Bayesian Estimation of Augmented Exponential Strength Reliability Models Under Non-informative Priors

2016 ◽  
Vol 5 (1) ◽  
pp. 15-31
Author(s):  
N. CHANDRA ◽  
◽  
V. K. RATHAUR
Keyword(s):  
Bayesian Estimation ◽  
Informative Priors ◽  
Reliability Models

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.

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.

scholarly journals Bayesian Approximation Techniques for Scale Parameter of Laplace Distribution

2019 ◽  
Vol 17 (2) ◽  
Author(s):  
Uzma Jan ◽  
S. P. Ahmad
Keyword(s):  
Bayesian Estimation ◽  
Scale Parameter ◽  
Normal Approximation ◽  
Laplace Distribution ◽  
Informative Priors ◽  
Approximation Techniques ◽  
Bayesian Approximation

The Bayesian estimation of the scale parameter of a Laplace Distribution is obtained using two approximation techniques, like Normal approximation and Tierney and Kadane (T-K) approximation, under different informative priors.

scholarly journals Systematically Defined Informative Priors in Bayesian Estimation: An Empirical Application on the Transmission of Internalizing Symptoms Through Mother-Adolescent Interaction Behavior

2021 ◽  
Vol 12 ◽  
Author(s):  
Susanne Schulz ◽  
Mariëlle Zondervan-Zwijnenburg ◽  
Stefanie A. Nelemans ◽  
Duco Veen ◽  
Albertine J. Oldehinkel ◽  
...  
Keyword(s):  
Bayesian Estimation ◽  
Internalizing Symptoms ◽  
Specific Information ◽  
Informative Priors ◽  
Negative Interaction ◽  
Conflict Task ◽  
Mediation Effects ◽  
Weighting System ◽  
Interaction Behavior ◽  
The Impact

BackgroundBayesian estimation with informative priors permits updating previous findings with new data, thus generating cumulative knowledge. To reduce subjectivity in the process, the present study emphasizes how to systematically weigh and specify informative priors and highlights the use of different aggregation methods using an empirical example that examined whether observed mother-adolescent positive and negative interaction behavior mediate the associations between maternal and adolescent internalizing symptoms across early to mid-adolescence in a 3-year longitudinal multi-method design.MethodsThe sample consisted of 102 mother-adolescent dyads (39.2% girls, Mage T1 = 13.0). Mothers and adolescents reported on their internalizing symptoms and their interaction behaviors were observed during a conflict task. We systematically searched for previous studies and used an expert-informed weighting system to account for their relevance. Subsequently, we aggregated the (power) priors using three methods: linear pooling, logarithmic pooling, and fitting a normal distribution to the linear pool by means of maximum likelihood estimation. We compared the impact of the three differently specified informative priors and default priors on the prior predictive distribution, shrinkage, and the posterior estimates.ResultsThe prior predictive distributions for the three informative priors were quite similar and centered around the observed data mean. The shrinkage results showed that the logarithmic pooled priors were least affected by the data. Most posterior estimates were similar across the different priors. Some previous studies contained extremely specific information, resulting in bimodal posterior distributions for the analyses with linear pooled prior distributions. The posteriors following the fitted normal priors and default priors were very similar. Overall, we found that maternal, but not adolescent, internalizing symptoms predicted subsequent mother-adolescent interaction behavior, whereas negative interaction behavior seemed to predict subsequent internalizing symptoms. Evidence regarding mediation effects remained limited.ConclusionA systematic search for previous information and an expert-built weighting system contribute to a clear specification of power priors. How information from multiple previous studies should be included in the prior depends on theoretical considerations (e.g., the prior is an updated Bayesian distribution), and may also be affected by pragmatic considerations regarding the impact of the previous results at hand (e.g., extremely specific previous results).

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