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Bernoulli's 1713 golden theorem is viewed retrospectively in the context of modern model-based frequentist inference that revolves around the concept of a prespecified statistical model M θ x , defining the inductive premises of inference. It is argued that several widely-accepted claims relating to the golden theorem and frequentist inference are either misleading or erroneous: (a) Bernoulli solved the problem of inference 'from probability to frequency', and thus (b) the golden theorem cannot justify an approximate Confidence Interval (CI) for the unknown parameter θ , (c) Bernoulli identified the probability P A with the relative frequency 1 n ∑ k = 1 n x k of event A as a result of conflating f (x 0 | θ) with f (θ | x 0) , where x 0 denotes the observed data, and (d) the same 'swindle' is currently perpetrated by the p value testers. In interrogating the claims (a)–(d), the paper raises several foundational issues that are particularly relevant for statistical induction as it relates to the current discussions on the replication crises and the trustworthiness of empirical evidence, arguing that: [i] The alleged Bernoulli swindle is grounded in the unwarranted claim θ ^ n x 0 ≃ θ ∗ , for a large enough n, where θ ^ n X is an optimal estimator of the true value θ ∗ of θ. [ii] Frequentist error probabilities are not conditional on hypotheses (H0 and H1) framed in terms of an unknown parameter θ since θ is neither a random variable nor an event. [iii] The direct versus inverse inference problem is a contrived and misplaced charge since neither conditional distribution f (x 0 | θ) and f (θ | x 0) exists (formally or logically) in model-based ( M θ x ) frequentist inference. [ABSTRACT FROM AUTHOR]

The debates between Bayesian, frequentist, and other methodologies of statistics have tended to focus on conceptual justifications, sociological arguments, or mathematical proofs of their long run properties. Both Bayesian statistics and frequentist ("classical") statistics have strong cases on these grounds. In this article, we instead approach the debates in the "Statistics Wars" from a largely unexplored angle: simulations of different methodologies' performance in the short to medium run. We used Big Data methods to conduct a large number of simulations using a straightforward decision problem based around tossing a coin with unknown bias and then placing bets. In this simulation, we programmed four players, inspired by Bayesian statistics, frequentist statistics, Jon Williamson's version of Objective Bayesianism, and a player who simply extrapolates from observed frequencies to general frequencies. The last player served a benchmark function: any worthwhile statistical methodology should at least match the performance of simplistic induction. We focused on the performance of these methodologies in guiding the players towards good decisions. Unlike an earlier simulation study of this type, we found no systematic difference in performance between the Bayesian and frequentist players, provided the Bayesian used a flat prior and the frequentist used a low confidence level. The Williamsonian player was also able to perform well given a low confidence level. However, the frequentist and Williamsonian players performed poorly with high confidence levels, while the Bayesian was surprisingly harmed by biased priors. Our study indicates that all three methodologies should be taken seriously by philosophers and practitioners of statistics. [ABSTRACT FROM AUTHOR]

The statistical methodology described in the Guide to the Expression of Uncertainty in Measurement (GUM) is known to be flawed. Type A evaluation in the GUM appeals to the classical idea that probability represents the frequency-behaviour of errors in a measurement procedure, while Type B evaluation seems to make unknown constants the subjects of probability distributions, which is not permitted in the classical approach. This paper shows how Type B evaluation can be understood in terms of error distributions, so that the GUM methodology can be made coherent and hence extensible. Subsequently, a modification is described for better properties and performance.

If statisticians see themselves as flag bearers of the acknowledgment and communication of uncertainty (and I think we should define ourselves in this way), this task puts statisticians in a difficult position with a public that expects certainty and quick results. Keywords: Bayesian statistics; frequentist statistics; statistical testing EN Bayesian statistics frequentist statistics statistical testing 1 3 3 10/04/22 20221001 NES 221001 INTRODUCTION In her editorial "The Statistics Wars and Intellectual Conflicts of Interest" in I Conservation Biology i , D. Mayo discusses and ultimately rejects demands to abandon claims of statistical significance. Not all data analyses can be done by highly qualified statisticians, and society cannot wait for data analyses while statisticians attempt to achieve perfect understanding and agreement. [Extracted from the article]

Nonresponse weighting adjustment using the response propensity score is a popular tool for handling unit nonresponse. Statistical inference after the nonresponse weighting adjustment is an important problem and Taylor linearization method is often used to reflect the effect of estimating the propensity score weights. In this article, we propose an approximate Bayesian approach to handle unit nonresponse with parametric model assumptions on the response probability, but without model assumptions for the outcome variable. The proposed Bayesian method is calibrated to the frequentist inference in that the credible region obtained from the posterior distribution asymptotically matches to the frequentist confidence interval obtained from the Taylor linearization method. The proposed Bayesian method is also extended to incorporate the auxiliary information from full sample. Results from limited simulation studies confirm the validity of the proposed methods. The proposed method is applied to data from a Korean longitudinal survey. [ABSTRACT FROM AUTHOR]

We consider exact algorithms for Bayesian inference with model selection priors (including spike-and-slab priors) in the sparse normal sequence model. Because the best existing exact algorithm becomes numerically unstable for sample sizes over n = 500, there has been much attention for alternative approaches like approximate algorithms (Gibbs sampling, variational Bayes, etc.), shrinkage priors (e.g. the Horseshoe prior and the Spike-and-Slab LASSO) or empirical Bayesian methods. However, by introducing algorithmic ideas from online sequential prediction, we show that exact calculations are feasible for much larger sample sizes: for general model selection priors we reach n = 25 000, and for certain spike-and-slab priors we can easily reach n = 100 000. We further prove a de Finettilike result for finite sample sizes that characterizes exactly which model selection priors can be expressed as spike-and-slab priors. The computational speed and numerical accuracy of the proposed methods are demonstrated in experiments on simulated data, on a differential gene expression data set, and to compare the effect of multiple hyper-parameter settings in the beta-binomial prior. In our experimental evaluation we compute guaranteed bounds on the numerical accuracy of all new algorithms, which shows that the proposed methods are numerically reliable whereas an alternative based on long division is not. [ABSTRACT FROM AUTHOR]

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it incorporates Occam’s razor via the multiplicity or trials factor in the look-elsewhere effect. However, if the prior is not known completely, the frequentist hypothesis test via the false-positive rate is a better approach, as it is less sensitive to the prior choice. We argue that when only partial prior information is available, it is best to combine the two methodologies by using the Bayes factor as a test statistic in the frequentist analysis. We show that the standard frequentist maximum likelihood-ratio test statistic corresponds to the Bayes factor with a non-informative Jeffrey’s prior. We also show that mixed priors increase the statistical power in frequentist analyses over the maximum likelihood test statistic. We develop an analytic formalism that does not require expensive simulations and generalize Wilks’ theorem beyond its usual regime of validity. In specific limits, the formalism reproduces existing expressions, such as the p-value of linear models and periodograms. We apply the formalism to an example of exoplanet transits, where multiplicity can be more than 107. We show that our analytic expressions reproduce the p-values derived from numerical simulations. We offer an interpretation of our formalism based on the statistical mechanics. We introduce the counting of states in a continuous parameter space using the uncertainty volume as the quantum of the state. We show that both the p-value and Bayes factor can be expressed as an energy versus entropy competition.

Background: Application of clinical study findings to surgical decision making requires accurate interpretation of the results, integration of the findings within the context of pre-existing knowledge and use of statistics to answer clinically relevant questions. Bayesian analyses are optimally suited for interpretation of study findings, supporting translation to the bedside. Discussion: Surgical decision making is a complex process that draws on an individual clinician's medical knowledge, experience, data, and the patient's unique characteristics and preferences. Subjective and objective knowledge may be merged to derive a probability of benefit or harm of a treatment under consideration. Bayesian reasoning complements the clinical decision-making process by incorporating known evidence and data from a new study to determine the probability of an outcome of interest. Bayesian analyses are statistically robust and intuitive when translating findings of a study into clinical care. In contrast, frequentist statistics are poorly suited to translate study findings to clinical application. This review aims to highlight the benefits of incorporating Bayesian analyses into clinical research. Conclusion: Bayesian analyses offer clinically relevant information including the probability of benefit or harm of a treatment under consideration while accounting for uncertainty. This information may be incorporated easily and accurately into surgical decision making. [ABSTRACT FROM AUTHOR]

This work is motivated by the analysis of ecological interaction networks. Poisson stochastic block models are widely used in this field to decipher the structure that underlies a weighted network, while accounting for covariate effects. Efficient algorithms based on variational approximations exist for frequentist inference, but without statistical guaranties as for the resulting estimates. In the absence of variational Bayes estimates, we show that a good proxy of the posterior distribution can be straightforwardly derived from the frequentist variational estimation procedure, using a Laplace approximation. We use this proxy to sample from the true posterior distribution via a sequential Monte Carlo algorithm. As shown in the simulation study, the efficiency of the posterior sampling is greatly improved by the accuracy of the approximate posterior distribution. The proposed procedure can be easily extended to other latent variable models. We use this methodology to assess the influence of available covariates on the organization of several ecological networks, as well as the existence of a residual interaction structure. [ABSTRACT FROM AUTHOR]

In this article, we offer a primer on "classical" frequentist statistics. In doing so, we aim to (1) provide social workers with a nuanced overview of common statistical concepts and tools, (2) clarify ways in which these ideas have oft been misused or misinterpreted in research and practice, and (3) help social workers better understand what frequentist statistics can and cannot offer. We begin broadly, starting with foundational issues in the philosophy of statistics. Then, we outline the Fisherian and Neyman–Pearson approaches to statistical inference and the practice of null hypothesis significance testing. We then discuss key statistical concepts including α, power, p values, effect sizes, and confidence intervals, exploring several common misconceptions about their use and interpretation. We close by considering some limitations of frequentist statistics and by offering an opinionated discussion on how social workers may promote more fruitful, responsible, and thoughtful statistical practice. [ABSTRACT FROM AUTHOR]

The use of real-world data became more and more popular in the pharmaceutical industry. The impact of real-world evidence is now well emphasized by the regulatory authorities. Indeed, the analysis of this type of data can play a key role for treatment efficacy and safety. The aim of this work is to assess various methods and give guidance on the comparisons of drugs, mostly with respect to time-to-event data, in non-randomized studies with potentially confounding variables. For that purpose, several statistical methodologies are compared based on simulation studies. These methodologies belong to family classes of methods that are widely used for this type of problem: regression, matching, weighting and subclassification methods. The evaluation criteria used to compare methods performances are the relative bias, the mean square error, the coverage probability and the width of the confidence interval. In this paper, we consider different scenarios of dataset features in order to study the effect of the sample size, the number of covariates and the magnitude of the treatment effect on the statistical methodologies performances. These statistical analyses are conducted within a proportional hazard model framework. Furthermore, we highlight the advantage of using techniques to identify relevant covariates for time-to-event outcomes by comparing two variable selection methods under a frequentist and a Bayesian inference. Based on simulation results, recommendations on each of the family of methods are provided to guide decision making. [ABSTRACT FROM AUTHOR]

Summary: Stochastic subspace identification (SSI) and Bayesian methods are now the main representative approaches for high‐performance system identification and uncertainty quantification. Both methods have been extensively used in engineering applications for the last 10 years despite them having quite different views in principle. However, no comparison has been carried out to inform which method is actually better for engineering applications in terms of modal identification accuracy, uncertainty quantification, and so forth. This paper therefore investigates the differences between these two quantifications of parameter uncertainty in system identification. Synthetic data for a six‐degree‐of‐freedom spring–mass numerical system are first studied to compare their identification accuracy and applicable conditions. The investigation is then extended to field data from actual structures, which involves ambient modal testing of Heritage Court Tower in Canada, Canton Tower in China, and Ting Kau Bridge in Hong Kong. Results from the synthetic data show that, under white‐noise excitation, identified modal parameters and quantified uncertainty for both methods are highly consistent with the values of frequentist statistics. However, when the excitation is not white noise, there may be some spurious modes identified via SSI, and the uncertainty quantified under colored‐noise excitation via SSI is almost always larger than those under white noise, while the Bayesian method is not disturbed. Results for the structural field data indicate that in general applications under environmental excitation the identified modal parameters from both methods are almost identical; the quantified uncertainty of the SSI method is slightly larger than that of the Bayesian method, but they are of the same order of magnitude and can meet engineering requirements. [ABSTRACT FROM AUTHOR]

This paper analyzes the concept of probability in Keynes' work and proposes a method for formalizing the notion of uncertainty in the General Theory using Bayes' theorem and the principle of maximum entropy. One of the main conclusions is that, despite sharing his rejection of the frequentist approach to statistics, it is unreasonable to think that numerical probabilities cannot be determined, even if some criterion of objectivity is met. [ABSTRACT FROM AUTHOR]

This paper reconciles the asymptotic disagreement between Bayesian and frequentist inference in set‐identified models by adopting a multiple‐prior (robust) Bayesian approach. We propose new tools for Bayesian inference in set‐identified models and show that they have a well‐defined posterior interpretation in finite samples and are asymptotically valid from the frequentist perspective. The main idea is to construct a prior class that removes the source of the disagreement: the need to specify an unrevisable prior for the structural parameter given the reduced‐form parameter. The corresponding class of posteriors can be summarized by reporting the 'posterior lower and upper probabilities' of a given event and/or the 'set of posterior means' and the associated 'robust credible region'. We show that the set of posterior means is a consistent estimator of the true identified set and the robust credible region has the correct frequentist asymptotic coverage for the true identified set if it is convex. Otherwise, the method provides posterior inference about the convex hull of the identified set. For impulse‐response analysis in set‐identified Structural Vector Autoregressions, the new tools can be used to overcome or quantify the sensitivity of standard Bayesian inference to the choice of an unrevisable prior. [ABSTRACT FROM AUTHOR]

Our main contribution is to examine the reliability of confidence intervals using the SAM state-space fish stock assessment model used for the assessment of many stocks by the International Council for the Exploration of the Seas. We focus on frequentist statistical inferences and more specifically on inference conditioned on specific values of the state-space model random effects drawn from their process distribution. This is somewhat consistent with simulation self-test procedures that are commonly used to examine the reliability of state-space assessment model results. However, recent research has indicated that some estimation bias may be expected in the conditional setting. Hence, we also investigate recently proposed bias corrected confidence intervals appropriate for the conditional inference setting. The SAM simulation coverage probabilities of 95% confidence intervals for SSB and Fbar were usually slightly larger than 95%, but in a small number of years these coverage probabilities could be much smaller than 95%. The bias corrected confidence intervals were more reliable. When averaged over years, the SAM and bias corrected confidence interval coverage probabilities were similar for the Northeast Artic cod and saithe case studies, but the bias corrected confidence intervals performed much better overall for the haddock case study. [ABSTRACT FROM AUTHOR]

• Unconscious processes are debated, due to issues with showing absence of awareness. • We tested unconscious semantic priming using different analysis strategies. • Adopting common practices, we produced false evidence for unconscious priming. • Recently proposed best practices could prevent such erroneous conclusions. • We suggest improvements for future studies on unconscious processing. One widely used scientific approach to studying consciousness involves contrasting conscious operations with unconscious ones. However, challenges in establishing the absence of conscious awareness have led to debates about the extent and existence of unconscious processes. We collected experimental data on unconscious semantic priming, manipulating prime presentation duration to highlight the critical role of the analysis approach in attributing priming effects to unconscious processing. We demonstrate that common practices like post-hoc data selection, low statistical power, and frequentist statistical testing can erroneously support claims of unconscious priming. Conversely, adopting best practices like direct performance-awareness contrasts, Bayesian tests, and increased statistical power can prevent such erroneous conclusions. Many past experiments, including our own, fail to meet these standards, casting doubt on previous claims about unconscious processing. Implementing these robust practices will enhance our understanding of unconscious processing and shed light on the functions and neural mechanisms of consciousness. [ABSTRACT FROM AUTHOR]

Aim: Mangrove wetlands span broad geographical gradients, resulting in functionally diverse tree communities. We asked whether latitudinal variation, allometric scaling relationships and species composition influence mangrove forest structure and biomass allocation across biogeographical regions and distinct coastal morphologies. Location: Global. Time period: Present. Major taxa studied: Mangrove ecosystems. Methods: We built the largest field‐based dataset on mangrove forest structure and biomass to date (c. 2,800 plots from 67 countries) to address macroecological questions pertaining to structural and functional diversity of mangroves spanning biogeographical and coastal morphology gradients. We used frequentist inference statistics and machine learning models to determine environmental drivers that control biomass allocation within and across mangrove communities globally. Results: Allometric scaling relationships and forest structural complexity were consistent across biogeographical and coastal morphology gradients, suggesting that mangrove biomass is controlled by regional forcings rather than by latitude or species composition. For instance, nearly 40% of the global variation in biomass was explained by regional climate and hydroperiod, revealing nonlinear thresholds that control biomass accumulation across broad geographical gradients. Furthermore, we found that ecosystem‐level carbon stocks (average 401 ± 48 MgC/ha, covering biomass and the top 1 m of soil) varied little across diverse coastal morphologies, reflecting regional bottom‐up geomorphic controls that shape global patterns in mangrove biomass apportioning. Main conclusions: Our findings reconcile views of wetland and terrestrial forest macroecology. Similarities in stand structural complexity and cross‐site size–density relationships across multiscale environmental gradients show that resource allocation in mangrove ecosystems is independent of tree size and invariant to species composition or latitude. Mangroves follow a universal fractal‐based scaling relationship that describes biomass allocation for several other terrestrial tree‐dominated communities. Understanding how mangroves adhere to these universal allometric rules can improve our ability to account for biomass apportioning and carbon stocks in response to broad geographical gradients. [ABSTRACT FROM AUTHOR]

Adaptive experimental designs can dramatically improve efficiency in randomized trials. But with adaptively collected data, common estimators based on sample means and inverse propensity-weighted means can be biased or heavy-tailed. This poses statistical challenges, in particular when the experimenter would like to test hypotheses about parameters that were not targeted by the data-collection mechanism. In this paper, we present a class of test statistics that can handle these challenges. Our approach is to adaptively reweight the terms of an augmented inverse propensity-weighting estimator to control the contribution of each term to the estimator's variance. This scheme reduces overall variance and yields an asymptotically normal test statistic. We validate the accuracy of the resulting estimates and their CIs in numerical experiments and show that our methods compare favorably to existing alternatives in terms of mean squared error, coverage, and CI size. [ABSTRACT FROM AUTHOR]

Background: Routine influenza vaccine effectiveness (VE) surveillance networks use frequentist methods to estimate VE. With data from more than a decade of VE surveillance from diverse global populations now available, using Bayesian methods to explicitly account for this knowledge may be beneficial. This study explores differences between Bayesian vs. frequentist inference in multiple seasons with varying VE.Methods: We used data from the United States Influenza Vaccine Effectiveness (US Flu VE) Network. Ambulatory care patients with acute respiratory illness were enrolled during seasons of varying observed VE based on traditional frequentist methods. We estimated VE against A(H1N1)pdm in 2015/16, dominated by A(H1N1)pdm; against A(H3N2) in 2017/18, dominated by A(H3N2); and compared VE for live attenuated influenza vaccine (LAIV) vs. inactivated influenza vaccine (IIV) among children aged 2-17 years in 2013/14, also dominated by A(H1N1)pdm. VE was estimated using both frequentist and Bayesian methods using the test-negative design. For the Bayesian estimates, prior VE distributions were based on data from all published test-negative studies of the same influenza type/subtype available prior to the season of interest.Results: Across the three seasons, 16,342 subjects were included in the analyses. For 2015/16, frequentist and Bayesian VE estimates were essentially identical (41% each). For 2017/18, frequentist and Bayesian estimates of VE against A(H3N2) viruses were also nearly identical (26% vs. 23%, respectively), even though the presence of apparent antigenic match could potentially have pulled Bayesian estimates upward. Precision of estimates was similar between methods in both seasons. Frequentist and Bayesian estimates diverged for children in 2013/14. Under the frequentist approach, LAIV effectiveness was 62 percentage points lower than IIV, while LAIV was only 27 percentage points lower than IIV under the Bayesian approach.Conclusion: Bayesian estimates of influenza VE can differ from frequentist estimates to a clinically meaningful degree when VE diverges substantially from previous seasons. [ABSTRACT FROM AUTHOR]

Forecasting the outstanding claim liabilities to set adequate reserves is critical for a nonlife insurer's solvency. Chain–Ladder and Bornhuetter–Ferguson are two prominent actuarial approaches used for this task. The selection between the two approaches is often ad hoc due to different underlying assumptions. We introduce a Dirichlet model that provides a common statistical framework for the two approaches, with some appealing properties. Depending on the type of information available, the model inference naturally leads to either Chain–Ladder or Bornhuetter–Ferguson prediction. Using claims data on Worker's compensation insurance from several U.S. insurers, we discuss both frequentist and Bayesian inference. [ABSTRACT FROM AUTHOR]

This article presents three empirical studies on the effectiveness of serious games for learning and motivation, while it compares the results arising from Frequentist (classical) Statistics with those from Bayesian Statistics. For a long time it has been technically impracticable to apply Bayesian Statistics and benefit from its conceptual superiority, but the emergence of automated sampling algorithms and user-friendly tools has radically simplified its usage. The three studies include two within-subjects designs and one betweensubjects design. Unpaired t-tests, mixed factorial ANOVAs and multiple linear regression are used for the analyses. Overall, the games are found to have clear positive effects on learning and motivation, be it that the results from Bayesian Statistics are more strict and more informative, and possess several conceptual advantages. Accordingly, the paper calls for more emphasis on Bayesian Statistics in serious games research and beyond, as to reduce the present domination by the Frequentist Paradigm. [ABSTRACT FROM AUTHOR]

We discuss and characterise connections between frequentist, confidence distribution and objective Bayesian inference, when considering higher-order asymptotics, matching priors, and confidence distributions based on pivotal quantities. The focus is on testing precise or sharp null hypotheses on a scalar parameter of interest. Moreover, we illustrate that the application of these procedures requires little additional effort compared to the application of standard first-order theory. In this respect, using the R software, we indicate how to perform in practice the computation with three examples in the context of data from inter-laboratory studies, of the stress–strength reliability, and of a growth curve from dose–response data. [ABSTRACT FROM AUTHOR]

Additionally, by presenting both estimation paradigms, Fieberg illustrates the differences in inference more evidently than a text that chooses one paradigm. After choosing the response model in Part I and the covariate structure in Part II, Part III introduces the 2 main paradigms for estimation and inference: frequentist and Bayesian statistics. I Statistics for Ecologists i is an open access textbook targeted at graduate students in ecology with prerequisite knowledge of statistics and R programming. [Extracted from the article]

Copyright of Computational Science & Techniques is the property of Klaipeda University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Agricultural Research in the Tropics / Pesquisa Agropecuária Tropical is the property of Pesquisa Agropecuaria Tropical and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Multiple imputation has become one of the most popular approaches for handling missing data in statistical analyses. Part of this success is due to Rubin's simple combination rules. These give frequentist valid inferences when the imputation and analysis procedures are so-called congenial and the embedding model is correctly specified, but otherwise may not. Roughly speaking, congeniality corresponds to whether the imputation and analysis models make different assumptions about the data. In practice, imputation models and analysis procedures are often not congenial, such that tests may not have the correct size, and confidence interval coverage deviates from the advertised level. We examine a number of recent proposals which combine bootstrapping with multiple imputation and determine which are valid under uncongeniality and model misspecification. Imputation followed by bootstrapping generally does not result in valid variance estimates under uncongeniality or misspecification, whereas certain bootstrap followed by imputation methods do. We recommend a particular computationally efficient variant of bootstrapping followed by imputation. [ABSTRACT FROM AUTHOR]

Expectation propagation is a general prescription for approximation of integrals in statistical inference problems. Its literature is mainly concerned with Bayesian inference scenarios. However, expectation propagation can also be used to approximate integrals arising in frequentist statistical inference. We focus on likelihood-based inference for binary response mixed models and show that fast and accurate quadrature-free inference can be realized for the probit link case with multivariate random effects and higher levels of nesting. The approach is supported by asymptotic calculations in which expectation propagation is seen to provide consistent estimation of the exact likelihood surface. Numerical studies reveal the availability of fast, highly accurate and scalable methodology for binary mixed model analysis. [ABSTRACT FROM AUTHOR]

Foot rot disease poses a devastating threat to pepper agriculture. In Vietnam, conventionally, fungicides are the control methods used against the disease. However, the practical effectiveness of fungicide treatment has yet to be quantitatively assessed. To fill this gap a three-factorial experiment was conducted, the factors of which were fungicide application, soil type, and infection pathway, with plant mortality and plant growth as the target variables. Two of the most common fungicides were chosen, including Agrifos 400 (potassium phosphonate) and Aliette 800WG (fosetyl-Al). The two fungicides were used in multiple treatment plans, with soil drenching selected as the means of controlling foot rot disease on red basalt soil and red basalt soil added with organic matter in a greenhouse experiment. Three-month-old pepper (Piper nigrum) plants were treated with Agrifos (application interval of 10 and 20 days), Aliette (application interval of 30 and 60 days), and a combination of both fungicides at half doses. Pepper plants were infected with the fungus Pythium spp. from soil or by direct inoculation. To assess the effect of fungicides on foot rot mortality and the growth of pepper plants, multiple generalized linear models were set up using frequentist and Bayesian approaches. Generally, both procedures suggest the same conclusions for model selection in terms of the Akaike information criterion (AIC) and the deviance information criterion (DIC). Fungicide type was found to be the main factor that affected the survival of plants. Most of the treatments (except Aliette, with an interval of 60 days) effectively reduced the mortality. The usage of fungicides affected the growth of plants in interaction with soil types. Aliette suppressed the growth of plants, especially on red soil, while Agrifos had no effect on the growth of pepper plants. The combined application of Agrifos and Aliette with half doses proves to be a promising solution for balancing cost and effectiveness in protecting plants against foot rot pathogens without affecting their growth. In our case, under the inhomogeneity of variance and unbalanced samples, the Bayesian inference appeared to be the most useful because of its flexibility in terms of model structure.

This paper is a reader-friendly introduction to Bayesian inference applied to psychological science. We begin by explaining the difference between frequentist and epistemic interpretations of probability that underpin respectively frequentist and Bayesian statistics. We use a concrete example—a student wondering whether s/he carries the virus statisticus malignum—to explain how both approaches are different one from another. We illustrate Bayesian inference with intuitive examples, before introducing the mathematical framework. Different schools of thoughts and recommendations are discussed to illustrate how to use priors in Bayes Factor testing. We discuss how psychology could benefit from a greater reliance on Bayesian methods. Finally, we illustrate how to compute Bayes Factors analyses with real data and provide the R code. [ABSTRACT FROM AUTHOR]

Frequently in experiments there is not only variance in the reaction of participants to treatment. The heterogeneity is patterned: discernible types of participants react differently. In principle, a finite mixture model is well suited to simultaneously estimate the probability that a given participant belongs to a certain type, and the reaction of this type to treatment. Yet finite mixture models may need more data than the experiment provides. The approach in principle requires ex ante knowledge about the number of types. Finite mixture models make distributional assumptions that one may not feel comfortable with. They are hard to estimate for panel data, which is what experiments often generate. For experiments with repeated measurements, this paper offers a simple two-step alternative that is much less data hungry, that allows to find the number of types in the data, that does not make distributional assumptions about the type space, and that allows for the estimation of panel data models. It combines machine learning methods with classic frequentist statistics. [ABSTRACT FROM AUTHOR]

Copyright of Zeitschrift für Bildungsforschung is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Assuming a banded structure is one of the common practice in the estimation of high-dimensional precision matrices. In this case, estimating the bandwidth of the precision matrix is a crucial initial step for subsequent analysis. Although there exist some consistent frequentist tests for the bandwidth parameter, bandwidth selection consistency for precision matrices has not been established in a Bayesian framework. In this paper, we propose a prior distribution tailored to the bandwidth estimation of high-dimensional precision matrices. The banded structure is imposed via the Cholesky factor from the modified Cholesky decomposition. We establish strong model selection consistency for the bandwidth as well as consistency of the Bayes factor. The convergence rates for Bayes factors under both the null and alternative hypotheses are derived which yield similar order of rates. As a by-product, we also propose an estimation procedure for the Cholesky factors yielding an almost optimal order of convergence rates. Twosample bandwidth test is also considered, and it turns out that our method is able to consistently detect the equality of bandwidths between two precision matrices. The simulation study confirms that our method in general outperforms the existing frequentist and Bayesian methods. [ABSTRACT FROM AUTHOR]

Background: Various methods exist for statistical inference about a prevalence that consider misclassifications due to an imperfect diagnostic test. However, traditional methods are known to suffer from truncation of the prevalence estimate and the confidence intervals constructed around the point estimate, as well as from under-performance of the confidence intervals' coverage.Methods: In this study, we used simulated data sets to validate a Bayesian prevalence estimation method and compare its performance to frequentist methods, i.e. the Rogan-Gladen estimate for prevalence, RGE, in combination with several methods of confidence interval construction. Our performance measures are (i) error distribution of the point estimate against the simulated true prevalence and (ii) coverage and length of the confidence interval, or credible interval in the case of the Bayesian method.Results: Across all data sets, the Bayesian point estimate and the RGE produced similar error distributions with slight advantages of the former over the latter. In addition, the Bayesian estimate did not suffer from the RGE's truncation problem at zero or unity. With respect to coverage performance of the confidence and credible intervals, all of the traditional frequentist methods exhibited strong under-coverage, whereas the Bayesian credible interval as well as a newly developed frequentist method by Lang and Reiczigel performed as desired, with the Bayesian method having a very slight advantage in terms of interval length.Conclusion: The Bayesian prevalence estimation method should be prefered over traditional frequentist methods. An acceptable alternative is to combine the Rogan-Gladen point estimate with the Lang-Reiczigel confidence interval. [ABSTRACT FROM AUTHOR]

A 1200 m‐long river segment of Carmel River (California) was constructed to bypass trapped reservoir sediment when San Clemente Dam was removed from the Carmel River in 2015. Hundreds of large boulders were used to construct 53 steps in an 800 m‐long reach of the project. Nearly all the boulders were scattered to new locations in high flows of 2017, and have been relatively stable since that time. We analysed the causes of incipient motion and distance travelled for 226 randomly selected large boulders (0.5–1.8 m) impacted by a flood event in winter of 2019. Channel width, water depth, and isolation from neighbouring boulders were the main variables controlling individual large boulder incipient motion during a 10‐year peak flow event in the 'auto‐naturalized' constructed step‐pool river in 2019. There is weak statistical evidence that a combination of shear stress and the presence of boulders located laterally downstream of the subject boulder controlled the distance the boulder moved. Frequentist statistics and Akaike information criterion model comparison determined that boulder size, boulder shape, boulder roundness, and local thalweg slope were not good predictors of large boulder incipient motion or distance transported. Average dimensionless critical shear value for the four largest mobilized boulders (1.5–1.6 m) was 0.014. We describe the geomorphic history of the site and use our results to discuss potential causes of unanticipated large boulder transport at the site that occurred in a <2‐year peak flow of winter 2016 soon after step construction. © 2020 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The biological organism is a complex structure regulated by interactions of genes and proteins. Various linear and nonlinear models can define activations of these interactions. In this study, we have aimed to improve the Gaussian graphical model (GGM), which is one of the well-known probabilistic and parametric models describing steady-state activations of biological systems, and its inference based on the graphical lasso, shortly Glasso, method. Because, GGM with Glasso can have low accuracy when the system has many genes and data are far from the normal distribution. Hereby, we construct the model like GGM, but, suggest the long-tailed symmetric distribution (LTS), rather than the normality, and use the modified maximum likelihood (MML) estimator, rather than Glasso, in inference. From the assessment of simulated and real data analyses, it is seen that LTS with MML has higher accuracy and less computational demand with explicit expressions than results of GGM with Glasso. [ABSTRACT FROM AUTHOR]

Eutrophication of coastal ecosystems and decline of essential benthic ecosystems are growing concerns globally. Understanding the drivers associated with a response of an indicator species at an ecosystem or even regional-scale hinges on a robust evaluation of data that spans both space and time. Consistent data, suitable and methodical data-handling procedures, appropriate statistical evaluation and logical assessment of hypotheses are essential. Lapointe et al. (Mar Biol 166:108, 2019) suggest that decline of stony coral at Looe Key reef is attributed to local and regional (i.e., discharge > 200 km away) nutrient discharges causing eutrophication of coastal waters and the degradation of essential habitat. Furthermore, Lapointe et al. (Mar Biol 166:108, 2019) posit that the restored freshwater flows to the Everglades ecosystem is a causative agent for the observed coral decline observed at Looe Key Reef. While the decline in coral coverage is alarming, rigorous statistical analysis is needed to attribute a true cause-and-effect relationship. This commentary discusses data handling techniques, the application of statistical methods, interoperability of data and evaluation of hypotheses presented by Lapointe et al. (Mar Biol 166:108, 2019) specific to Looe Key reef within the Florida Key Marine Sanctuary. This commentary is not merely a critique of the statistics used by the authors but rather the inappropriate statistical methods utilized and how it affects the acceptance or rejection of the authors' hypotheses and the overall conclusions drawn. [ABSTRACT FROM AUTHOR]

Ecological data often violate common assumptions of traditional parametric statistics (e.g., that residuals are Normally distributed, have constant variance, and cases are independent). Modern statistical methods are well equipped to handle these complications, but they can be challenging for non-statisticians to understand and implement. Rather than default to increasingly complex statistical methods, resampling-based methods can sometimes provide an alternative method for performing statistical inference, while also facilitating a deeper understanding of foundational concepts in frequentist statistics (e.g., sampling distributions, confidence intervals, p-values). Using simple examples and case studies, we demonstrate how resampling-based methods can help elucidate core statistical concepts and provide alternative methods for tackling challenging problems across a broad range of ecological applications. [ABSTRACT FROM AUTHOR]

Due to the risk in outsourcing, supplier selection is a critical issue for companies. Considerable evidence shows that among the criteria for selecting a supplier, quality is the most critical factor and the process yield index is an efficient tool for assessing the process quality of the supplier. Although the frequentist approach has been adopted to discriminate the degrees of two yield indices to solve the supplier selection problem, unknown parameters must be estimated from samples, which potentially introduce uncertainty into the statistical testing process. Instead of the frequentist inference, this study proposes using the Bayesian inference to derive the posterior distribution of the ratio of two yield indices. Furthermore, a Markov chain Monte Carlo technique is applied to discern the empirical posterior distribution of the ratio with the aim of discriminating the degrees of two yield indices. The simulations show that the proposed method is not only of reasonable empirical size but tests well in terms of power. [ABSTRACT FROM AUTHOR]

Statistical thinking is essential to understanding the nature of scientific results as a consumer. Statistical thinking also facilitates thinking like a scientist. Instead of emphasizing a "correct" procedure for data analysis and its outcome, statistical thinking focuses on the process of data analysis. This article reviews frequentist and Bayesian approaches such that teachers can promote less well-known statistical perspectives to encourage statistical thinking. Within the frequentist and Bayesian approaches, we highlight important distinctions between statistical evaluation versus estimation using an example on the facial feedback hypothesis. We first introduce some elementary statistical concepts, which are then illustrated with simulated data. Finally, we demonstrate how these approaches are applied to empirical data obtained from a Registered Replication Report. Data and R code for the example are provided as supplementary teaching material. We conclude with a discussion of key learning outcomes centred on promoting statistical thinking. [ABSTRACT FROM AUTHOR]

We define and solve classes of sparse matrix problems that arise in multilevel modelling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation, in which data on level-1 units are grouped within a two-level structure. We provide full solutions for two-level and three-level problems, and their derivations provide blueprints for the challenging, albeit rarer in applications, higher-level versions of the problem. While our linear system solutions are a concise recasting of existing results, our matrix inverse sub-block results are novel and facilitate streamlined computation of standard errors in frequentist inference as well as allowing streamlined mean field variational Bayesian inference for models containing higher-level random effects. [ABSTRACT FROM AUTHOR]

Researchers often conclude an effect is absent when a null-hypothesis significance test yields a nonsignificant p value. However, it is neither logically nor statistically correct to conclude an effect is absent when a hypothesis test is not significant. We present two methods to evaluate the presence or absence of effects: Equivalence testing (based on frequentist statistics) and Bayes factors (based on Bayesian statistics). In four examples from the gerontology literature, we illustrate different ways to specify alternative models that can be used to reject the presence of a meaningful or predicted effect in hypothesis tests. We provide detailed explanations of how to calculate, report, and interpret Bayes factors and equivalence tests. We also discuss how to design informative studies that can provide support for a null model or for the absence of a meaningful effect. The conceptual differences between Bayes factors and equivalence tests are discussed, and we also note when and why they might lead to similar or different inferences in practice. It is important that researchers are able to falsify predictions or can quantify the support for predicted null effects. Bayes factors and equivalence tests provide useful statistical tools to improve inferences about null effects. [ABSTRACT FROM AUTHOR]