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.

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.

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