DEMPSTER BELIEF FUNCTIONS ARE BASED ON THE PRINCIPLE OF COMPLETE IGNORANCE

2000 ◽  
Vol 08 (03) ◽  
pp. 271-284 ◽  
Author(s):  
PETER P. WAKKER
Keyword(s):  
Bayesian Approach ◽  
Belief Function ◽  
Belief Functions ◽  
Strict Adherence ◽  
Second Stage ◽  
Subjective Information ◽  
State Of Nature ◽  
Complete Ignorance ◽  
True State ◽  
The Bayesian Approach

This paper shows that a "principle of complete ignorance" plays a central role in decisions based on Dempster belief functions. Such belief functions occur when, in a first stage, a random message is received and then, in a second stage, a true state of nature obtains. The uncertainty about the random message in the first stage is assumed to be probabilized, in agreement with the Bayesian principles. For the uncertainty in the second stage no probabilities are given. The Bayesian and belief function approaches part ways in the processing of the uncertainty in the second stage. The Bayesian approach requires that this uncertainty also be probabilized, which may require a resort to subjective information. Belief functions follow the principle of complete ignorance in the second stage, which permits strict adherence to objective inputs.

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.

Extended two-dimensional belief function based on divergence measurement

2020 ◽  
pp. 1-8
Author(s):  
Jianping Fan ◽  
Jing Wang ◽  
Meiqin Wu
Keyword(s):  
Belief Function ◽  
Distribution Functions ◽  
Divergence Measure ◽  
Uncertain Information ◽  
Belief Functions ◽  
Two Dimensional ◽  
Probability Distribution Functions ◽  
Basic Probability ◽  
The Difference ◽  
Supporting Degree

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

scholarly journals The Bayesian Approach and the Results of the ISAR-REACT 5 Trial

2021 ◽  
Vol 14 (2) ◽  
pp. 231-232
Author(s):  
Adnan Kastrati ◽  
Alexander Hapfelmeier
Keyword(s):  
Bayesian Approach ◽  
The Bayesian Approach

A new Bayesian approach for QTL mapping of family data

2021 ◽  
Author(s):  
Daiane Aparecida Zuanetti ◽  
Luis Aparecido Milan
Keyword(s):  
Qtl Mapping ◽  
Random Effects ◽  
Bayesian Approach ◽  
Variance Component ◽  
Mendelian Inheritance ◽  
Family Data ◽  
Data Sets ◽  
Mendelian Segregation ◽  
Gaw17 Data ◽  
The Bayesian Approach

In this paper, we propose a new Bayesian approach for QTL mapping of family data. The main purpose is to model a phenotype as a function of QTLs’ effects. The model considers the detailed familiar dependence and it does not rely on random effects. It combines the probability for Mendelian inheritance of parents’ genotype and the correlation between flanking markers and QTLs. This is an advance when compared with models which use only Mendelian segregation or only the correlation between markers and QTLs to estimate transmission probabilities. We use the Bayesian approach to estimate the number of QTLs, their location and the additive and dominance effects. We compare the performance of the proposed method with variance component and LASSO models using simulated and GAW17 data sets. Under tested conditions, the proposed method outperforms other methods in aspects such as estimating the number of QTLs, the accuracy of the QTLs’ position and the estimate of their effects. The results of the application of the proposed method to data sets exceeded all of our expectations.

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