Frequentist Methods Research Articles

Whitespotted eagle ray (Aetobatus narinari) age and growth in wild (in situ) versus aquarium-housed (ex situ) individuals: Implications for conservation and management

Elasmobranchs typically display slow growth, late maturity and low fecundity life history characteristics, making them vulnerable to fishing pressures and environmental perturbations. The whitespotted eagle ray (Aetobatus narinari), a large pelagic migratory ray with an endangered status on the IUCN Red List, fits this pattern based on available literature. Historically, age and growth parameters for this ray have been reported through vertebral ageing methods. However, the periodicity of vertebrate band pair formation, which is used for ageing, has not been validated for this species, making ageing accuracy and thus the resulting growth parameters uncertain. In this study, we used both a frequentist and Bayesian method of estimating sex-specific von Bertalanffy growth parameters (DW∞, k) in wild recaptured versus aquarium-housed rays. Additionally, we estimated growth from repeated measurement data collected from aquarium-housed rays, as an alternative approach to obtain growth parameters while allowing for individual variability. Between 2009 and 2020, 589 whitespotted eagle rays were caught, measured, tagged and released along the southwest coast of Florida. Of these rays, 34 were recaptured between 5–1413 days at liberty. Nineteen additional rays were collected during the same period, transported and maintained at Georgia Aquarium, Atlanta, where they were regularly weighted and measured. Data from Association of Zoos and Aquariums accredited facilities provided prior information on maximum size for the Bayesian estimations, and size at birth, size at maturity, and maximum life span. These data were used to plot and interpret von Bertalanffy growth curves. Wild whitespotted eagle rays were found to grow faster and mature earlier than previously thought, with Bayesian estimates of k = 0.28 year-1 in females, and k = 0.30 year-1 in males. Aquarium-housed individuals seemed to grow slower and reach smaller sizes, although data provided by the aquariums showed variable growth patterns depending on the facility. Longevity was estimated at 14-15 years in wild rays while maximum lifespan observed in aquariums was 19-20+ years. Life history parameters and growth trajectories generated from this study offer valuable information to aid with future conservation management strategies of this endangered species.

Methods for estimation of genetic parameters in soybeans: an alternative to adjust residual variability

Selection practices are maximized when plant breeders have the availability of consolidated parameters, which will guide direct and indirect selection methods. This study aimed to apply a biometric alternative to minimize residual variance and maximize selection parameters by parent-progeny regression, interim controls, and mixed linear models intrinsic to breeding. The obtained data were subjected to the assumptions of the statistical model, which identified the normality and homogeneity of the residual variances and model additivity. Subsequently, two analysis scenarios were created. The first preserved all information obtained in the experiment, both from segregating families and pure-line cultivars, and was called original scenario. The other scenario preserved progeny data, but the residual variability of controls was restricted using as criterion observations contained between the interval of the first sample standard deviation. Thereby, an acceptable residue limit could be obtained. Both scenarios were submitted to three consolidated frequentist methods (genitor-progeny regression; sum of squares of augmented block design with interim controls; and mixed linear models, wherein random genetic effects are taken as weighted genetic parameters by the genealogical matrix). Restricting residual variation in parents or controls can maximize genetic parameters and genetic gains in soybean breeding. Significant heritability estimate gains were obtained in the augmented blocks with interim control approach. Mixed linear models with random genetic effects can be considered a great tool to obtain genetic parameters in experiments with a high magnitude of common and regular treatments.

Uncertainty quantification for characterization of rock elastic modulus based on P-velocity

ABSTRACT The elastic modulus of rock is an important parameter in rock engineering, but the common methods based on laboratory tests are laborious, especially for obtaining the probability distribution of the elastic modulus that is required in reliability-based design. Many scholars have studied the regression model between the elastic modulus and P-wave velocity; however, most previous reports have ignored the characterization of parameter variability and model uncertainty. To address this problem, a large number of granite samples are collected from the Yingliangbao hydropower station (YLB), compressive wave velocity (P-wave velocity) and uniaxial compression tests are carried out in the laboratory. Then, four different regression models based on the frequentist method and Bayesian method are established to estimate the elastic modulus, the normal priors are adopted by prior analysis and the widely applicable information criterion (WAIC) is used to select the most appropriate Bayesian regression model. Finally, the effects of sample size and sample selection on different methods are studied, the results obtained from different priors are compared. The results show that the Bayesian method provides estimations that are more consistent with the test data and has better robustness in given sets of different sample selections, especially in small sample size.

Frequentist and Bayesian Hypothesis Testing: An Intuitive Guide for Urologists and Clinicians

AbstractGiven the limitations of frequentist method for null hypothesis significance testing, different authors recommend alternatives such as Bayesian inference. A poor understanding of both statistical frameworks is common among clinicians. The present is a gentle narrative review of the frequentist and Bayesian methods intended for physicians not familiar with mathematics. The frequentist p-value is the probability of finding a value equal to or higher than that observed in a study, assuming that the null hypothesis (H0) is true. The H0 is rejected or not based on a p threshold of 0.05, and this dichotomous approach does not express the probability that the alternative hypothesis (H1) is true. The Bayesian method calculates the probability of H1 and H0 considering prior odds and the Bayes factor (Bf). Prior odds are the researcher's belief about the probability of H1, and the Bf quantifies how consistent the data is concerning H1 and H0. The Bayesian prediction is not dichotomous but is expressed in continuous scales of the Bf and of the posterior odds. The JASP software enables the performance of both frequentist and Bayesian analyses in a friendly and intuitive way, and its application is displayed at the end of the paper. In conclusion, the frequentist method expresses how consistent the data is with H0 in terms of p-values, with no consideration of the probability of H1. The Bayesian model is a more comprehensive prediction because it quantifies in continuous scales the evidence for H1 versus H0 in terms of the Bf and the posterior odds.

Multicomponent Stress-Strength Reliability estimation based on Unit Generalized Exponential Distribution

Estimation of stress-strength reliability is considered based on frequentist and Bayesian methods of estimation when both stress and strength variables follow unit generalized exponential distributions. In frequentist method we consider maximum likelihood, least squares, weighted least squares and maximum product spacing methods to estimate system reliability when a common scale parameter is unknown. Further asymptotic and bootstrap intervals of system reliability are obtained. Next, we discuss Bayesian procedure under different loss functions using gamma and weighted Lindley priors for model parameters to estimate system reliability. Subsequently, highest posterior density credible intervals are also obtained. Besides, uniformly minimum variance unbiased estimator of system reliability is obtained when the common scale parameter is known. Extensive Monte-Carlo simulation studies are conducted to evaluate the performance of proposed estimates with respect to various criteria. Finally, to show the applicability of the proposed methodologies in a real-life scenario, an engineering data set is analyzed.

Pseudo Bayesian Mixed Models under Informative Sampling

Abstract When random effects are correlated with survey sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no longer produces asymptotically unbiased inference. We construct a weight-exponentiated formulation for the random effects distribution that achieves approximately unbiased inference for generating hyperparameters of the random effects. We contrast our approach with frequentist methods that rely on numerical integration to reveal that the pseudo Bayesian method achieves both unbiased estimation with respect to the sampling design distribution and consistency with respect to the population generating distribution. Our simulations and real data example for a survey of business establishments demonstrate the utility of our approach across different modeling formulations and sampling designs. This work serves as a capstone for recent developmental efforts that combine traditional survey estimation approaches with the Bayesian modeling paradigm and provides a bridge across the two rich but disparate sub-fields.

Analyzing dispersion effects from replicated order-of-addition experiments

Dispersion effects may play a vital role, in addition to location effects, in exploring optimal addition orders of several materials in some chemical, industrial and pharmaceutical studies. Two replication-based statistical methods developed using frequentist and fiducial probability arguments are introduced in this paper to identify active dispersion effects from replicated order-of-addition experiments. Simulation results show that both approaches can maintain empirical sizes sufficiently close to the nominal level while their finite-sample performances are very similar. From a statistical perspective, the fiducial method can provide a unified probability framework to analyze dispersion effects as well as location effects. However, it is computationally more expensive than the frequentist method. Consequently, the frequentist method is recommended for real-world applications due to its low computational cost. A drug combination study is used to illustrate these two approaches. In addition, some eligible order-of-addition designs are collected in a catalogue for future work.

Statistical approaches to make sense of data in biology and medicine

There are four major paradigms in statistics: Frequentist, Bayesian, likelihood, and modeling. A quadrangle approach that makes use of all these four paradigms is proposed to get a complete understanding of any biological phenomenon. Each of these paradigms can be used to study different aspects of a biological phenomenon. The elements are defined here as an observer, observed, and context, and the model generated should have information derived from these three elements. They can be analyzed, respectively, by Bayesian, frequentist, likelihood, and modeling methods. There is a continuous debate on frequentist and Bayesian approaches in statistics. Biologists often use frequentist methods whereas clinicians are interested in Bayesian methods. In this article, the debate on both these approaches has been discussed in light of understanding uncertainty. The Dempster-Shafer theory addresses the relationship between belief and plausibility but has been criticized for producing counterintuitive results in conflict situations. It is argued here that this can be resolved by inferring that frequentist and Bayesian approaches are inverse to each other.

Left atrial appendage occlusion should be offered only to select atrial fibrillation patients.

Left atrial appendage occlusion should be offered only to select atrial fibrillation patients.

Before/after Bayes: A comparison of frequentist and Bayesian mixed-effects models in applied psychological research.

Bayesian methods are becoming increasingly used in applied psychological research. Previous researchers have thoroughly written about much of the details already, including the philosophy underlying Bayesian methods, computational issues associated with Bayesian model estimation, Bayesian model development and summary, and the role of Bayesian methods in the so-called replication crisis. In this paper, we seek to provide case studies comparing the use of frequentist methods to the use of Bayesian methods in applied psychological research. These case studies are intended to 'illustrate by example' the ways that Bayesian modelling differs from frequentist modelling and the differing conclusions that one may arrive at using the two methods. The intended audience is applied psychological researchers who have been trained in the traditional frequentist framework, who are familiar with mixed-effects models and who are curious about how statistical results might look in a Bayesian context. Along with our case studies, we provide general opinions and guidance on the use of Bayesian methods in applied psychological research.

Analysis of Wilson‐Hilferty distribution under progressive Type‐II censoring

AbstractA new re‐parameterize form of the Wilson‐Hilferty distribution for data modelling with increasing, decreasing and bathtub shape hazard rates has been considered. This paper takes into account the estimation for the unknown model parameters, reliability function and hazard function based on two frequentist methods and Bayesian method of estimation using Type‐II progressively censored data. In frequentist method, besides conventional likelihood based estimation, another competitive method, known as maximum product of spacing (MPS) method is proposed to estimate the model parameters, reliability function and hazard function as an alternative approach to the common likelihood method. In Bayesian paradigm, we have also considered the MPS function as an alternative to the traditional likelihood function and both are also discussed under the Bayesian set up for unknown parameters, reliability function and hazard function. Moreover, for all considered unknown quantities, the approximate confidence intervals under the proposed frequentist approaches as well as the Bayes credible intervals are constructed. Extensive Monte‐Carlo simulation studies are conducted to evaluate the performance of the proposed estimates with respect to various criteria quantities. Furthermore, we discuss an optimal progressive censoring plan among different competing censoring plans using three optimality criteria. Finally, to show the applicability of the proposed methodologies in a real‐life scenario, an engineering dataset is analysed.

Adjusting for Publication Bias in JASP and R: Selection Models, PET-PEESE, and Robust Bayesian Meta-Analysis

Meta-analyses are essential for cumulative science, but their validity can be compromised by publication bias. To mitigate the impact of publication bias, one may apply publication-bias-adjustment techniques such as precision-effect test and precision-effect estimate with standard errors (PET-PEESE) and selection models. These methods, implemented in JASP and R, allow researchers without programming experience to conduct state-of-the-art publication-bias-adjusted meta-analysis. In this tutorial, we demonstrate how to conduct a publication-bias-adjusted meta-analysis in JASP and R and interpret the results. First, we explain two frequentist bias-correction methods: PET-PEESE and selection models. Second, we introduce robust Bayesian meta-analysis, a Bayesian approach that simultaneously considers both PET-PEESE and selection models. We illustrate the methodology on an example data set, provide an instructional video ( https://bit.ly/pubbias ) and an R-markdown script ( https://osf.io/uhaew/ ), and discuss the interpretation of the results. Finally, we include concrete guidance on reporting the meta-analytic results in an academic article.

Seed quality of Brachiaria brizantha by X-ray image analysis using a Bayesian approach

Brachiaria brizantha is the most economically important forage grass in Brazil and is propagated through sowing. Producing high-quality seeds has been a constant challenge due to their uneven maturation. The development and application of precise and non-destructive methods for identifying internal damages to seeds, such as the X-ray test, which quickly indicates the quality of the lots, is of fundamental importance for the seed industry. In this work, the quality of Brachiaria brizantha seeds was analyzed based on the morphological characteristics observed in X-ray images that were related to viability using a mixture model under a Bayesian approach, with the following objectives: i) verify the adequacy of the Bayesian modeling used in the data analysis; ii) associate the efficiency of using radiographs as a way to assess the viability of the seeds; and iii) relate the classifications carried out by evaluators with the probability of originating normal or abnormal seedlings. The methodology applied for the analysis proved to be adequate. Further, the Bayesian estimates for parameters related to internal morphology were established with associated levels of uncertainty, which represents an advantage over usual frequentist methods. Based on the model's estimates, seeds evaluated as potentially unviable by three evaluators had practically no probability of germination and did not germinate in the test applied later. Seeds classified as potentially viable had a high probability of developing into normal seedlings, while 73.27% showed this property in the germination test.

Quantifying uncertainty of sediment fingerprinting mixing models using frequentist and Bayesian methods: A case study from the Iranian loess Plateau

Sediment fingerprinting is widely used in drainage basin analysis to identify the provenance and source contributions of sediments (or other material) in transit from source-to-sink. By enabling source areas of sediment supply to be targeted, the method has become an integral part of sustainable landscape management. The precision and accuracy of sediment fingerprinting is contingent on the choice of mixing model, which quantifies the contribution of potential sediment sources by minimizing the difference between observed properties of sink samples and characteristic properties of the sources. Here, we apply a set of frequentist and Bayesian mixing models with the aim of identifying the optimum composite fingerprint of four sediment sources (viz., agricultural land, rangeland, gullies, and landslides) in a small catchment draining the Iranian Loess Plateau in the Golestan province of northeastern Iran. Forty-four soil samples were collected from the four potential source zones. Based on seven synthetic mixtures with known source contributions we compared the performance of a frequentist Monte Carlo model, GLUE model, a Bayesian end-member model (BEMMA), MixSIAR Bayesian model, and a Brewer Bayesian model. We found that, in terms of uncertainty estimation, the best results were obtained with GLUE and BEMMA. Applying GLUE to our study catchment, we estimated the following source contributions to an earth dam reservoir: agricultural land (55.8 %), rangeland (33.7 %), gullies (15.7 %), and landslides (14.2 %), confirming the view that agriculture is the main cause of reservoir sedimentation. All source contributions exhibited high variability, which we attribute to storm frequency, sediment delivery due to hillslope-sink connectivity, and human activities involving removal of vegetation.

The efficacy and tolerability of antibiotics in scrub typhus: an updated network meta-analysis of randomized controlled trials

ObjectivesInadequate treatment of scrub typhus results in severe complications such as septic shock and is also associated with a high median mortality rate of 6%. However, there has been no conclusive evidence about the superiority of different antibiotics in managing scrub typhus in terms of efficacy and tolerability. MethodsWe conducted a network meta-analysis (NMA) using the frequentist method. The included participants were pediatric and adult patients infected with scrub typhus. The primary outcome was the cure rate in the patients included. The subgroup analysis was done according to pediatric or adult patients. ResultsOverall, 14 randomized controlled trials (RCTs) with 1264 participants were included in this study. The NMA revealed that all the investigated antibiotics were associated with cure rates similar to those of doxycycline. The chloramphenicol and minocycline were ranked to be associated with the highest cure rate in the pediatric subgroup and adult subgroup, respectively. Second-generation quinolones, including ofloxacin, ciprofloxacin, and chloramphenicol, were associated with significantly lower adverse event rates than doxycycline. ConclusionThe current updated NMA provides evidence for the efficacy of chloramphenicol and minocycline in scrub typhus management. However, future large-scale RCTs with longer follow-up times are warranted.

Death and invasive mechanical ventilation risk in hospitalized COVID-19 patients treated with anti-SARS-CoV-2 monoclonal antibodies and/or antiviral agents: A systematic review and network meta-analysis protocol.

The ongoing COVID-19 pandemic has claimed >4 million lives globally, and these deaths often occurred in hospitalized patients with comorbidities. Therefore, the proposed review aims to distinguish the inpatient mortality and invasive mechanical ventilation risk in COVID-19 patients treated with the anti-SARS-CoV-2 monoclonal antibodies and/or the antiviral agents. A search in PubMed, Embase, and Scopus will ensue for the publications on randomized controlled trials testing the above, irrespective of the publication date or geographic boundary. Risk of bias assessment of the studies included in the review will occur using the Cochrane risk of bias tool for randomized trials (RoB 2). Frequentist method network meta-analyses (NMA) will compare each outcome's risk across both types of anti-SARS-CoV-2 agents in one model and each in separate models. Additional NMA models will compare these in COVID-19 patients who were severely or critically ill, immunocompromised, admitted to the intensive care unit, diagnosed by nucleic acid amplification test, not treated with steroids, <18 years old, and at risk of infection due to variants of concern. The plan of excluding non-hospitalized patients from the proposed review is to minimize intransitivity risk. The acceptance of the network consistency assumption will transpire if the local and overall inconsistency assessment indicates no inconsistency. For each NMA model, the effect sizes (risk ratio) and their 95% confidence intervals will get reported in league tables. The best intervention prediction and quality of evidence grading will happen using the surface under the cumulative ranking curve values and the Grading of Recommendations Assessment, Development and Evaluation-based Confidence in Network Meta-Analysis approach, respectively. Sensitivity analysis will repeat the preliminary NMA while excluding the trials at high risk of bias. The Stata statistical software (v16) will be used for analysis. The statistical significance will get determined at p<0.05 and 95% confidence interval. PROSPERO Registration No: https://www.crd.york.ac.uk/prospero/display_record.php?ID=CRD42021277663.

Comparison of the Efficacy and Safety Endpoints of Five Therapies for Atrial Fibrillation: A Network Meta-Analysis

IntroductionAtrial fibrillation (AF) is a prevalent arrhythmia that occurs in 2–4% of adults and poses a threat to human health. Thus, comparison of the efficacy and safety of therapies for AF is warranted. Here, we used network analysis to compare efficacy (arrhythmia recurrence and re-hospitalization) and safety (ischemic cerebral vascular events, all-cause mortality, and cardiovascular mortality) endpoints among five major therapies for AF.MethodsThe PubMed, Cochrane, and Embase databases were searched, and relevant literature was retrieved. Only studies that made comparisons among the therapies of interest and involved patients with AF were included. Pairwise comparisons and frequentist method (SUCRA plot) analyses were conducted.ResultsIn total, 62 studies were included in the pooled analysis. In pairwise comparisons, atrioventricular nodal ablation plus permanent pacemaker (AVN + PPM) was associated with a significantly higher risk of atrial arrhythmia recurrence than surgical ablation [odds ratio (OR): 23.82, 95% confidence interval (CI): 1.97–287.59, fixed-effect model; 3.82, 95% CI: 1.01–559.74, random-effects model]. Furthermore, radiofrequency ablation was associated with a significantly lower risk of cardiovascular mortality than medication in pairwise comparison (OR: 0.49, 95% CI: 0.29–0.83, fixed-effect model; OR: 0.49, 95% CI: 0.27–0.9, random-effects model). Frequentist analysis indicated that AVN + PPM had the best performance in reducing the risk of safety and efficacy endpoints.ConclusionNon-pharmaceutical therapies showed superior performance to traditional drug therapy in lowering the risk of safety and efficiency endpoint events. AVN + PPM performed best in reducing the risk of safety and efficacy endpoints.

Inference of Intensity-Based Models for Load-Sharing Systems With Damage Accumulation

To model damage accumulation for load-sharing systems, two models given by intensity functions of self-exciting point processes are proposed: a model with additive damage accumulation and a model with multiplicative damage accumulation. Both models include the model without damage accumulation as a special case. For both models, the likelihood functions are derived and maximum likelihood estimators and likelihood ratio tests are given in a scale-invariant version and a scale-dependent version. Furthermore, a Bayesian approach using Markov chain Monte Carlo methods for posterior computation is provided. The frequentist and Bayesian methods are applied to a data set of failures of tension wires of concrete beams where a significant damage accumulation effect is confirmed by both additive and multiplicative damage accumulation models. This is all the more remarkable as a simulation study indicates that the tests for an existing damage accumulation effect are rather conservative. Moreover, prediction intervals for the failure times of the tension wires in a new experiment are given, which improve former prediction intervals derived without damage accumulation. The simulation study considers a scenario with a fixed time horizon and one with fixed numbers of failed components of the systems.

Bayesian, frequentist, and information geometric approaches to parametric uncertainty quantification of classical empirical interatomic potentials

In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (Markov Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface these tools with the Open Knowledgebase of Interatomic Models and study three models based on the Lennard-Jones, Morse, and Stillinger-Weber potentials. We confirm that IPs are typically sloppy, i.e., insensitive to coordinated changes in some parameter combinations. Because the inverse problem in such models is ill-conditioned, parameters are unidentifiable. This presents challenges for traditional statistical methods, as we demonstrate and interpret within both Bayesian and frequentist frameworks. We use information geometry to illuminate the underlying cause of this phenomenon and show that IPs have global properties similar to those of sloppy models from fields, such as systems biology, power systems, and critical phenomena. IPs correspond to bounded manifolds with a hierarchy of widths, leading to low effective dimensionality in the model. We show how information geometry can motivate new, natural parameterizations that improve the stability and interpretation of uncertainty quantification analysis and further suggest simplified, less-sloppy models.

Half circular modified burr-III distribution, application with different estimation methods.

The data related to many medical, environmental and ecological variables are often measured in terms of angles wherein its range is defined in [0,π). This type of data is referred to as axial or half circular data. Modeling based on half circular data has not received its due share of attention in statistical literature. In this paper, we introduce a new half circular distribution based on inverse stereographic projection technique on modified Burr−III distribution, called the half circular modified Burr−III (hcMB−III) distribution. The basic properties of the proposed distribution are derived. It is common observation that while estimating the parameters of a model, one usually adopts maximum likelihood estimation method as the starting point. In this paper, we consider seven frequentist methods of estimation, besides using maximum likelihood method for estimating the parameters of the hcMB−III distribution. Monte Carlo simulations are performed for investigating the performances of the considered methods in terms of their biases and mean square errors using small, medium and large sample sizes. Finally, one data set related to posterior corneal curvature of the eyes of 23 patients, is analyzed to check potentiality of the newly proposed model.