scholarly journals Bayesian Estimation with Informative Priors is Indistinguishable from Data Falsification

2019 ◽  
Vol 22 ◽  
Author(s):  
Miguel Ángel García-Pérez
Keyword(s):  
Bayesian Estimation ◽  
Likelihood Function ◽  
Research Integrity ◽  
Statistical Characteristics ◽  
Informative Priors ◽  
Bayesian Analyses ◽  
Interval Estimates ◽  
Frequentist Statistics ◽  
Qualitative Level ◽  
Strong Inference

Abstract Criticism of null hypothesis significance testing, confidence intervals, and frequentist statistics in general has evolved into advocacy of Bayesian analyses with informative priors for strong inference. This paper shows that Bayesian analysis with informative priors is formally equivalent to data falsification because the information carried by the prior can be expressed as the addition of fabricated observations whose statistical characteristics are determined by the parameters of the prior. This property of informative priors makes clear that only the use of non-informative, uniform priors in all types of Bayesian analyses is compatible with standards of research integrity. At the same time, though, Bayesian estimation with uniform priors yields point and interval estimates that are identical or nearly identical to those obtained with frequentist methods. At a qualitative level, frequentist and Bayesian outcomes have different interpretations but they are interchangeable when uniform priors are used. Yet, Bayesian interpretations require either the assumption that population parameters are random variables (which they are not) or an explicit acknowledgment that the posterior distribution (which is thus identical to the likelihood function except for a scale factor) only expresses the researcher’s beliefs and not any information about the parameter of concern.

Assessing and Comparing Anesthesiologists’ Performance on Mandated Metrics Using a Bayesian Approach

2015 ◽  
Vol 123 (1) ◽  
pp. 101-115 ◽  
Author(s):  
Emine Ozgur Bayman ◽  
Franklin Dexter ◽  
Michael M. Todd
Keyword(s):  
Blood Pressure ◽  
Information Management System ◽  
Covariate Adjustment ◽  
Time Interval ◽  
Anesthesia Induction ◽  
Bayesian Analyses ◽  
Bayesian Hierarchical ◽  
Professional Performance ◽  
Frequentist Statistics ◽  
American Society

Abstract Background: Periodic assessment of performance by anesthesiologists is required by The Joint Commission Ongoing Professional Performance Evaluation program. Methods: The metrics used in this study were the (1) measurement of blood pressure and (2) oxygen saturation (Spo2) either before or less than 5 min after anesthesia induction. Noncompliance was defined as no measurement within this time interval. The authors assessed the frequency of noncompliance using information from 63,913 cases drawn from the anesthesia information management system. To adjust for differences in patient and procedural characteristics, 135 preoperative variables were analyzed with decision trees. The retained covariate for the blood pressure metric was patient’s age and, for Spo2 metric, was American Society of Anesthesiologist’s physical status, whether the patient was coming from an intensive care unit, and whether induction occurred within 5 min of the start of the scheduled workday. A Bayesian hierarchical model, designed to identify anesthesiologists as “performance outliers,” after adjustment for covariates, was developed and was compared with frequentist methods. Results: The global incidences of noncompliance (with frequentist 95% CI) were 5.35% (5.17 to 5.53%) for blood pressure and 1.22% (1.14 to 1.30%) for Spo2 metrics. By using unadjusted rates and frequentist statistics, it was found that up to 43% of anesthesiologists would be deemed noncompliant for the blood pressure metric and 70% of anesthesiologists for the Spo2 metric. By using Bayesian analyses with covariate adjustment, only 2.44% (1.28 to 3.60%) and 0.00% of the anesthesiologists would be deemed “noncompliant” for blood pressure and Spo2, respectively. Conclusion: Bayesian hierarchical multivariate methodology with covariate adjustment is better suited to faculty monitoring than the nonhierarchical frequentist approach.

scholarly journals The Quantitative Assessment Of Market Risk In Small And Medium - Sized Enterprise In The Slovak Republic

2016 ◽  
Vol 6 (2) ◽  
pp. 214-221
Author(s):  
Mária Hudáková ◽  
Ján Dvorský
Keyword(s):  
Risk Analysis ◽  
Quantitative Assessment ◽  
Preventive Measures ◽  
Slovak Republic ◽  
Market Risk ◽  
Mathematical Statistics ◽  
Statistical Characteristics ◽  
Interval Estimates ◽  
Market Risks ◽  
The Impact

Small and medium-sized enterprises (SMEs) in Slovakia do not pay sufficient attention to market risks, they do not form the prerequisites, or preventive measures of the risks assessed, which would prevent the problem. The essence of the article is based on the collected and processed data from the survey to analyze, assess and evaluate the impact of the factor, which is the number of employees to evaluate the market risk identified by managers of SMEs in the Žilina region of Slovakia. The analysis of market risk is carried out through the analysis of the selected statistical characteristics using the point and interval estimates and methods of mathematical statistics. The results of the survey showed that the number of employees has an impact on the amount of the value of the market risk of SMEs in the Žilina region and therefore it is not possible to underestimate it.   Keywords: risk, analysis, assessment, evaluation, market, small and medium-sized enterprise.

Multi-Mode Failure Models for Attribute Test Data in Reliability Systems, a Bayesian Analysis Approach Using Multi-Nomial Distribution Model

2014 ◽  
Vol 903 ◽  
pp. 419-424 ◽  
Author(s):  
Ismed Iskandar ◽  
Noraini Mohd Razali
Keyword(s):  
Bayesian Estimation ◽  
Test Data ◽  
Likelihood Function ◽  
Reliability Theory ◽  
Distribution Model ◽  
Distribution Models ◽  
Failure Models ◽  
Reliability Systems ◽  
Multi Mode ◽  
Mode Failure

This paper describes the extending model of Multi-mode Failure Models by using the Weibull and Gamma distribution models presented in a conference [1,2]. Different than the models in the previous papers which are for variable test data, in this paper we will describe the use of attribute test data for our model. In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components. Another problem in reliability theory is one of estimating the parameters of the assumed failure models. The estimation may be based on data collected over censored or uncensored life tests. In many reliability problems, the failure data are simply quantitatively inadequate. The Bayesian analyses are more beneficial than classical analyses in such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in the form of an apriori distribution with life test data to make inferences of the parameter of interest. In this paper, we have investigated the application of the Bayesian estimation analyses to multi-mode failure systems for attribute test data. The cases are limited to the models with independent causes of failure. We select our investigation by using the Multi-nomial distribution as our model. This distribution is widely used in reliability analysis for attribute test data. This model describes the likelihood function and follows with the description of the posterior function. A Beta prior is used in our analysis for each model and it is followed by the estimation of the point, interval, and reliability estimations.

Bayesian Structural Equation Modeling in Sport and Exercise Psychology

2015 ◽  
Vol 37 (4) ◽  
pp. 410-420 ◽  
Author(s):  
Andreas Stenling ◽  
Andreas Ivarsson ◽  
Urban Johnson ◽  
Magnus Lindwall
Keyword(s):  
Structural Equation Modeling ◽  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Bayesian Approach ◽  
Structural Equation ◽  
Equation Modeling ◽  
Exercise Psychology ◽  
Informative Priors ◽  
Sport And Exercise ◽  
Bayesian Structural Equation Modeling

Bayesian statistics is on the rise in mainstream psychology, but applications in sport and exercise psychology research are scarce. In this article, the foundations of Bayesian analysis are introduced, and we will illustrate how to apply Bayesian structural equation modeling in a sport and exercise psychology setting. More specifically, we contrasted a confirmatory factor analysis on the Sport Motivation Scale II estimated with the most commonly used estimator, maximum likelihood, and a Bayesian approach with weakly informative priors for cross-loadings and correlated residuals. The results indicated that the model with Bayesian estimation and weakly informative priors provided a good fit to the data, whereas the model estimated with a maximum likelihood estimator did not produce a well-fitting model. The reasons for this discrepancy between maximum likelihood and Bayesian estimation are discussed as well as potential advantages and caveats with the Bayesian approach.

Performance of informative priors skeptical of large treatment effects in clinical trials: A simulation study

2015 ◽  
Vol 27 (1) ◽  
pp. 79-96 ◽  
Author(s):  
Claudia Pedroza ◽  
Weilu Han ◽  
Van Thi Thanh Truong ◽  
Charles Green ◽  
Jon E Tyson
Keyword(s):  
Clinical Trials ◽  
Simulation Study ◽  
Treatment Effects ◽  
Mean Squared Error ◽  
Binary Outcomes ◽  
Control Group ◽  
Informative Priors ◽  
Bayesian Analyses ◽  
Credible Intervals ◽  
True Treatment Effect

One of the main advantages of Bayesian analyses of clinical trials is their ability to formally incorporate skepticism about large treatment effects through the use of informative priors. We conducted a simulation study to assess the performance of informative normal, Student- t, and beta distributions in estimating relative risk (RR) or odds ratio (OR) for binary outcomes. Simulation scenarios varied the prior standard deviation (SD; level of skepticism of large treatment effects), outcome rate in the control group, true treatment effect, and sample size. We compared the priors with regards to bias, mean squared error (MSE), and coverage of 95% credible intervals. Simulation results show that the prior SD influenced the posterior to a greater degree than the particular distributional form of the prior. For RR, priors with a 95% interval of 0.50–2.0 performed well in terms of bias, MSE, and coverage under most scenarios. For OR, priors with a wider 95% interval of 0.23–4.35 had good performance. We recommend the use of informative priors that exclude implausibly large treatment effects in analyses of clinical trials, particularly for major outcomes such as mortality.

Bayesian estimation and inference

2019 ◽  
pp. 186-203
Author(s):  
M. D. Edge
Keyword(s):  
Hypothesis Testing ◽  
Bayesian Statistics ◽  
Bayesian Estimation ◽  
Computational Methods ◽  
Posterior Distribution ◽  
Bayes Factor ◽  
Central Tendency ◽  
Prior Beliefs ◽  
Interval Estimates ◽  
Bayesian Hypothesis Testing

Bayesian methods allow researchers to combine precise descriptions of prior beliefs with new data in a principled way. The main object of interest in Bayesian statistics is the posterior distribution, which describes the uncertainty associated with parameters given prior beliefs about them and the observed data. The posterior can be difficult to compute mathematically, but computational methods can give arbitrarily good approximations in most cases. Bayesian point and interval estimates are features of the posterior, such as measures of its central tendency or intervals into which the parameter falls with specified probability. Bayesian hypothesis testing is complicated and controversial, but one relevant tool is the Bayes factor, which compares the probability of observing the data under a pair of distinct hypotheses.

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