scholarly journals Bayes, Jeffreys, Prior Distributions and the Philosophy of Statistics

2009 ◽  
Vol 24 (2) ◽  
pp. 176-178 ◽  
Author(s):  
Andrew Gelman
Keyword(s):  
Jeffreys Prior ◽  
Prior Distributions ◽  
Philosophy Of Statistics

Investigating the Effect of Prior Distributions on Posterior Estimates of Common Cause Failure Parameters Using Bayesian Method

2020 ◽  
Vol 6 (3) ◽  
Author(s):  
Edward Shitsi ◽  
Emmanuel K. Boafo ◽  
Felix Ameyaw ◽  
H. C. Odoi
Keyword(s):  
Bayesian Analysis ◽  
Confidence Level ◽  
Bayesian Method ◽  
Jeffreys Prior ◽  
Uncertainty Interval ◽  
Prior Distributions ◽  
Common Cause ◽  
Common Cause Failure ◽  
Dirichlet Prior ◽  
The Mean

Abstract Quantification of common cause failure (CCF) parameters and their application in multi-unit PSA are important to the safety and operation of nuclear power plants (NPPs) on the same site. CCF quantification mainly involves the estimation of potential failure of redundant components of systems in a NPP. The components considered in quantification of CCF parameters include motor operated valves, pumps, safety relief valves, air-operated valves, solenoid-operated valves, check valves, diesel generators, batteries, inverters, battery chargers, and circuit breakers. This work presents the results of the CCF parameter quantification using check valves and pumps. The systems considered as case studies for the demonstration of the proposed methodology are auxiliary feedwater system (AFWS) and high-pressure safety injection (HPSI) systems of a pressurized water reactor (PWR). The posterior estimates of alpha factors assuming two different prior distributions (Uniform Dirichlet prior and Jeffreys prior) using the Bayesian method were investigated. This analysis is important due to the fact that prior distributions assumed for alpha factors may affect the shape of posterior distribution and the uncertainty of the mean posterior estimates. For the two different priors investigated in this study, the shape of the posterior distribution is not influenced by the type of prior selected for the analysis. The mean of the posterior distributions was also analyzed at 90% confidence level. These results show that the type of prior selected for Bayesian analysis could have effects on the uncertainty interval (or the confidence interval) of the mean of the posterior estimates. The longer the confidence interval, the better the type of prior selected at a particular confidence level for Bayesian analysis. These results also show that Jeffreys prior is preferred over Uniform Dirichlet prior for Bayesian analysis because it yields longer confidence intervals (or shorter uncertainty interval) at 90% confidence level discussed in this work.

Reference priors for Bayesian fisheries models

2002 ◽  
Vol 59 (9) ◽  
pp. 1492-1502 ◽  
Author(s):  
Russell B Millar
Keyword(s):  
Prior Knowledge ◽  
Population Analysis ◽  
Production Model ◽  
Model Parameters ◽  
Jeffreys Prior ◽  
Unknown Parameters ◽  
Prior Distributions ◽  
Reference Priors ◽  
Surplus Production ◽  
Surplus Production Model

Bayesian models require the specification of prior distributions for all unknown parameters, and this formal utilization of prior knowledge (if any) can be used to great advantage in some fisheries. However, regardless of whether prior knowledge about model parameters is available, specification of prior distributions is seldom unequivocal. This work addresses the problem of specifying default priors for several common fisheries models. To maintain consistency of terminology with the statistical literature, such priors are herein called reference priors to recognize that they can be interpreted as providing a sensible reference point against which the implications of alternative priors can be compared. Here, the Jeffreys' prior is demonstrated for the Ricker and Beverton–Holt stock–recruit curves, von Bertalanffy growth curve, Schaefer surplus production model, and sequential population analysis. The Jeffreys' priors for relevant derived parameters are demonstrated, including the steepness parameter of the Beverton–Holt stock–recruit curve. The sequential population analysis example is used to show that the Jeffreys' prior should not be automatically accepted as a reference prior in all models—this needs to be decided on a case-by-case basis.

scholarly journals Inference with Normal-Jeffreys Prior Distributions in Quantile Regression

2017 ◽  
Vol 13 (03) ◽  
pp. 04-09
Author(s):  
Rahim Alhamzawi ◽  
Intisar Ibrahim Allyas
Keyword(s):  
Quantile Regression ◽  
Jeffreys Prior ◽  
Prior Distributions

scholarly journals BNNpriors: A library for Bayesian neural network inference with different prior distributions

2021 ◽  
pp. 100079
Author(s):  
Vincent Fortuin ◽  
Adrià Garriga-Alonso ◽  
Mark van der Wilk ◽  
Laurence Aitchison
Keyword(s):  
Neural Network ◽  
Network Inference ◽  
Bayesian Neural Network ◽  
Prior Distributions

scholarly journals An FDA-Based Approach for Clustering Elicited Expert Knowledge

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 184-204
Author(s):  
Carlos Barrera-Causil ◽  
Juan Carlos Correa ◽  
Andrew Zamecnik ◽  
Francisco Torres-Avilés ◽  
Fernando Marmolejo-Ramos
Keyword(s):  
Functional Data ◽  
Expert Knowledge ◽  
Probability Distributions ◽  
Knowledge Elicitation ◽  
Parallel Analysis ◽  
Data Sets ◽  
Dimensional Problem ◽  
Prior Distributions ◽  
Infinite Dimensional ◽  
Finite Dimensional

Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian inference is then to find ways to reconcile discrepant elicited prior distributions. This paper proposes the parallel analysis of clusters of prior distributions through a hierarchical method for clustering distributions and that can be readily extended to functional data. The proposed method consists of (i) transforming the infinite-dimensional problem into a finite-dimensional one, (ii) using the Hellinger distance to compute the distances between curves and thus (iii) obtaining a hierarchical clustering structure. In a simulation study the proposed method was compared to k-means and agglomerative nesting algorithms and the results showed that the proposed method outperformed those algorithms. Finally, the proposed method is illustrated through an EKE experiment and other functional data sets.

Jeffreys' prior is asymptotically least favorable under entropy risk

1994 ◽  
Vol 41 (1) ◽  
pp. 37-60 ◽  
Author(s):  
Bertrand S. Clarke ◽  
Andrew R. Barron
Keyword(s):  
Jeffreys Prior
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