Interval Estimation Research Articles (Page 1)

In this paper, we adopt the Ishita lifetime distribution to analyze biomedical science and engineering lifetime data under an accelerated life test (ALT) model. This data is exposed concerning the mechanism of a type-I generalized hybrid censoring scheme under a partially step-stress ALT model. The model parameters and the parameters of life (survival and hazard rate function) are estimated using maximum likelihood and Bayesian estimation. Also, the interval estimators are formulated with respect to the normal distribution of the maximum likelihood estimate, two parametric bootstrap confidence techniques, and Bayesian credible intervals. Two real data sets are analyzed to illustrate the proposed methods. Monte Carlo simulation is used to compare various methods.

This study implements Bayesian along with non-Bayesian approaches to estimate the parameters of the three-parameter quadratic hazard rate distribution using hybrid Type-II censoring. The model expands upon linear hazard rate, exponential, and Rayleigh distributions. In the non-Bayesian framework, point estimates and survival and hazard functions are calculated using maximum likelihood estimation (MLE). Asymptotic confidence intervals are derived, with a focus on the delta method. By applying independent normal and gamma priors, Bayesian inference produces point estimates and credible intervals using different symmetric and asymmetric loss functions. The analytical intractability of posterior distributions makes Markov chain Monte Carlo (MCMC) methods necessary for sampling purposes. The evaluation of point and interval estimates depends on root mean squared error (RMSE) in combination with mean relative absolute bias (MRAB), average confidence interval length (AL), and coverage probability (CP). The performance evaluation through different sample sizes and censoring schemes is conducted by simulation studies, while real-world data from COVID-19 mortality demonstrates the practical implementation of methods. Graphical and numerical analyses confirm the existence and uniqueness of the estimates. Results indicate that Bayesian methods deliver superior accuracy and more robust estimates than their non-Bayesian counterparts for survival analysis purposes in clinical and medical research.

Artificial Intelligence (AI) and Machine Learning (ML) are rapidly transforming microbiome and colorectal cancer (CRC) research by enabling high-throughput data analysis and predictive modelling. This review highlights the current applications of AI/ML tools, such as Convolutional Neural Networks, Random Forest classifiers, and Support Vector Machines, in CRC diagnostics and microbiome profiling. It discusses how AI-integrated endoscopic and imaging systems improve polyp detection accuracy and reduce diagnostic delays. The manuscript also introduces the novel use of AI and microbial fingerprints in forensic science, including postmortem interval estimation and individual identification. Lastly, emerging trends in microbiotabased precision medicine and ethical considerations surrounding AI deployment are explored. These insights underscore AI/ML's potential in reshaping clinical diagnostics, prognostics, and forensic practices related to CRC. This review emphasizes the translational impact of AI/ML in CRC, from bench to bedside to the courtroom, highlighting both current challenges and future research directions.

ABSTRACT This article presents a novel quantile‐based process capability index (PCI), denoted as , which is suitable for both normal and non‐normal process distributions, particularly in the cases where the process mean or process standard deviation cannot be easily evaluated. Here, we have considered the log‐logistic process distribution for this present study. Both point and interval estimates of the proposed PCI are derived using classical as well as Bayesian estimation methods. In the classical approach, five different point estimation methods are considered. For the Bayesian analysis, the symmetric loss function, namely, squared error loss function is incorporated to assess the proposed PCI . The Markov Chain Monte Carlo simulation technique has been effectively employed to obtain an approximate solution for . Interval estimation of the proposed index is obtained using both the asymptotic confidence interval and the parametric bootstrap confidence interval from the classical point of view and the Bayes credible interval is obtained from the Bayesian point of view. Finally, the paper compares the results through an extensive Monte Carlo simulation study with four real‐life data sets. This comparison highlights the applicability of the proposed index in practical scenarios.

Artificial intelligence-assisted estimation of postmortem intervals in bacterially infected cadavers using pathological imaging across variable temperature conditions

Examining the impact of physiological stress on time perception: A systematic review and meta-analysis.

Blowfly species, which play a crucial role in forensic investigations as primary colonizers of cadavers, are influenced by environmental factors. However, most research conducted on blowfly species in South Korea remains limited to a single province. We investigated the spatiotemporal distribution of forensically relevant blowflies (Diptera: Calliphoridae) in the southern provinces of South Korea to enhance forensic entomology databases and improve postmortem interval (PMI) estimation. Overall, 3,934 adult blowflies representing 14 species across 5 genera were collected from 4 regions (Changnyeong, Pohang, Yeosu, and Jeju) over a 1-yr period using baited traps. The dominant species included Chrysomya megacephala (Fabricius), Lucilia illustris (Meigen), Lucilia caesar (Linnaeus), and Lucilia sericata (Meigen); Ch. megacephala exhibited a significantly higher abundance in Jeju than in the other regions, particularly during the warmer seasons. A self-organizing map (SOM) and principal component analysis (PCA) were employed to visualize and validate the spatiotemporal clustering of blowfly populations, confirming that seasonal factors strongly influence distribution patterns. The combination of SOM and PCA effectively distinguished seasonal and regional clustering patterns, demonstrating the influence of environmental factors on species-specific distributions. These findings emphasize the importance of considering regional and seasonal variations in forensic casework and the need to expand entomological databases to reflect geographic differences. Furthermore, the observed regional differences in species dominance underscore the need to incorporate environmental variability into forensic models to improve the accuracy of PMI estimates. This study provides fundamental data for improving forensic applications based on insect evidence, particularly PMI estimation and crime scene reconstruction.

ABSTRACT In this article, we focus on the estimation of the generalized process capability index, , for the Log–Log distribution under a progressive type II censoring scheme. To facilitate robust inference, we employ three distinct estimation methodologies, including maximum likelihood, maximum product of spacings, and Bayesian approaches. Within the Bayesian framework, estimators of are derived under both the squared error loss function and the LEL function, assuming independent gamma priors for the unknown parameters. Furthermore, approximate confidence intervals for the index are constructed using conventional frequentist methods and are compared with the Bayesian HPD intervals. To comprehensively evaluate the efficacy of the proposed estimation procedures, a comprehensive Monte Carlo simulation is carried out. The accuracy of the point estimators is measured by their mean squared errors and biases, whereas the reliability of the interval estimates is judged by their average widths along with coverage probabilities. The practical applicability of the proposed index and estimation methodologies is further illustrated through a real data example concerning the failure times of transmission components in Caterpillar tractors.

Accurate epidemic forecasting is critical for effective public health interventions. This study compares Bayesian and Frequentist estimation frameworks within deterministic compartmental epidemic models, focusing on nonlinear least squares (NLS) optimization versus Bayesian inference assuming a normal likelihood and using MCMC sampling in Stan. Rather than evaluating all methodological variants, we assess forecasting performance under a shared modeling structure and error assumption. The findings apply to specific implementations of both approaches. Performance is evaluated using simulated datasets (with and 1.5) and historical outbreaks, including the 1918 influenza pandemic, the 1896-1897 Bombay plague epidemic, and the COVID-19 pandemic. Metrics include mean absolute error (MAE), root mean squared error (RMSE), weighted interval score (WIS), and 95% prediction interval coverage. Forecasting performance varies by epidemic phase and dataset; no method consistently dominates. The Frequentist method performs well at the peak in simulations and in the post-peak phases of real outbreaks but is less accurate pre-peak. Bayesian methods, especially those with uniform priors, offer higher predictive accuracy early in epidemics and stronger uncertainty quantification when data are sparse or noisy. Frequentist methods often yield more accurate point forecasts with lower MAE, RMSE, and WIS, though their interval estimates are less robust. We also discuss the influence of prior choice and the effects of longer forecasting horizons on convergence and computational efficiency. These findings provide practical guidance for selecting estimation strategies suited to epidemic phase and data quality, aiding forecast-based decision-making.

This study aims to determine reliable reference intervals (RIs) for total cortisol (TC) in adults considering the effects of both age and blood collection time, using indirect methods and machine learning approaches. Serum TC results from blood samples collected between 08:00 and 10:00 am at the first outpatient visit were included in the study. Serum TC were measured using a Roche Elecsys Cortisol II kit. Estimated RIs by indirect methods withthe support of R packages (refineR and reflimR) for the implementation of machine learning algorithms (mclust and rpart) were compared with the manufacturer's reference interval (RI) (48-195 μg/L). Estimated RIs by refineR and reflimR (57-256 μg/L and 62-271 μg/L, respectively) were wider than the manufacturer's RI. When reflimR was applied to Box-Cox-transformed data with the lambda value of 0.284 suggested by refineR, an RI of 57-251 μg/L was obtained, which was like that obtained with refineR. An even better match with the manufacturer's RI was achieved using Gaussian mixture modelling with the mclust, which suggested one out of four clusters with an RI of 55.8-187 μg/L. Clustering the data with rpart suggested stratification into two age groups (≤35 and >35 years) and three blood collection periods (08:00-08:45, 08:45-09:35, and 09:35-10:00). The TC levels demonstrated the highest concentrations in the early morning (8:00-08:45) and in young adults (18-35 years). This study highlights the necessity of considering both age and blood collection time in clinical interpretation and demonstrates the effectiveness of indirect methods and machine learning approaches in the verification of RIs for hormones with known heterogeneity.

Reference intervals (RIs) are essential for interpreting laboratory test results. It is recommended that each medical laboratory establishes and reviews its own RIs. The use of direct methods is often unfeasible for most laboratories, while indirect methods are a more viable alternative. However, these methods require not only medical, but also statistical and technical expertise, thereby limiting accessibility for many laboratories. To address this challenge, a web-based application was developed to facilitate the estimation and verification of RIs using real-world laboratorydata. The application was developed using R Studio and the Shiny web framework. The tool supports five indirect methods for reference interval estimation: refineR, TMC, TML, kosmic and reflimR. Furthermore, a Docker container was designed to enable a secure local deployment. Up to 200,000 laboratory test results can be included via a straightforward copy-and-paste input. The tool provides recommendations for sex-based stratification by performing statistical analysis. In addition, a drift-detection algorithm was developed to analyze whether age-based stratification is necessary. The results of RI estimation are displayed and visualized alongside the underlying data distribution. Existing RIs can be verified by comparing them against calculated intervals. ReferenceRangeR is a user-friendly tool for estimating and verifying RIs using real-world laboratory data, eliminating the need for statistical or technological expertise, thereby supporting laboratory professionals in meeting the current regulatory standards.

Pavement performance prediction serves as a core basis for maintenance decision-making. Although numerous studies have been conducted, most focus on road segments and aggregate indicators such as IRI and PCI, with limited attention to the daily deterioration of individual distresses. Subject to the combined influence of multiple factors, pavement distress deterioration exhibits pronounced nonlinear and time-lag characteristics, making distress-level predictions prone to disturbances and highly uncertain. To address this challenge, this study investigates the distress-level deterioration of three representative distresses—transverse cracks, alligator cracks, and potholes—with causal analysis and uncertainty quantification. Based on two years of high-frequency road inspection data, a continuous tracking dataset comprising 164 distress sites and 9038 records was established using a three-step matching algorithm. Convergent cross mapping was applied to quantify the causal strength and lag days of environmental factors, which were subsequently embedded into an encoder–decoder framework to construct a BayesLSTM model. Monte Carlo Dropout was employed to approximate Bayesian inference, enabling probabilistic characterization of predictive uncertainty and the construction of prediction intervals. Results indicate that integrating causal and time-lag characteristics improves the model’s capacity to identify key drivers and anticipate deterioration inflection points. The proposed BayesLSTM achieved high predictive accuracy across all three distress types, with a prediction interval coverage of 100%, thereby enhancing the reliability of prediction by providing both deterministic results and interval estimates. These findings facilitate the identification of high-risk distresses and their underlying mechanisms, offering support for rational allocation of maintenance resources.

The analysis of lifetime data under censoring schemes plays a vital role in reliability studies and survival analysis, where complete information is often difficult to obtain. This work focuses on the estimation of the parameters of the recently proposed generalized Kavya–Manoharan exponential (GKME) distribution under progressive Type-I interval censoring, a censoring scheme that frequently arises in medical and industrial life-testing experiments. Estimation procedures are developed under both classical and Bayesian paradigms, providing a comprehensive framework for inference. In the Bayesian setting, parameter estimation is carried out using Markov Chain Monte Carlo (MCMC) techniques under two distinct loss functions: the squared error loss function (SELF) and the general entropy loss function (GELF). For interval estimation, asymptotic confidence intervals as well as highest posterior density (HPD) credible intervals are constructed. The performance of the proposed estimators is systematically evaluated through a Monte Carlo simulation study in terms of mean squared error (MSE) and the average lengths of the interval estimates. The practical usefulness of the developed methodology is further demonstrated through the analysis of a real dataset on survival times of guinea pigs exposed to virulent tubercle bacilli. The findings indicate that the proposed methods provide flexible and efficient tools for analyzing progressively interval-censored lifetime data.

The importance of estimating time since death has been acknowledged for centuries. One of the key elements in crime investigation lies in the reckoning of post-mortem interval(PMI). It’s evident why an accurate post-mortem interval estimation is needed in all criminal cases. There is ample literature regarding the techniques for estimating postmortem interval, but these techniques must be as precise, reliable, and scientific as possible. Conventional methods for determining PMI are fixed on physical, metabolic, autolysis, histochemistry, and physicochemical processes. These parameters are employed in the initial period of postmortem, and over time its reliability decreases. Recent research attempts the improvement of post-mortem interval estimation by more predictable and quantifiable parameters. This study presents the current headway in estimating time since death. Chemical changes in biological samples, Spectroscopical analysis for detection of biochemical changes, thanatomicrobiome analysis, predictable protein degradation process in human muscles, and dating of skeletal remains -improved the postmortem interval estimates. Further research is needed in these many parameters, the field still has a long way to go in terms of finding the exclusive formula for accurate post-mortem interval estimation. This is a review that emphasizes several recent methods for precisely estimating post-mortem intervals by instrumental analysis.

Estimating time of death based on entomological evidence commonly relies on the "law of total effective temperature", which requires developmental parameters of specific insect taxa. These are often calculated using the method of Ikemoto and Takai. However, this approach has key limitations. Most importantly, the lack of interval estimates may give the false impression of population homogeneity, which contradicts the substantial variation typically observed in insect populations. In this study, we propose an alternative method. It estimates interval values for developmental parameters while simultaneously identifying component populations within a dataset. The method involves fitting a finite mixture of Weibull distributions to development time data using the Expectation-Maximization (EM) algorithm. This allows for the inclusion of individual-level variability in the estimation process. We tested the method using previously published developmental data on two beetle species, Creophilus maxillosus and Necrodes littoralis (Staphylinidae). Our approach yielded 95% intervals with coverage close to the nominal level, in contrast to Ikemoto and Takai's method, which captured only 59% and 75% of actual cases, respectively. These findings suggest that our method improves the accuracy of insect-based postmortem interval estimates in forensic entomology and, more broadly, provides a general framework for interval estimation of developmental parameters applicable in thermal ecology and applied entomology.

Blow flies (Diptera: Calliphoridae) arrive to remains and deposit eggs soon after death, making them useful for estimating a minimum postmortem interval. There can be delays in blow fly arrival due to environmental conditions, concealment, or other modifications of the remains. If there is a delay in blow fly arrival, then, the time of colonization and postmortem interval will be different estimates. Field and laboratory studies were conducted to assess how delays in insect accessibility influence blow fly oviposition behavior by allowing small pigs to decompose indoors with insect activity excluded prior to exposing them to blow flies. The aged treatments included were 24-, 48-, 72-, 96-h along with fresh controls. This research assessed oviposition sites, time to oviposition, and number of eggs laid by Phormia regina Meigen in the laboratory. The field component of this research also looked at initial colonizing species of the aged treatments in addition to time to oviposition and oviposition sites. Phormia regina laid the largest number of eggs on the 48-h treatments and had the shortest time to oviposition on the 48- and 72-h treatments. The 48-h treatment also had the greatest number of unique oviposition sites compared to other treatments. The results of this study indicate that P. regina may prefer to colonize aged remains. More research on this topic could clarify how the postmortem interval estimation should be adjusted when there is a delay in insect colonization.

Microbial communities are critical drivers of mammalian carcass decomposition in natural ecosystems. Many studies have attempted to establish a microbial clock to estimate the postmortem interval (PMI); however, several obstacles remain to be solved. This study examines how age and insect activity influence microbial dynamics and emphasizes the role of 'rupture' in the decay. Notably, microbial diversity exhibited more pronounced shifts in immature cadavers, while insect activity suppressed overall diversity. Conversely, older age and insect colonization promoted the dominance of the Pseudomonadota phylum. We constructed random forest models (MAE: 0.62-0.95 days, R²: 0.976-0.987) for PMI estimation. These findings provide novel insights into refining PMI estimation in forensic contexts. Future research will further investigate the mechanisms behind these changes. Additionally, it will explore how other factors influence the decay, improving the accuracy and applicability of PMI estimation in various contexts.

Adverse weather events have a negative impact on the productivity of construction site activities. Understanding these effects is essential for developing realistic construction schedules. The influence of weather is shaped by both environmental factors (climate, geography, topography) and construction-related aspects such as technologies, materials, equipment, and site exposure. This paper proposes a model to quantify the influence of adverse weather by estimating monthly intervals of expected days with reduced construction productivity, based on data regarding specific weather events, including precipitation, wind, extreme temperatures, snow cover, fog, and high humidity. Data analysis employs the inclusion–exclusion principle, a combinatorial technique, alongside confidence interval estimation, a standard statistical approach. The model was applied in three Croatian cities to demonstrate its practicality and accuracy. Contractors with extensive on-site experience reviewed the results, providing insights into weather-sensitive activities and organizational practices.

Interpreting p values and interval estimates based on practical relevance: guidance for the sports medicine clinician

Minimum ranked set sampling offers an effective approach for collecting failure time data while optimizing testing resources. This paper examines dependent competing risks model within the context of m-cycle minimum ranked set sampling data. Assuming that component lifetimes adhere to a two-parameter generalized inverted exponential distribution, we develop dependence structures utilizing the Marshall-Olkin distribution framework. The study establishes maximum likelihood estimation and Bayesian inference procedures under both unrestricted parameters and ordered restrictions. The theoretical analysis confirms the existence and uniqueness conditions for maximum likelihood estimators, with corresponding interval estimators being subsequently derived. For Bayesian inference, we derive posterior estimates under flexible prior specifications, employing Metropolis-Hastings and importance sampling algorithms to address complex posterior calculations. Through comprehensive numerical simulations and real-world case analysis, this study systematically evaluates the comparative performance of different estimation approaches while examining how cyclic sampling strategies influence estimation precision. Finally, implementation guidelines and production-oriented conclusions are provided based on the study results.