scholarly journals Prior Setting In Practice: Strategies and rationales used in choosing prior distributions for Bayesian analysis

2020 ◽  
Author(s):  
Abhraneel Sarma ◽  
Matthew Kay
Keyword(s):  
Statistical Analysis ◽  
Bayesian Analysis ◽  
Design Tools ◽  
Informative Priors ◽  
Prior Distributions ◽  
Normative Approach ◽  
Interactive Visualizations ◽  
Probability Mass ◽  
Different Levels ◽  
Mass Allocation

Bayesian statistical analysis is steadily growing in popularity and use. Choosing priors is an integral part of Bayesian inference. While there exist extensive normative recommendations for prior setting, little is known about how priors are chosen in practice. We conducted a survey (N = 50) and interviews (N = 9) where we used interactive visualizations to elicit prior distributions from researchers experienced with Bayesian statistics and asked them for rationales for those priors. We found that participants' experience and philosophy influence how much and what information they are willing to incorporate into their priors, manifesting as different levels of informativeness and skepticism. We also identified three broad strategies participants use to set their priors: centrality matching, interval matching, and visual probability mass allocation. We discovered that participants' understanding of the notion of "weakly informative priors"---a commonly-recommended normative approach to prior setting---manifests very differently across participants. Our results have implications both for how to develop prior setting recommendations and how to design tools to elicit priors in Bayesian analysis.

PSYCHOLOGICAL FEATURES OF EDUCATION AND TOLERANCE IN STUDENTS

2018 ◽  
Vol 16 (1) ◽  
pp. 112-119
Author(s):  
VLADIMIR GLEB NAYDONOV
Keyword(s):  
Statistical Analysis ◽  
Training Program ◽  
Rich Diversity ◽  
Interethnic Differences ◽  
The World ◽  
The Rich ◽  
Correct Understanding ◽  
Psychological Features ◽  
Different Levels

The article considers the students’ tolerance as a spectrum of personal manifestations of respect, acceptance and correct understanding of the rich diversity of cultures of the world, values of others’ personality. The purpose of the study is to investgate education and the formation of tolerance among the students. We have compiled a training program to improve the level of tolerance for interethnic differences. Based on the statistical analysis of the data obtained, the most important values that are significant for different levels of tolerance were identified.

Who Wins and Who Loses in the Provincial Courts of Appeal? A Statistical Analysis, 1920–1990

1994 ◽  
Vol 9 (2) ◽  
pp. 21-40 ◽  
Author(s):  
Peter McCormick
Keyword(s):  
United States ◽  
Statistical Analysis ◽  
Great Britain ◽  
Data Base ◽  
The United States ◽  
Different Types ◽  
Party Capability ◽  
Time Periods ◽  
Appeal Courts ◽  
Different Levels

AbstractGiven the visibility and obvious importance of judicial power in the age of the Charter, it is important to develop the conceptual vocabulary for desribing and assessing this power. One such concept that has been applied to the study of appeal courts in the United States and Great Britain is “party capability”, a theory which suggests that different types of litigant will enjoy different levels of success as both appellant and respondent. Using a data base derived from the reported decisions of the provincial courts of appeal for the second and seventh year of each decade since the 1920s, this article applies party capability theory to the performance of the highest courts of the ten provinces; comparisons are attempted across regions and across time periods, as well as with the findings of similar studies of American and British courts.

DERIVING ROBUST BAYESIAN PREMIUMS UNDER BANDS OF PRIOR DISTRIBUTIONS WITH APPLICATIONS

2018 ◽  
Vol 49 (1) ◽  
pp. 147-168 ◽  
Author(s):  
M. Sánchez-Sánchez ◽  
M.A. Sordo ◽  
A. Suárez-Llorens ◽  
E. Gómez-Déniz
Keyword(s):  
Bayesian Analysis ◽  
Likelihood Ratio ◽  
Requirements Elicitation ◽  
Likelihood Ratio Order ◽  
Prior Distributions ◽  
Propagation Of Uncertainty ◽  
Distortion Functions ◽  
Wide Family ◽  
Class Of Priors ◽  
Quantities Of Interest

AbstractWe study the propagation of uncertainty from a class of priors introduced by Arias-Nicolás et al. [(2016) Bayesian Analysis, 11(4), 1107–1136] to the premiums (both the collective and the Bayesian), for a wide family of premium principles (specifically, those that preserve the likelihood ratio order). The class under study reflects the prior uncertainty using distortion functions and fulfills some desirable requirements: elicitation is easy, the prior uncertainty can be measured by different metrics, and the range of quantities of interest is easily obtained from the extremal members of the class. We illustrate the methodology with several examples based on different claim counts models.

scholarly journals SHAMAN: a user-friendly website for metataxonomic analysis from raw reads to statistical analysis

2020 ◽  
Author(s):  
Stevenn Volant ◽  
Pierre Lechat ◽  
Perrine Woringer ◽  
Laurence Motreff ◽  
Christophe Malabat ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Data Processing ◽  
Web Application ◽  
Graphical Representation ◽  
Statistical Modelling ◽  
Metagenomic Data ◽  
Sequencing Data ◽  
Microbiome Research ◽  
Interactive Visualizations ◽  
User Friendly

Abstract BackgroundComparing the composition of microbial communities among groups of interest (e.g., patients vs healthy individuals) is a central aspect in microbiome research. It typically involves sequencing, data processing, statistical analysis and graphical representation of the detected signatures. Such an analysis is normally obtained by using a set of different applications that require specific expertise for installation, data processing and in some case, programming skills. ResultsHere, we present SHAMAN, an interactive web application we developed in order to facilitate the use of (i) a bioinformatic workflow for metataxonomic analysis, (ii) a reliable statistical modelling and (iii) to provide among the largest panels of interactive visualizations as compared to the other options that are currently available. SHAMAN is specifically designed for non-expert users who may benefit from using an integrated version of the different analytic steps underlying a proper metagenomic analysis. The application is freely accessible at http://shaman.pasteur.fr/, and may also work as a standalone application with a Docker container (aghozlane/shaman), conda and R. The source code is written in R and is available at https://github.com/aghozlane/shaman. Using two datasets (a mock community sequencing and published 16S rRNA metagenomic data), we illustrate the strengths of SHAMAN in quickly performing a complete metataxonomic analysis. ConclusionsWe aim with SHAMAN to provide the scientific community with a platform that simplifies reproducible quantitative analysis of metagenomic data.

scholarly journals Section 4: Investigation of Potential Sources of Variation

Radiocarbon ◽  
2003 ◽  
Vol 45 (2) ◽  
pp. 175-212 ◽  
Keyword(s):  
Statistical Analysis ◽  
Limited Information ◽  
Potential Sources ◽  
Sources Of Variation ◽  
Background Material ◽  
Laboratory Procedures ◽  
Different Levels ◽  
Modern Standard

The design of FIRI is such that for each laboratory, we have some basic, though limited, information on the laboratory procedures, including the method of pretreatment applied to the samples, the modern standard, and the background material used. These can be considered as factors in the experiment and through statistical analysis, we can investigate whether they offer a statistically significant explanation of the observed variation. The different levels of the factors are described in Table 4.1. In addition, the laboratory type is also considered as a further factor (with 3 levels of LSC, GPC, and AMS).

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.

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