Traditional Frequentist Approach Research Articles

A cautionary note against selective applications of the Bayes factor.

Bayes factor analysis becomes increasingly popular, among other reasons, because it allows to provide evidence for the null hypothesis, which is not easily possible with the traditional frequentist approach. A conceivable strategy that apparently takes favorable aspects of both approaches on board is to use traditional frequentist analyses first and to support theoretically interesting nil effects by Bayesian analyses thereafter. Here, we asked whether such a selective application of Bayesian analyses to only nonsignificant effects of foregoing frequentist analyses creates bias. In two simulation studies, we observed that such selective application of Bayesian analyses, in fact, severely overestimates evidence in favor of the null hypotheses, when a true population effect exists. While this bias can be attenuated by using more informative priors in the Bayesian analyses, we recommend to not apply such selective combination of analytical approaches, but instead to use either frequentist or Bayesian analyses consistently. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Bayesian statistical analysis reveals spatial heterogeneity in Cyclone Thane deposits from Southeast India

Modern and geological records of storm sedimentary deposits preserved on siliciclastic coastlines are important archives to evaluate the past and current magnitude and impacts of.storms. Examination of modern storm deposits also offers the opportunity to evaluate the similarities and differences between storm and other coastal overwash processes and hazards.We examined the stratigraphy and sedimentary characteristics of the 31st December 2012 Cyclone Thane and underlying coastal units from 14 pits from six sites from the coastal zone of Tamil Nadu Province, southeast India. We analysed the grain size parameters, grain shape, and heavy mineral proportions of each deposit in high resolution and examined the sedimentary structures of each unit. For the first time, we use Bayesian factors to quantitatively evaluate the similarities and differences between the storm sedimentary deposits and other co-located coastal sedimentary deposits. At several sites, the storm deposits differ in several parameters from the underlying coastal deposits, but at some locations, distinguishing between different depositional units cannot be achieved. In comparing the storm deposits from the different sites, mean grain size results in the most coherent pattern with closely located sites having similar mean grain size, and more southerly sites being finer grained. The other measured parameters show a far less coherent pattern with adjacent sites often preserving larger differences than more distal sites attesting to very local hydrodynamic variations during sediment deposition. As with the sedimentary parameters, the sedimentary structures formed during sediment deposition preserved at each site are highly variable. To date, the presence of terminal foresets at the landward edge of washover fans remains the only diagnostic feature of storm deposition, but that this feature is not ubiquitous across all storm deposits. Our findings demonstrate the spatially heterogeneous nature of storm sediment deposition and the challenges of identifying storm deposits in coastal siliciclastic sequences. The use of Bayesian statistical approaches also offers a robust method for evaluating and discriminating between coastal sediment deposits that has many advantages over traditional frequentist approaches. This method can easily be applied to other sedimentary depositional environments.

Confidence distributions and hypothesis testing

The traditional frequentist approach to hypothesis testing has recently come under extensive debate, raising several critical concerns. Additionally, practical applications often blend the decision-theoretical framework pioneered by Neyman and Pearson with the inductive inferential process relied on the p-value, as advocated by Fisher. The combination of the two methods has led to interpreting the p-value as both an observed error rate and a measure of empirical evidence for the hypothesis. Unfortunately, both interpretations pose difficulties. In this context, we propose that resorting to confidence distributions can offer a valuable solution to address many of these critical issues. Rather than suggesting an automatic procedure, we present a natural approach to tackle the problem within a broader inferential context. Through the use of confidence distributions, we show the possibility of defining two statistical measures of evidence that align with different types of hypotheses under examination. These measures, unlike the p-value, exhibit coherence, simplicity of interpretation, and ease of computation, as exemplified by various illustrative examples spanning diverse fields. Furthermore, we provide theoretical results that establish connections between our proposal, other measures of evidence given in the literature, and standard testing concepts such as size, optimality, and the p-value.

Sequential Bayesian updating for time-variant reliability analysis of ageing structures

This paper proposes a new method for time-variant reliability analysis of existing ageing structures under epistemic uncertainty from limited recurrent field measurement data. A growth model and a noise factor are introduced to account for the ageing changes of distribution parameters that take place while the reliability interval is sequentially updated using inspection data acquired over the service period. The method is applied to quantify the reliability of deteriorating concrete bridges under routine inspections of reinforcement steel corrosion. The interval estimation of corrosion and reliability shows narrower uncertainty bounds than a traditional frequentist approach, particularly when relatively sparse inspection datasets are available. In the case study presented, the relative variation of reliability bounds could be reduced by at least half when compared to a frequentist estimation.

An Expected Score Approach to Ordinal Outcomes in a Bayesian, Response Adaptive, Randomized Trial

Ordinal outcomes are common in medicine and can be analyzed in many ways, but the distribution of ordinal data can present unique challenges. The proposed KESETT study is a three-armed, randomized trial comparing two doses of ketamine plus levetiracetam to levetiracetam alone for treating patients with benzodiazepine-refractory status epilepticus. A Bayesian, adaptive clinical trial is proposed employing an ordinal primary outcome at 60 min ranging from 1 (improving consciousness and seizure cessation) to 5 (life-threatening event/death). Based on a previous study, the ordinal outcome is expected to have a bimodal distribution, with the effect of treatment expected to be nonproportional across the outcome scale. As such, approaches relying on assuming proportionality of the odds are not appropriate. We propose for this scenario an analytic approach to compare ordinal outcomes using the expected score derived from the posterior distribution for each treatment group. This approach requires minimal assumptions, maintains the benefit of using the full ordinal scale, is interpretable, and can be used in a Bayesian analysis framework. We compare this new approach under multiple simulated scenarios to three traditional frequentist approaches. The new approach controls Type I error and power, resulting in a sizable reduction in sample size relative to a nonparametric test.

Evidence of parameters underestimation from nonlinear growth models for data classified as limited

Some growth data in aquaculture have peculiar characteristics that generate consequences in the analysis and modeling. They are usually incomplete or limited, as classified in this article. This means data are restricted to a few observations and often are limited to observations below the curve’s inflection point due to economic interests in farm settings, or due to limitation of physical space in controlled research laboratories, for example. This possibly causes under and/or overestimation in the inference of nonlinear models. Through shrimp growth simulations from the Michaelis–Menten curve, the limited data were synthesized with threshold observation up to the first 7, 13, 18, 36, and 82 weeks. Seven sigmoid growth functions (Logistic, Gompertz, von Bertalanffy, Richard, Weibull, Morgan–Mercer–Flodin, and the own Michaelis–Menten growth) were fitted to respective limited data, in order to assess the research hypothesis. Taking the scenarios with incompleteness in the first 7, 13 and 18 weeks, the parameters of all growth curves modeled under a frequentist approach were underestimated. Thus, we propose a correction for this possible problem through a hierarchical Bayesian approach. Real data from shrimp farming in northeastern Brazil were used to compare it with the traditional frequentist approach employed. The sensitivity in detecting outstanding treatment (pond or batch level hierarchy) can make the new method a powerful management tool in animal production, and also in trials designed for scientific research.

An Empirically Driven Guide on Using Bayes Factors for M/EEG Decoding

Bayes factors can be used to provide quantifiable evidence for contrasting hypotheses and have thus become increasingly popular in cognitive science. However, Bayes factors are rarely used to statistically assess the results of neuroimaging experiments. Here, we provide an empirically driven guide on implementing Bayes factors for time-series neural decoding results. Using real and simulated magnetoencephalography (MEG) data, we examine how parameters such as the shape of the prior and data size affect Bayes factors. Additionally, we discuss the benefits Bayes factors bring to analysing multivariate pattern analysis data and show how using Bayes factors can be used instead or in addition to traditional frequentist approaches.

Equivalent statistics for a one-sample t-test.

Recent insights into problems with common statistical practice in psychology have motivated scientists to consider alternatives to the traditional frequentist approach that compares p-values to a significance criterion. While these alternatives have worthwhile attributes, Francis (Behavior Research Methods, 40, 1524-1538, 2017) showed that many proposed test statistics for the situation of a two-sample t-test are based on precisely the same information in a given data set; and for a given sample size, one can convert from any statistic to the others. Here, we show that the same relationship holds for the equivalent of a one-sample t-test. We derive the relationships and provide an on-line app that performs the computations. A key conclusion of this analysis is that many types of tests are based on the same information, so the choice of which approach to use should reflect the intent of the scientist and the appropriateness of the corresponding inferential framework for that intent.

Bayesian Estimation and Testing of a Linear Logistic Test Model for Learning during the Test

ABSTRACT The present study proposes a Bayesian approach for estimating and testing the operation-specific learning model, a variant of the linear logistic test model that allows for the measurement of the learning that occurs during a test as a result of the repeated use of the operations involved in the items. The advantages of using a Bayesian framework compared to the traditional frequentist approach are discussed. The application of the model is illustrated with real data from a logical ability test. The results show how the incorporation of previous practice into the linear logistic model improves the fit of the model as well as the prediction of the Rasch item difficulty estimates. The model provides evidence of learning associated with two of the logic operations involved in the items, which supports the hypothesis of practice effects in deductive reasoning tasks.

3 Estimating the Burden of Dementia in Latin America and the Caribbean: A Systematic Review and Meta-Analysis

Abstract Background and Objectives Rapid increase in life expectancy has resulted in an increase in the global burden of dementia that is expected to become a leading cause of morbidity in the future. Low- and middle-income countries are expected to bear an increasing majority of the burden, but lack data for accurate burden estimates that are key for informing policy and planning. Bayesian methods have recently gained recognition over traditional frequentist approaches for modelling disease burden for their superiority in dealing with severely limited data. This study provides updated estimates of dementia prevalence in Latin America and the Caribbean (LAC) for the years 2015, 2020 and 2030. Given the paucity of data, estimates were developed using a Bayesian methodology and confirmed by the traditional frequentist approach, with the aim of providing methodological insights for future disease burden estimates. Methods A comprehensive systematic literature search was conducted to identify all relevant primary studies published between the years 2010–2018. The quality of the included studies was critically assessed. A random-effects model (REM) and a Bayesian normal-normal hierarchical model (NNHM) were used to obtain the pooled prevalence estimate of dementia for people aged 60 and above. The latter model was also developed to estimate age-specific dementia prevalence. Using UN population estimates, total and age-specific projections of the burden of dementia were calculated. Results The prevalence of dementia in LAC was found to be 14% (10–21%) in those above age 60 based on REM, and 8% (5–11.5%) based on NNHM. The prevalence increased from 2% (1–4%) in people aged 60–69 to 29% (20–37%) in people above the age of 80. The number of people living with dementia in LAC in 2015 was estimated at 5.68 million, with future projections of 6.86 million in 2020 and 9.94 million in 2030. Conclusions The findings of this review found that burden of dementia in LAC is substantial and continues to rapidly grow. The projected rise in dementia cases in the future should prompt urgent governmental response to address this growing public health issue. We were also able to demonstrate that given the overall paucity of data, a Bayesian approach was superior for estimating disease prevalence and burden.

Bayesian survival analysis with BUGS.

Survival analysis is one of the most important fields of statistics in medicine and biological sciences. In addition, the computational advances in the last decades have favored the use of Bayesian methods in this context, providing a flexible and powerful alternative to the traditional frequentist approach. The objective of this article is to summarize some of the most popular Bayesian survival models, such as accelerated failure time, proportional hazards, mixture cure, competing risks, multi-state, frailty, and joint models of longitudinal and survival data. Moreover, an implementation of each presented model is provided using a BUGS syntax that can be run with JAGS from the R programming language. Reference to other Bayesian R-packages is also discussed.

Systematic review estimating the burden of dementia in the WHO Southeast Asia Region using Bayesian and frequentist approaches

BackgroundRapid increase in life expectancy in low- and middle-income countries including the World Health Organization’s Southeast Asia Region (SEAR) has resulted in an increase in the global burden of dementia, which is expected to become a leading cause of morbidity. Accurate burden estimates are key for informing policy and planning. Given the paucity of data, estimates were developed using both a Bayesian methodology and as well as a traditional frequentist approach to gain better insights into methodological approaches for disease burden estimates.MethodsSeven databases were searched for studies published between 2010-2018 regarding dementia prevalence in SEAR, generating 8 relevant articles. A random-effects model (REM) and a Bayesian normal-normal hierarchical model (NNHM) were used to obtain the pooled prevalence estimate of dementia for people aged 60 and above in SEAR. The latter model was also developed to estimate age-specific dementia prevalence. Using UN population estimates for SEAR, total and age-specific projections of the burden of dementia in 2015, 2020 and 2030 were calculated.ResultsThe prevalence of dementia in SEAR was found to be 3% (95% confidence interval (CI) = 2-6%) in those above age 60 based on REM, and 3.1% (95% credible interval = 1.5-5.0%) based on the NNHM. The estimated prevalence varies with age, increasing from 1.6% (95% credible interval = 0.8-2.5%) in people aged 60-69 to 12.4% (95% credible interval = 5.6-20%) in people above the age of 80. The risk of developing dementia increased exponentially with age. The number of people living with dementia in SEAR in 2015 was estimated at 5.51 million (95% credible interval = 2.66-8.82), with projections of 6.66 million (95% credible interval = 3.21-10.7) in 2020 and 9.6 million (95% credible interval = 4.62-15.36) in 2030.ConclusionThe burden of dementia in SEAR is substantial and will continue to increase rapidly by 2030. The lack of research focusing on dementia in SEAR points to a significant under-recognition of this disease. The projected rise in dementia cases in the future should prompt urgent governmental response to address this growing public health issue. We also argue that given the overall paucity of data for the region, the Bayesian approach offers a promising methodology for improved estimates of disease prevalence and burden and should continue to be explored.

Analysis of type I and II error rates of Bayesian and frequentist parametric and nonparametric two-sample hypothesis tests under preliminary assessment of normality

Testing for differences between two groups is among the most frequently carried out statistical methods in empirical research. The traditional frequentist approach is to make use of null hypothesis significance tests which use p values to reject a null hypothesis. Recently, a lot of research has emerged which proposes Bayesian versions of the most common parametric and nonparametric frequentist two-sample tests. These proposals include Student’s two-sample t-test and its nonparametric counterpart, the Mann–Whitney U test. In this paper, the underlying assumptions, models and their implications for practical research of recently proposed Bayesian two-sample tests are explored and contrasted with the frequentist solutions. An extensive simulation study is provided, the results of which demonstrate that the proposed Bayesian tests achieve better type I error control at slightly increased type II error rates. These results are important, because balancing the type I and II errors is a crucial goal in a variety of research, and shifting towards the Bayesian two-sample tests while simultaneously increasing the sample size yields smaller type I error rates. What is more, the results highlight that the differences in type II error rates between frequentist and Bayesian two-sample tests depend on the magnitude of the underlying effect.

Bayesian methods for clinicians.

Background: The Bayesian methods have received more attention in medical research. It is considered as a natural paradigm for dealing with applied problems in the sciences and also an alternative to the traditional frequentist approach. However, its concept is somewhat difficult to grasp by nonexperts. This study aimed to explain the foundational ideas of the Bayesian methods through an intuitive example in medical science and to illustrate some simple examples of Bayesian data analysis and the interpretation of results delivered by Bayesian analyses. In this study, data sparsity, as a problem which could be solved by this approach, was presented through an applied example. Moreover, a common sense description of Bayesian inference was offered and some illuminating examples were provided for medical investigators and nonexperts. Methods: Data augmentation prior, MCMC, and Bayes factor were introduced. Data from the Khuzestan study, a 2-phase cohort study, were applied for illustration. Also, the effect of vitamin D intervention on pregnancy outcomes was studied. Results: Unbiased estimate was obtained by the introduced methods. Conclusion: Bayesian and data augmentation as the advanced methods provide sufficient results and deal with most data problems such as sparsity.

Bayesian analysis on interactions of exotic nuclear systems

Even though the Bayesian method has been proved to be powerful in the field of nuclear physics, it has not yet been implemented to study the properties of the reaction systems with exotic nuclei, for instance, the gross feature of the phenomenological interaction potential. So far, the optical model potential was typically evaluated by the traditional frequentist approach. However, contradictive conclusions were drawn, especially on the near-threshold behavior of the imaginary potential: threshold anomaly and abnormal threshold anomaly were derived for 6Li+209Bi and 6He+208Pb even with the same elastic scattering data. In this study, we first applied the Bayesian framework to analyze the elastic scattering data of 6Li+209Bi. It was found that the results of Bayesian statistics strongly depend on the imposed prior distributions. Therefore, the Bayesian method has to be used with extreme caution, since the improper prior knowledge could lead to completely wrong conclusions. Since the elastic scattering data is not informative enough to constrain the prior and posterior distributions, our analysis further indicates that the results from the non-constraint frequentist approach or the flat prior distribution with a reasonable physical-boundary can be employed as convincing prior knowledge of the Bayesian framework. Based on this result, we further applied the Bayesian approach to the transfer reaction 208Pb(7Li,6He)209Bi, to investigate the optical potentials of the neutron halo system 6He+209Bi in the outgoing channel. With the proper prior distributions, the Bayesian analysis on both the 6Li+209Bi and 6He+208Pb confirm the presence of the abnormal threshold anomaly. Therefore the applicability of the dispersion relation remains in doubt.

Bayes factor: A useful tool to quantitatively evaluate and compare performance of multiple stature estimation equations

When stature estimation of incomplete skeletal remains is necessary, researchers select an estimation equation which will produce the most accurate estimates. The purpose of this study is to propose that, given prior information of a target sample, the Bayes factor can be a useful tool to quantitatively evaluate and compare performance of multiple equations in this regard. This study also explores the best-performing equations to reconstruct statures of Korean War casualties with a demonstration of equation comparisons by the Bayes factor.Thirty-three sets of stature estimates were generated using different equations based on the osteometric data of the Korean War casualties. The distribution of each set was compared to that of the population (i.e., Korean servicemen during the Korean War) using the Bayes factors and posterior probabilities generated by the R codes in the LearnBayes package.A higher Bayes factor indicates a closer similarity between the two distributions under comparison. The equation with the highest Bayes factor in this study was Choi et al.’s (1997) humerus equation (bf=9.84), followed by the femur equation of the same authors (bf=5.3).The Bayesian approach has advantages over the traditional frequentist approach primarily based on the p-value. Particularly, the Bayes factor can provide practical interpretations on the models under comparison, which allows for a quantitative prioritization of different models. Researchers can obtain more accurate stature estimates of a target sample by using the equation of the highest Bayes factor.

An automatic robust Bayesian approach to principal component regression

Principal component regression uses principal components (PCs) as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We introduce a Bayesian approach that is robust to outliers in both the dependent variable and the covariates. Outliers can be thought of as observations that are not in line with the general trend. The proposed approach automatically penalises these observations so that their impact on the posterior gradually vanishes as they move further and further away from the general trend, corresponding to a concept in Bayesian statistics called whole robustness. The predictions produced are thus consistent with the bulk of the data. The approach also exploits the geometry of PCs to efficiently identify those that are significant. Individual predictions obtained from the resulting models are consolidated according to model-averaging mechanisms to account for model uncertainty. The approach is evaluated on real data and compared to its nonrobust Bayesian counterpart, the traditional frequentist approach and a commonly employed robust frequentist method. Detailed guidelines to automate the entire statistical procedure are provided. All required code is made available, see ArXiv:1711.06341.

Higher-Order Asymptotics and Its Application to Testing the Equality of the Examinee Ability Over Two Sets of Items.

In educational and psychological measurement, researchers and/or practitioners are often interested in examining whether the ability of an examinee is the same over two sets of items. Such problems can arise in measurement of change, detection of cheating on unproctored tests, erasure analysis, detection of item preknowledge, etc. Traditional frequentist approaches that are used in such problems include the Wald test, the likelihood ratio test, and the score test (e.g., Fischer, Appl Psychol Meas 27:3-26, 2003; Finkelman, Weiss, & Kim-Kang, Appl Psychol Meas 34:238-254, 2010; Glas & Dagohoy, Psychometrika 72:159-180, 2007; Guo & Drasgow, Int J Sel Assess 18:351-364, 2010; Klauer & Rettig, Br J Math Stat Psychol 43:193-206, 1990; Sinharay, J Educ Behav Stat 42:46-68, 2017). This paper shows that approaches based on higher-order asymptotics (e.g., Barndorff-Nielsen & Cox, Inference and asymptotics. Springer, London, 1994; Ghosh, Higher order asymptotics. Institute of Mathematical Statistics, Hayward, 1994) can also be used to test for the equality of the examinee ability over two sets of items. The modified signed likelihood ratio test (e.g., Barndorff-Nielsen, Biometrika 73:307-322, 1986) and the Lugannani-Rice approximation (Lugannani & Rice, Adv Appl Prob 12:475-490, 1980), both of which are based on higher-order asymptotics, are shown to provide some improvement over the traditional frequentist approaches in three simulations. Two real data examples are also provided.

A Practical Guide to Gaussian Process Regression for Energy Measurement and Verification within the Bayesian Framework

Measurement and Verification (M&V) aims to quantify savings achieved as part of energy efficiency and energy management projects. M&V depends heavily on metered energy data, modelling parameters and uncertainties that govern the energy system under consideration. M&V therefore requires a stringent handle on the inherent uncertainties in the calculated savings. The Bayesian framework of data analysis in the form of non-parametric, nonlinear Gaussian Process (GP) regression provides a mechanism by which these uncertainties can be quantified thoroughly, and is therefore an attractive alternative to the more traditional frequentist approach. It is important to select appropriate kernels to construct the prior when performing GP regression. This paper aims to construct a guideline for a practical GP regression within the energy M&V framework. It does not attempt to quantify energy losses or savings, but rather presents a case study that could act as a road map for energy managers and M&V professionals to apply the GP regression as a Bayesian alternative to base-line adjustment. Special attention will be given to the selection of appropriate kernels for the application of baseline adjustment and energy savings quantification in a model-independent manner.

Estimation of Profit Efficiency in the Hotel Industry Using a Bayesian Stochastic Frontier Model

The present study measured profit efficiency and its determinants in the hotel sector in Spain from 2010 to 2014, using a Bayesian stochastic frontier approach. This model provides estimates of efficiency and more accurate confidence intervals than the traditional frequentist approach. The results revealed that the hotels are operating with significant profit inefficiencies. These inefficiencies are significantly affected by size, location, occupancy rate by region, customer satisfaction, and whether the hotel is affiliated or independent. Finally, the study points out the strategic implications of these findings, to improve the efficiency of the hotels.