A Predictive Bayesian Approach to Multistate Reliability Analysis

2003 ◽  
Vol 10 (03) ◽  
pp. 221-234 ◽  
Author(s):  
T. Aven ◽  
A. Hjorteland
Keyword(s):  
Reliability Analysis ◽  
Bayesian Approach ◽  
Probability Models ◽  
Bayesian Paradigm ◽  
Bayesian Procedures ◽  
Starting Point ◽  
The World ◽  
The Bayesian Approach

In this paper we discuss how to implement a Bayesian thinking for multistate reliability analysis. The Bayesian paradigm comprises a unified and consistent framework for analysing and expressing reliability, but in our view the standard Bayesian procedures gives too much emphasis on probability models and inference on fictional parameters. We believe that there is a need for a rethinking on how to implement the Bayesian approach, and in this paper we present and discuss such a rethinking for multistate reliability analysis. The starting point of the analysis should be observable quantities, expressing states of the world, not fictional parameters.

Likelihood Ratio in Evidential Evaluation of Polygraph Examination

2019 ◽  
Vol 11 (1) ◽  
pp. 95-112
Author(s):  
Jerzy Konieczny ◽  
Paulina Wolańska-Nowak
Keyword(s):  
Likelihood Ratio ◽  
Bayesian Approach ◽  
Forensic Identification ◽  
Internal Security ◽  
Evaluation Practice ◽  
Examination Result ◽  
Starting Point ◽  
Polygraph Examination ◽  
New Perspective ◽  
The Bayesian Approach

The starting point of the paper is the observation that the likelihood ratio (LR) is not used in the evaluation practice of — so important in the field of internal security — polygraph examinations. Meanwhile, LR is the only scientifically justifiable parameter that shows the evidential weight of particular evidence. The authors present theoretical attempts to use LR for evidential assessment of the polygraph examinations value and subject them to criticism. The main objective of the paper is to present the LR calculation procedure in the context of interpretation of a polygraph examination result treated as evaluative expertise. The following assumptions are made: the analysis includes only comparison question techniques; examination results enable to include a relevant subject only in one of the three categories: deception indicated, no deception indicated, inconclusive; there are various ways to assign LR; in the course of LR assignment, the arbitrary adoption of the values of some variables is admissible. Several examples of LR calculations are presented in different tactical configurations of polygraph examinations. The significance of including the inconclusive results in the examination technique characteristics is analysed. The possibility of applying the cumulative LR is indicated, however, leaving this question open. Consequences of the LR application in the interpretation of polygraph examinations are also presented as an argument in the criminal analysis. Conclusions show that treating polygraph examinations as evaluative expertise opens a new perspective on this method of forensic identification and deserves to be continued; however, the issue of the evidential use of polygraph examination results, in the light of the evaluation made with the use of the Bayesian approach, requires a number of further discussions among lawyers and scientists.

scholarly journals Principles of Statistical Inference: Likelihood and the Bayesian Paradigm

2010 ◽  
Vol 16 ◽  
pp. 1-18 ◽  
Author(s):  
Steve C. Wang
Keyword(s):  
Maximum Likelihood ◽  
Statistical Inference ◽  
Bayesian Approach ◽  
Subjective Probability ◽  
Prior Information ◽  
Maximum Likelihood Estimators ◽  
Likelihood Ratio Tests ◽  
Bayesian Paradigm ◽  
Point Estimators ◽  
The Bayesian Approach

We review two foundations of statistical inference, the theory of likelihood and the Bayesian paradigm. We begin by applying principles of likelihood to generate point estimators (maximum likelihood estimators) and hypothesis tests (likelihood ratio tests). We then describe the Bayesian approach, focusing on two controversial aspects: the use of prior information and subjective probability. We illustrate these analyses using simple examples.

Integrating QRA and SRA Methods Within a Bayesian Framework When Calculating Risk in Marine Operations: Two Examples

2000 ◽  
Vol 122 (3) ◽  
pp. 181-187 ◽  
Author(s):  
Wenche K. Rettedal ◽  
Terje Aven ◽  
Ove T. Gudmestad
Keyword(s):  
Risk Analysis ◽  
Reliability Analysis ◽  
Bayesian Approach ◽  
Structural Reliability ◽  
Fault Tree ◽  
Bayesian Approaches ◽  
Objective Risk ◽  
Suitable Framework ◽  
Fully Bayesian ◽  
The Bayesian Approach

This paper concerns itself with the integration of QRA (quantitative risk analysis) and SRA (structural reliability analysis) methods. For simplicity, we will use the term SRA instead of SRA methods in the paper. The Bayesian (subjective) approach seems to be the most appropriate framework for such integrated analyses. It may, however, not be clear to all what the Bayesian approach really means. There exists alternative Bayesian approaches, and the integration of SRA and QRA is very much dependent on what the basis is. The purpose of this paper is to present two marine operation examples, implementing two different Bayesian approaches: the “classical Bayesian approach” and the “fully Bayesian approach.” Following the classical Bayesian approach, we estimate a true, objective risk, whereas in the fully Bayesian approach, risk is a way of expressing uncertainty about future observable quantities. In both examples, one initial accidental event is investigated by using a fault tree and by integrating SRA into this fault tree. We conclude that the most suitable framework for integrating SRA and QRA is to adopt the “fully Bayesian approach.” [S0892-7219(00)00703-2]

Bayesian Procedures for Discriminating Among Hypotheses With Discrete Distributions: Inheritance in the Tetraploid Astilbe biternata

Genetics ◽  
1997 ◽  
Vol 147 (4) ◽  
pp. 1933-1942
Author(s):  
Matthew S Olson
Keyword(s):  
Bayesian Analysis ◽  
Prior Knowledge ◽  
Bayesian Approach ◽  
Discrete Distributions ◽  
Southern Appalachians ◽  
Herbaceous Plant ◽  
Bayesian Procedures ◽  
Disomic Inheritance ◽  
Cytogenetic Evidence ◽  
The Bayesian Approach

Abstract Discrimination between disomic and tetrasomic inheritance aids in determining whether tetraploids originated by allotetraploidy or autotetraploidy, respectively. Past assessments of inheritance in tetraploids have used analyses whereby each inheritance hypothesis is tested independently. I present a Bayesian analysis that is appropriate for discriminating among several inheritance hypotheses and can be used in any case where hypotheses are defined by discrete distributions. The Bayesian approach incorporates prior knowledge of the probability of occurrence of disomic and tetrasomic hypotheses so that the results of the analysis are not biased by the fact that there is a single tetrasomic hypothesis and multiple disomic hypotheses. This analysis is used to interpret data from crosses in the tetraploid Astilbe biternata, a herbaceous plant native to the southern Appalachians. The progeny ratios from all crosses favored the hypothesis of disomic inheritance at both the PGM and slow-PGI loci. These results support earlier cytogenetic evidence for the allotetraploid origin of Astilbe biternata.

scholarly journals Selectivity of a fishing gear used in the catch of Anomalocardia flexuosa in the Northeast of Brazil

2020 ◽  
Vol 50 (8) ◽  
Author(s):  
Severino Adriano de Oliveira Lima ◽  
Humber Agrelli Andrade ◽  
Alfredo Olivera Gálvez
Keyword(s):  
Logistic Regression ◽  
Bayesian Approach ◽  
Reference Value ◽  
The State ◽  
Fishing Gear ◽  
Selectivity Estimation ◽  
The World ◽  
The Bayesian Approach

ABSTRACT: A type of dredge was introduced as fishing gear along the extractive bank of Mangue Seco - PE from which the largest annual catch of Anomalocardia flexuosa in the world is extracted. This study was carried out with the objective of estimating the selectivity of the new fishing gear and quantitatively evaluating the length classes most compromised by the catches, especially considering 20 mm as the reference value. Specimens larger than this size are most likely to be mature. For the selectivity estimation, the methodology using codends (16 or 20 mm) and small meshed cover (2 mm) was used. To estimate the selectivity parameters, a logistic regression and the Bayesian approach were used. The transition between the state in which the specimen is invulnerable to the fishing gear and vulnerable occurs between 10 and 18 mm, using a 16 mm mesh, and using a 20 mm mesh, this transition is between 14 and 20 mm. Dredgers with 16 mm and 20 mm mesh compromise a large proportion of specimens smaller than 20 mm. If the intention is to protect this part of the population, measures such as total restriction of the 16 mm mesh and use of the 20 mm mesh should be necessary only in the months of less catching incidences, or increasing the mesh to 25 mm.

The Re-Evaluation of Structural Reliability based on Identification Results

1999 ◽  
Vol 15 (3) ◽  
pp. 109-116
Author(s):  
Pei-Ling Liu ◽  
Yi-Song Chen
Keyword(s):  
Sensitivity Analysis ◽  
System Identification ◽  
Reliability Analysis ◽  
Bayesian Approach ◽  
Structural Reliability ◽  
Service System ◽  
Maintenance Strategy ◽  
Prior Distributions ◽  
The Bayesian Approach

AbstractThis paper develops a method to re-evaluate the reliability of a structure after a period of service. System identification is performed on the structure to identify the current properties of the structure. The Bayesian approach is adopted to modify the prior distributions of the properties based on the identification results. Then, reliability analysis is performed on the structure using the updated distributions of the properties. Sensitivity analysis is also performed to attain the maintenance strategy.

Bayesianism: Objections and Rebuttals

2021 ◽  
pp. 267-286
Author(s):  
Norman Fenton ◽  
David Lagnado
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Bayesian Approach ◽  
Legal Reasoning ◽  
Statistical Evidence ◽  
Subjective Measure ◽  
Probability Judgments ◽  
Legal Case ◽  
The World ◽  
The Bayesian Approach

While the laws of probability are rarely disputed, the question of how we should interpret probability judgments is less straightforward. Broadly, there are two ways to conceive of probability—either as an objective feature of the world, or as a subjective measure of our uncertainty. Both notions have their place in science, but it is the latter subjective notion (the Bayesian approach) that is crucial in legal reasoning. This chapter explains the advantages of using Bayesian networks in adjudicative factfinding. It addresses a number of common objections to the Bayesian approach, such as “There is no such thing as a probability of a single specified event”; “The Bayesian approach only works with statistical evidence”; “The Bayesian approach is too difficult for legal factfinders to comprehend”; and “A Bayesian network can never capture the full complexity of a legal case.” Fenton and Lagnado offer rebuttals to each of these objections.

USING FULL PROBABILITY MODELS TO COMPUTE PROBABILITIES OF ACTUAL INTEREST TO DECISION MAKERS

2001 ◽  
Vol 17 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Frank E. Harrell ◽  
Ya-Chen Tina Shih
Keyword(s):  
Bayesian Approach ◽  
Posterior Distribution ◽  
Prior Distribution ◽  
Likelihood Function ◽  
Scientific Evidence ◽  
A Priori ◽  
Relevant Information ◽  
Decision Makers ◽  
Probability Models ◽  
The Bayesian Approach

The objective of this paper is to illustrate the advantages of the Bayesian approach in quantifying, presenting, and reporting scientific evidence and in assisting decision making. Three basic components in the Bayesian framework are the prior distribution, likelihood function, and posterior distribution. The prior distribution describes analysts' belief a priori; the likelihood function captures how data modify the prior knowledge; and the posterior distribution synthesizes both prior and likelihood information. The Bayesian approach treats the parameters of interest as random variables, uses the entire posterior distribution to quantify the evidence, and reports evidence in a “probabilistic” manner. Two clinical examples are used to demonstrate the value of the Bayesian approach to decision makers. Using either an uninformative or a skeptical prior distribution, these examples show that the Bayesian methods allow calculations of probabilities that are usually of more interest to decision makers, e.g., the probability that treatment A is similar to treatment B, the probability that treatment A is at least 5% better than treatment B, and the probability that treatment A is not within the “similarity region” of treatment B, etc. In addition, the Bayesian approach can deal with multiple endpoints more easily than the classic approach. For example, if decision makers wish to examine mortality and cost jointly, the Bayesian method can report the probability that a treatment achieves at least 2% mortality reduction and less than $20,000 increase in costs. In conclusion, probabilities computed from the Bayesian approach provide more relevant information to decision makers and are easier to interpret.

scholarly journals Bayesian Benefits for Binomial Applications in Practice

2019 ◽  
pp. 1-9
Author(s):  
Frank Tuyl ◽  
Peter Howley
Keyword(s):  
Bayesian Methods ◽  
Prior Information ◽  
Statistical Software ◽  
Practical Applications ◽  
Bayesian Techniques ◽  
Bayesian Paradigm ◽  
The World ◽  
Binomial Parameter ◽  
Authentic Learning Experiences ◽  
The Bayesian Approach

Introduction: When it comes to the practice, and teaching, of statistics, the world has primarily focused on what is known as classical or frequentist methods, rather than Bayesian methods. Scope of the Study: This paper demonstrates some beneficial properties of Bayesian methods within the commonly practiced domain of inference by utilizing consultancy case studies, one concerning an unusual sample size question and one on the detection of mail items with high biosecurity risk material. Methods: We introduce through practical applications two more aspects of the Bayesian approach which we believe are invaluable to practitioners and instructors. Having in mind readers who may be less familiar with statistical software, we have added Excel instructions which are easy to translate for those who are familiar with any such software. Findings: These cases reflect two valuable aspects for both practitioners and instructors which are unique to the Bayesian paradigm. They are: 1. including prior information to improve inference and how to apply sensitivity analysis to this inclusion and 2. the effortless inference for functions of parameters, compared with frequentist approaches. These examples involving the binomial parameter have not been considered from this perspective before, are of significant practical value and thus benefit students and instructors of courses teaching Bayesian techniques and endeavoring to include authentic learning experiences.

Justification and belief as the basis for proof in criminal trial

2019 ◽  
Vol specjalny (XIX) ◽  
pp. 123-137
Author(s):  
Jerzy Konieczny
Keyword(s):  
Decision Making ◽  
Bayesian Approach ◽  
Belief Function ◽  
Criminal Trial ◽  
Starting Point ◽  
Inductive Character ◽  
The Bayesian Approach

The aim of the article is to present the role of justification and belief in the course of proving guilt in a criminal trial. The starting point is the indication of the inductive character of evidentiary reasoning and the acceptance of its conclusions on the basis of the decision making by trial authority. These decisions appear after the process in which this authority reaches the level of aspirations to make them; the second basis may be their expected usefulness. The requirements for proof are contrasted with the concept of knowledge. If one assumes that the attribution of knowledge to a particular subject consists in the possession of a justified, accurate belief by that subject, then one can assume that the possession of such knowledge is tantamount to proving in a trial sense. The tools supporting the pursuit of correctness of command are the Shafer-Dempster belief function and the Bayesian approach in making decisions about factual findings.

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