment results in the risk assessment framework and thus provides a qualitative or quantitative assessment of possible risks suffered by crops amid climate change. Due to the subjective assumptions on prior distributions (e.g., emission scenarios and climate model performance) and the assumption that variables are independent of one another, conventional risk assessment methods for crop production amid climate change could produce relatively large errors. In this study, a probability function for future weather scenarios is established based on the principle of maximum entropy using future weather scenario data from the Intergovernmental Panel on Climate Change. In addition, by linking future weather scenarios and winter wheat yields, the risks of winter wheat yield reduction caused by high temperatures as well as the risks of a decrease in rainfall on the North China Plain (NCP) amid climate change are systematically investigated. The results show the following. The risks of winter wheat yield reduction caused by high temperatures will be higher in the north than in the south of the NCP in 2030, 2050 and 2080. In particular, the probabilities of winter wheat yield reduction will be relatively high in central Hebei and northwestern Shandong. In addition, the risks of a decrease in rainfall during the winter wheat season will be higher in the northern NCP than in the southern NCP in 2030, 2050 and 2080. The probabilities of a decrease in rainfall will be relatively high in northern Hebei, Beijing and Tianjin in 2030, and the risks of a decrease in rainfall are gradually increasing. In this study, the principle of maximum entropy is successfully introduced into the field of risk assessments for crop production amid climate change and used to assess the risks to winter wheat production. The method used in this study could enrich the theories and technical methods for assessing crop production risks amid climate change. The results could provide a theoretical basis for developing measures and techniques for adapting winter wheat production to climate change.

Estimating sensitivity and specificity of a PCR for boot socks to detect Campylobacter in broiler primary production using Bayesian latent class analysis

Bayesian analysis of clinical trial data may provide useful information to aid in study interpretation, especially when trial evidence suggests that the benefits of an intervention are uncertain, such as in a trial that evaluated early extracorporeal membrane oxygenation (ECMO) for severe acute respiratory distress syndrome (ARDS). To demonstrate the potential utility of Bayesian analyses by estimating the posterior probability, under various assumptions, that early ECMO was associated with reduced mortality in patients with very severe ARDS in a randomized clinical trial (RCT). A post hoc Bayesian analysis of data from an RCT (ECMO to Rescue Lung Injury in Severe ARDS [EOLIA]) that included 249 patients with very severe ARDS who had been randomized to receive early ECMO (n = 124; mortality at 60 days, 35%) vs initial conventional lung-protective ventilation with the option for rescue ECMO (n = 125, mortality at 60 days, 46%). The trial was designed to detect an absolute risk reduction (ARR) of 20%, relative risk (RR) of 0.67. Statistical prior distributions were specified to represent varying levels of preexisting enthusiasm or skepticism for ECMO and by Bayesian meta-analysis of previously published studies (with downweighting to account for differences and quality between studies). The RR, credible interval (CrI), ARR, and probability of clinically important mortality benefit (varying from RR less than 1 to RR less than 0.67 and ARR from 2% or more to 20% or more) were estimated with Bayesian modeling. Combining a minimally informative prior distribution with the findings of the EOLIA trial, the posterior probability of RR less than 1 for mortality at 60 days after randomization was 96% (RR, 0.78 [95% CrI, 0.56-1.04]); the posterior probability of RR less than 0.67 was 18%, the probability of ARR of 2% or more was 92%, and the probability of ARR of 20% or more was 2%. With a moderately enthusiastic prior, equivalent to information from a trial of 264 patients with an RR of 0.78, the estimated RR was 0.78 (95% CrI, 0.63-0.96), the probability of RR less than 1 was 99%, the probability of RR less than 0.67 was 8%, the probability of ARR of 2% or more was 97%, and the probability of ARR of 20% or more was 0%. With a strongly skeptical prior, equivalent to information from a trial of 264 patients with an RR of 1.0, the estimated RR was 0.88 (95% CrI, 0.71-1.09), the probability of RR less than 1 was 88%, the probability of RR less than 0.67 was 0%, the probability of ARR of 2% or more was 78%, and the probability of ARR of 20% or more was 0%. If the prior was informed by previous studies, the estimated RR was 0.71 (95% CrI, 0.55-0.94), the probability of RR less than 1 was 99%, the probability of RR less than 0.67 was 48%, the probability of ARR of 2% or more was 98%, and the probability of ARR of 20% or more was 4%. Post hoc Bayesian analysis of data from a randomized clinical trial of early extracorporeal membrane oxygenation compared with conventional lung-protective ventilation with the option for rescue extracorporeal membrane oxygenation among patients with very severe acute respiratory distress syndrome provides information about the posterior probability of mortality benefit under a broad set of assumptions that may help inform interpretation of the study findings.

In this paper, the Bayesian analysis of scale parameter of inverse Gaussian distribution has been considered. The Bayes estimators along with corresponding risks have been derived under a class of priors and using various loss functions. The Bayesian credible intervals have been derived for the said parameter. In order to predict the future values of the variable the posterior predictive distributions have been constructed under different priors. A simulation study has been conducted for different parametric values to assess and compare the performance of different estimators.

BackgroundFamilies and friends provide a considerable proportion of care for patients and elderly people. Caregiving can have substantial effects on caregivers’ lives, health, and well-being. However, because clinical trials rarely assess these effects, no information on caregiver burden is available when evaluating the cost effectiveness of treatments.ObjectiveThis study develops an algorithm for estimating caregiver time using information that is typically available in clinical trials: the EQ-5D scores of patients and their gender.MethodsFour datasets with a total of 8012 observations of dyads of caregivers and a gamma model with a log-link estimated with the Bayesian approach were used to estimate the statistical association between patient scores on the EQ-5D-3L dimensions and the numbers of hours of care provided by caregivers during the previous week. The model predicts hours of care as mean point estimates with 95% credible intervals or entire distributions.ResultsModel predictions of hours of care based on the five EQ-5D dimensions ranged from 13.06 (12.7–14.5) h/week for female patients reporting no health problems but receiving informal care to 52.82 (39.38–66.26) for male patients with the highest level of problems on all EQ-5D dimensions.ConclusionsThe iCARE algorithm developed in this study allows researchers who only have patient-level EQ-5D data to estimate the mean hours of informal care received per week, including a 95% Bayesian credible interval. Caregiver time can be multiplied with a monetary value for caregiving, enabling the inclusion of informal care costs in economic evaluations. We recommend using the tool for samples that fall within the confidence intervals of the characteristics of our samples: men (age range 47.0–104.2 years), women (age range 55–103 years).Electronic supplementary materialThe online version of this article (10.1007/s40273-018-0706-6) contains supplementary material, which is available to authorized users.

Overactivation of the renin-angiotensin system (RAS) may contribute to poor clinical outcomes in patients with COVID-19. To determine whether angiotensin-converting enzyme (ACE) inhibitor or angiotensin receptor blocker (ARB) initiation improves outcomes in patients hospitalized for COVID-19. In an ongoing, adaptive platform randomized clinical trial, 721 critically ill and 58 non-critically ill hospitalized adults were randomized to receive an RAS inhibitor or control between March 16, 2021, and February 25, 2022, at 69 sites in 7 countries (final follow-up on June 1, 2022). Patients were randomized to receive open-label initiation of an ACE inhibitor (n = 257), ARB (n = 248), ARB in combination with DMX-200 (a chemokine receptor-2 inhibitor; n = 10), or no RAS inhibitor (control; n = 264) for up to 10 days. The primary outcome was organ support-free days, a composite of hospital survival and days alive without cardiovascular or respiratory organ support through 21 days. The primary analysis was a bayesian cumulative logistic model. Odds ratios (ORs) greater than 1 represent improved outcomes. On February 25, 2022, enrollment was discontinued due to safety concerns. Among 679 critically ill patients with available primary outcome data, the median age was 56 years and 239 participants (35.2%) were women. Median (IQR) organ support-free days among critically ill patients was 10 (-1 to 16) in the ACE inhibitor group (n = 231), 8 (-1 to 17) in the ARB group (n = 217), and 12 (0 to 17) in the control group (n = 231) (median adjusted odds ratios of 0.77 [95% bayesian credible interval, 0.58-1.06] for improvement for ACE inhibitor and 0.76 [95% credible interval, 0.56-1.05] for ARB compared with control). The posterior probabilities that ACE inhibitors and ARBs worsened organ support-free days compared with control were 94.9% and 95.4%, respectively. Hospital survival occurred in 166 of 231 critically ill participants (71.9%) in the ACE inhibitor group, 152 of 217 (70.0%) in the ARB group, and 182 of 231 (78.8%) in the control group (posterior probabilities that ACE inhibitor and ARB worsened hospital survival compared with control were 95.3% and 98.1%, respectively). In this trial, among critically ill adults with COVID-19, initiation of an ACE inhibitor or ARB did not improve, and likely worsened, clinical outcomes. ClinicalTrials.gov Identifier: NCT02735707.

Bayesian system reliability assessment method with maximum entropy as prior distribution is developed in the present analysis. The system reliability assessment model is established, and the method and process of system reliability assessment are put forward. The method is based on the theory of information entropy. The probability density function and distribution function of system reliability parameters are given by using maximum entropy method. Prior distribution of Bayesian analysis method is the distribution function. Likelihood function is given by a small amount of field test data. According to Bayesian methods, posterior distribution is determined by using prior distribution and likelihood function. The point estimation and interval estimation of system reliability parameters are calculated in order to evaluate the system reliability. The method solves better the problem of system reliability assessment for small sample cases, and is an optimum method for reliability assessment of large and complex systems.

This work presents a novel and comprehensive inferential framework for analyzing the stress-strength reliability parameter,R= P(Y X), where X and Y denote independent stress and strength variables, respectively, both modeled as Weibull-distributed with a shared shape parameter but distinct scale parameters. A key innovation of this study lies in its integration of the unified Type-I progressively hybrid censoring scheme, which simultaneously accommodates time constraints and partial failure information, conditions often encountered in real-world reliability testing. To estimate R, we propose and evaluate four distinct inferential strategies: two frequentist (maximum likelihood estimation and maximum spacings estimation) and two Bayesian, each tailored to either the likelihood or spacings-based posterior formulation. The Bayesian methods employ Monte Carlo sampling to compute both Bayes point estimates and credible intervals under informative priors, offering robustness in small-sample or heavily censored contexts. An extensive simulation study is conducted to systematically compare the estimators in terms of bias, efficiency, and interval coverage. To validate the practical applicability of our framework, we further analyze two real-world microdroplet datasets, revealing critical insights into stress-tolerance behavior under experimental constraints. This study not only advances methodological tools for reliability inference under hybrid censoring but also establishes a blueprint for combining classical and Bayesian paradigms in stress-strength modeling.OPEN ACCESS Received: 01/07/2025 Accepted: 02/09/2025 Published: 23/01/2026

Due to low quality of crowdsourced labelers, the integrated label of each example is usually inferred from its multiple noisy labels provided by different labelers. This paper proposes a novel algorithm, Ground Truth Inference using Clustering (GTIC), to improve the quality of integrated labels for multi-class labeling. For a K labeling case, GTIC utilizes the multiple noisy label sets of examples to generate features. Then, it uses a K-Means algorithm to cluster all examples into K different groups, each of which is mapped to a specific class. Examples in the same cluster are assigned a corresponding class label. We compare GTIC with four existing multi-class ground truth inference algorithms, majority voting (MV), Dawid & Skene's (DS), ZenCrowd (ZC) and Spectral DS (SDS), on one synthetic and eight real-world datasets. Experimental results show that the performance of GTIC is significantly superior to the others in terms of both accuracy and M-AUC. Besides, the running time of GTIC is about twenty times faster than EM-based complicated inference algorithms.