Interval Estimation Research Articles

Insights into COVID-19 epidemiology and control from temporal changes in serial interval distributions in Hong Kong.

The serial interval distribution is used to approximate the generation time distribution, an essential parameter to infer the transmissibility (${R}_t$) of an epidemic. However, serial interval distributions may change as an epidemic progresses. We examined detailed contact tracing data on laboratory-confirmed cases of COVID-19 in Hong Kong during the five waves from January 2020 to July 2022. We reconstructed the transmission pairs and estimated time-varying effective serial interval distributions and factors associated with longer or shorter intervals. Finally, we assessed the biases in estimating transmissibility using constant serial interval distributions. We found clear temporal changes in mean serial interval estimates within each epidemic wave studied and across waves, with mean serial intervals ranged from 5.5 days (95% CrI: 4.4, 6.6) to 2.7 (95% CrI: 2.2, 3.2) days. The mean serial intervals shortened or lengthened over time, which were found to be closely associated with the temporal variation in COVID-19 case profiles and public health and social measures and could lead to the biases in predicting ${R}_t$. Accounting for the impact of these factors, the time-varying quantification of serial interval distributions could lead to improved estimation of ${R}_t$, and provide additional insights into the impact of public health measures on transmission.

Evaluation of Maximal Reliability for Multidimensional Measuring Instruments Using Structural Equation Modeling

Multidimensional measuring instruments are often used in behavioral, social, educational, marketing, and biomedical research. For these scales, the paper discusses how to find the optimal score based on their components that is associated with the highest possible reliability. Within the framework of structural equation modeling, an approach to point and interval estimation of the maximal reliability coefficient of general structure measuring instruments is outlined. The procedure allows obtaining in addition the linear combination of all scale components that possesses maximal reliability. The described method is applicable in empirical research with popular statistical software, and is illustrated using an example.

A discrete Weibull proportional odds survival model

The purpose of this paper is to present the development of the Proportional Odds Model for discrete time-to-event data in a survival analysis context. In this work, inferences about the model parameters considering the discrete Weibull as baseline distribution are presented, obtaining the point and interval estimates of the model parameters. In addition, procedures for checking the proportional odds assumption were proposed. Simulation studies were performed to evaluate the asymptotic properties of the estimators. The proposed model is illustrated using a dataset on the survival time of patients with Leukemia.

Time to Diagnosis and Treatment for Ovarian Cancer and Associations with Outcomes: A Systematic Review.

Background: Ovarian cancer is commonly diagnosed symptomatically at an advanced stage. Better survival for early disease suggests improving diagnostic pathways may increase survival. This study examines literature assessing diagnostic intervals and their association with clinical and psychological outcomes. Methods: Medline, EMBASE, and EmCare databases were searched for studies including quantitative measures of at least one interval, published between January 1, 2000 and August 9, 2022. Interval measures and associations (interval, outcomes, analytic strategy) were synthesized. Risk of bias of association studies was assessed using the Aarhus Checklist and ROBINS-E tool. Results: In total, 65 papers (20 association studies) were included and 26 unique intervals were identified. Interval estimates varied widely and were impacted by summary statistic used (mean or median) and group focused on. Of Aarhus-defined intervals, patient (symptom to presentation, n = 23; range [median]: 7-168 days) and diagnostic (presentation to diagnosis, n = 22; range [median]: 7-270 days) were most common. Nineteen association studies examined survival or stage outcomes with most, including five low risk-of-bias studies, finding no association. Conclusions: Studies reporting intervals for ovarian cancer diagnosis are limited by inconsistent definitions and reporting. Greater utilization of the Aarhus statement to define intervals and appropriate analytic methods is needed to strengthen findings from future studies.

Robust Design Based on Cost-Quality Model in Micro-Manufacturing

This paper proposes a novel total cost model for the micro‐products' entire life cycle that takes into account the uncertainty of the model parameters. The total cost includes pre-sale manufacturing and post-sale warranty costs. Additionally, different marketing strategies are also given based on the weight of internal and external costs. Furthermore, limited data and unknown effects in experiments may cause large errors in parameter estimates. This could prevent the achievement of reliable designs. To address this, robust optimization and interval estimation are used. This approach reduces the impact of uncertainty on parameter estimates. It ensures optimality and robustness in micro-manufacturing parameters. Example analysis and numerical simulation results show that the proposed method assists companies in selecting the optimal manufacturing parameter level that aligns with their marketing strategies. Besides, considering uncertainty factors can ensure that the optimization results remain guaranteed, even under the worst-case scenarios.

Different Statistical Inference Algorithms for the New Pareto Distribution Based on Type-II Progressively Censored Competing Risk Data with Applications

In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples.

Different Statistical Inference Algorithms for the New Pareto Distribution Based on Type-II Progressively Censored Competing Risk Data with Applications

In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples.

Optimal Cut-Point Selection Methods Under Binary Classification When Subclasses Are Involved.

In practice, we often encounter binary classification problems where both main classes consist of multiple subclasses. For example, in an ovarian cancer study where biomarkers were evaluated for their accuracy of distinguishing noncancer cases from cancer cases, the noncancer class consists of healthy subjects and benign cases, while the cancer class consists of subjects at both early and late stages. This article aims to provide a large number of optimal cut-point selection methods for such setting. Furthermore, we also study confidence interval estimation of the optimal cut-points. Simulation studies are carried out to explore the performance of the proposed cut-point selection methods as well as confidence interval estimation methods. A real ovarian cancer data set is analyzed using the proposed methods.

Influence of photoperiod on the developmental times of the forensically relevant blow fly species Calliphora vicina (Diptera: Calliphoridae)

Blow flies (Diptera: Calliphoridae) are frequently used in forensic investigations due to their rapid colonization of cadavers. As with other insects, environmental temperature strongly influences their developmental rates. While published research has typically explored not only the impact of the environmental temperature, but also of other factors like tissue type and drug presence on developmental rates, the influence of photoperiod on the developmental rates of forensically relevant blow fly species has remained largely underexplored. Understanding the relationship between photoperiod and developmental times is crucial, as neglecting this aspect could compromise the accuracy of minimum post-mortem interval (minPMI) estimations. The present study investigates the impact of three photoperiod conditions (0:24, 8:16, and 12:12 light:darkness) on the developmental rates of Calliphora vicina, focusing on the duration of the different immature stages and on the total developmental time. Our results revealed significant variation in the intra-puparial stage and total development time across different photoperiods. Notably, a 12:12 photoperiod led to a significantly prolonged intra-puparial stage and total development time compared to the 0:24 photoperiod, suggesting that Calliphora vicina develops faster in total darkness. These findings highlight the importance of considering photoperiod in both laboratory rearing protocols and forensic casework to improve the accuracy and reliability of minPMI estimations. In this regard, preliminary guidelines and recommendations are provided.

Confidence intervals for median absolute deviations

The median absolute deviation (MAD) is a robust measure of scale that is simple to implement, easy to interpret and often reported as a measure of dispersion when data is skewed. However, confidence intervals either for a single MAD or for the comparison of two MADs are lacking, meaning that interpretations may be subjective. We introduce interval estimators of the MAD to make reliable inferences for dispersion based on MADs. Our simulation results show that the coverages of the intervals are very close to the nominal for a variety of distributions, including those heavily skewed. We also present examples that clearly highlight the advantages of using these intervals instead of the heavily criticized intervals derived from sample variances for skewed data.

Multi-task learning mixture density network for interval estimation of the remaining useful life of rolling element bearings

Existing remaining useful life (RUL) predictions of rolling element bearings have the following shortcomings. 1) Model-driven methods typically employ a sole model for processing the data of an individual, making it challenging to accommodate the variety of degradation behaviors and susceptible to abnormal interference. 2) Data-driven methods place greater emphasis on training data, and in reality, it can be challenging to acquire comprehensive data covering the lifecycle. 3) Many studies fail to give adequate attention to the assessment of RUL uncertainty. This paper proposes a multi-task learning mixture density network (MTL-MDN) method to address these issues. Firstly, the peak-of-Histogram (PoHG) is extracted and served as the novel health indicators. Secondly, multi-task learning dictionaries are constructed based on the evolution law of PoHG, thus combining both model-driven and data-driven strategies. Finally, a multi-task learning strategy is proposed with mixture density networks. It effectively accomplishes the collaborative learning objective of numerous degradation samples in the regression problem and accomplishes the uncertainty assessment of RUL. After analyzing the experimental and real-world degradation data of rolling element bearings throughout their lifecycle, and comparing it to other modern RUL prediction methods, it becomes evident that the proposed MTL-MDN method offers superior prediction accuracy and robustness.

Data analysis with applications in physics and engineering using XLindley model with improved adaptive Type-II progressively censored samples

Recently, a novel improved adaptive Type-II progressive censoring strategy has been suggested in order to obtain adequate data from trials that require a lengthy amount of time. Considering this scheme, this paper focuses on various classical and Bayesian estimation challenges for parameter and some reliability metrics for the XLindley distribution. Two classical estimation methods are considered from the classical perspective to get the point and interval estimations of the model parameter as well as reliability and hazard rate functions. In addition to the usual approaches, the Bayesian methodology is looked at by leveraging the squared error loss function and the Markov chain Monte Carlo technique. The Bayes point and credible intervals are obtained based on two forms of the posterior distribution. A simulation examination is implemented adopting multiple circumstances to distinguish between the conventional and Bayesian estimations. The simulation results demonstrate that the Bayesian approach using the likelihood function is superior for estimating the model parameter when compared with the other methods. In contrast, when estimating reliability metrics, it is advisable to utilize the Bayesian method with the spacings function. Two real-world data sets are analyzed to integrate the proposed approaches into practice, and the ideal progressive censoring strategy is chosen using some optimality criteria.

Estimation of Prediction Intervals for Performance Assessment of Building Using Machine Learning.

This study utilizes artificial neural networks (ANN) to estimate prediction intervals (PI) for seismic performance assessment of buildings subjected to long-term ground motion. To address the uncertainty quantification in structural health monitoring (SHM), the quality-driven lower upper bound estimation (QD-LUBE) has been opted for global probabilistic assessment of damage at local and global levels, unlike traditional methods. A distribution-free machine learning model has been adopted for enhanced reliability in quantifying uncertainty and ensuring robustness in post-earthquake probabilistic assessments and early warning systems. The distribution-free machine learning model is capable of quantifying uncertainty with high accuracy as compared to previous methods such as the bootstrap method, etc. This research demonstrates the efficacy of the QD-LUBE method in complex seismic risk assessment scenarios, thereby contributing significant enhancement in building resilience and disaster management strategies. This study also validates the findings through fragility curve analysis, offering comprehensive insights into structural damage assessment and mitigation strategies.

Doubly Robust Augmented Model Accuracy Transfer Inference with High Dimensional Features

Transfer learning is crucial for training models that generalize to unlabeled target populations using labeled source data, especially in real-world studies where label scarcity and covariate shift are common. While most research focuses on model estimation, there is limited literature on transfer inference for model accuracy despite its importance. We introduce a novel Doubly Robust Augmented Model Accuracy Transfer Inferen Ce (DRAMATIC) method for point and interval estimation of commonly used classification performance measures in an unlabeled target population with labeled source data. DRAMATIC derives and evaluates a potentially misspecified risk model for a binary response, leveraging high-dimensional adjustment features from both source and target data. It builds on an imputation model for the response mean and a density ratio model to characterize distributional shifts. The method constructs doubly robust estimators that are valid when either model is correctly specified and certain sparsity assumptions hold. Simulations show negligible bias in point estimation and satisfactory empirical coverage levels in confidence intervals. The utility of DRAMATIC is illustrated by transferring a genetic risk prediction model and its accuracy evaluation for type II diabetes across two patient cohorts in Mass General Brigham (MGB). Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Reliability estimation of s-out-of-k system with Kumaraswamy distribution based on partially constant stress accelerated life tests

In reliability theory, the reliability inference for s-out-of-k systems holds significant importance. In this paper, we explore the estimation of reliability for s-out-of-k systems based on partially constant stress accelerated life tests. Assume that the latent failure times of the components follow the Kumaraswamy distribution. Maximum likelihood estimates for the unknown parameters are established, and their uniqueness is demonstrated. In addition, confidence intervals for the unknown parameters are constructed using the covariance matrix. Confidence intervals for the reliability functions are determined by the Delta method, while Bootstrap intervals are provided for comparison purposes. Subsequently, Bayesian point and interval estimates based on MCMC techniques considering different loss functions are discussed. Lastly, we conduct an extensive simulation study and analyse one real data set, which reveals that the Bayesian approach yields the best results.

Zonotopic state estimation and sensor fault detection for a wastewater treatment bioprocess

AbstractIn this paper, a fault diagnosis method for the basic process of microbial growth in wastewater treatment based on interval estimation technology is proposed. First, a nonlinear microbial growth model is converted into a linear time‐varying system. A time‐varying observer is then designed for the generated system, which takes into account an performance. Furthermore, a zonotope‐based set‐membership estimation algorithm is analyzed to synchronize interval estimation operations. In addition, interval residuals are computed from the generated interval state estimation and fault diagnosis is performed for a wastewater treatment bioprocess with sensor fault signals. Finally, the feasibility of the proposed fault diagnosis strategy for the wastewater treatment bioprocess is illustrated through numerical simulations.

Identification of a single plasma parcel during a radial alignment of the Parker Solar Probe and Solar Orbiter

Configurations in which two spacecraft, such as the Parker Solar Probe (PSP) and Solar Orbiter, are radially aligned provide opportunities for studying the evolution of a single solar wind parcel during so-called plasma line-ups. The most critical part of these studies arguably is the identification of what can be considered the same plasma crossing both spacecraft. We present here a method that allowed us to determine what we think to be the same plasma parcel that passed through PSP (∼0.075 au) and Solar Orbiter (∼0.9 au) after their radial alignment on April 29, 2021. We started by modeling the plasma propagation in order to obtain a first estimation of the plasma line-up intervals. The identification of the same density structure (with a crossing duration ∼1.5 h) that passed through the two spacecraft allowed us to specify and confirm this estimate. Our main finding is that the density structure was very stable and remained well recognizable from PSP to Solar Orbiter despite its journey of ∼137 hours in the inner heliosphere. We found, moreover, that the slow solar wind plasma parcel was significantly accelerated (from ∼200 to ∼300 km s−1) during its propagation.

No evidence in favor of the existence of "intentional" binding.

Intentional binding refers to the subjective temporal compression between a voluntary action and its subsequent sensory outcome. Despite some studies challenging the link between temporal compression and intentional action, intentional binding is still widely used as an implicit measure for the sense of agency. The debate remains unsettled primarily because the experimental conditions used in previous studies were confounded with various alternative causes for temporal compression, and action intention has not yet been tested comprehensively against all potential alternative causes in a single study. Here, we solve this puzzle by jointly comparing participants' estimates of the interval between three types of triggering events with comparable predictability-voluntary movement, passive movement, and external sensory event-and an external sensory outcome (auditory or visual across experiments). The results failed to show intentional binding, that is, no shorter interval estimation for the voluntary than the passive movement conditions. Instead, we observed temporal (but not intentional) binding when comparing both movement conditions with the external sensory condition. Thus, temporal binding appears to originate from sensory integration and temporal prediction, not from action intention. As such, these findings underscore the need to reconsider the use of "intentional binding" as a reliable proxy of the sense of agency. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

An iterative interval estimation approach to nonlinear discrete-time systems

An iterative interval estimation approach to nonlinear discrete-time systems

Association between gender-affirming hormone therapy and measures of glucose metabolism: A longitudinal study.

The long-term effect of gender-affirming hormone therapy (GAHT) on glucose metabolism is an area of priority in transgender health research. To evaluate the relation between GAHT and changes in fasting blood glucose (FG) and glycosylated hemoglobin (HbA1c) in transmasculine (TM) and transfeminine (TF) persons relative to the corresponding temporal changes in presumably cisgender persons (i.e. without any evidence of TGD status). Retrospective cohort study. Three large integrated health systems. 2,425 TF and 2,127 TM persons compared with 33,995 cisgender males (CM) and 38,913 cisgender females (CF) enrolled in the same health plans. Temporal changes in FG and HbA1c levels examined using linear mixed models with main results expressed as ratios-of-ratios. The pre- versus post-GAHT ratios-of-ratio (95% confidence interval) estimates adjusted for age, race/ethnicity, study site, and body mass index in the model comparing TF and CM groups were 1.05 (1.01, 1.09) for FG and 1.03 (0.99, 1.06) for HbA1c. By contrast, the corresponding results in the models contrasting TM and cisgender cohort members were in the 0.99-1.00 range. The ratio-of-ratios comparing post-GAHT changes among transgender and cisgender persons were close to the null and without a discernable pattern. Though the within-transgender cohort data suggest an increase in the levels of FG and HbA1c following feminizing GAHT initiation, these changes were no longer evident when compared with the corresponding changes in cisgender referents. Based on these results, clinically important effects of GAHT on routine laboratory markers of glucose metabolism appear unlikely.