GRAPHOID PROPERTIES OF QUALITATIVE POSSIBILISTIC INDEPENDENCE RELATIONS

2005 ◽  
Vol 13 (01) ◽  
pp. 59-96 ◽  
Author(s):  
NAHLA BEN AMOR ◽  
SALEM BENFERHAT
Keyword(s):  
Bayesian Networks ◽  
Possibility Theory ◽  
Uncertain Reasoning ◽  
Joint Distributions ◽  
The World ◽  
Theory Framework ◽  
Independence Relations

Independence relations play an important role in uncertain reasoning based on Bayesian networks. In particular, they are useful in decomposing joint distributions into more elementary local ones. Recently, in a possibility theory framework, several qualitative independence relations have been proposed, where uncertainty is encoded by means of a complete pre-order between states of the world. This paper studies the well-known graphoid properties of these qualitative independences. Contrary to the probabilistic independence, several qualitative independence relations are not necessarily symmetric. Therefore, we also analyze the symmetric counterparts of graphoid properties (called reverse graphoid properties).

A THEORETICAL FRAMEWORK FOR POSSIBILISTIC INDEPENDENCE IN A WEAKLY ORDERED SETTING

2002 ◽  
Vol 10 (02) ◽  
pp. 117-155 ◽  
Author(s):  
N. BEN AMOR ◽  
K. MELLOULI ◽  
S. BENFERHAT ◽  
D. DUBOIS ◽  
H. PRADE
Keyword(s):  
Graphical Representation ◽  
Multiple Criteria Decision Making ◽  
Possibility Theory ◽  
General Definition ◽  
Uncertain Reasoning ◽  
Joint Distributions ◽  
The World ◽  
Definition Of ◽  
The Impact ◽  
Independence Relations

The notion of independence is central in many information processing areas, such as multiple criteria decision making, databases, or uncertain reasoning. This is especially true in the later case, where the success of Bayesian networks is basically due to the graphical representation of independence they provide. This paper first studies qualitative independence relations when uncertainty is encoded by a complete pre-order between states of the world. While a lot of work has focused on the formulation of suitable definitions of independence in uncertainty theories our interest in this paper is rather to formulate a general definition of independence based on purely ordinal considerations, and that applies to all weakly ordered settings. The second part of the paper investigates the impact of the embedding of qualitative independence relations into the scale-based possibility theory. The absolute scale used in this setting enforces the commensurateness between local pre-orders (since they share the same scale). This leads to an easy decomposability property of the joint distributions into more elementary relations on the basis of the independence relations. Lastly we provide a comparative study between already known definitions of possibilistic independence and the ones proposed here.

Hierarchical Bayesian Models

2015 ◽  
Author(s):  
N. Thompson Hobbs ◽  
Mevin B. Hooten
Keyword(s):  
Bayesian Networks ◽  
Hierarchical Models ◽  
Bayesian Models ◽  
Research Problem ◽  
Hierarchical Bayesian ◽  
Hierarchical Bayesian Models ◽  
Broad Application ◽  
Joint Distributions ◽  
Definition Of

This chapter seeks to explain hierarchical models and how they differ from simple Bayesian models and to illustrate building hierarchical models using mathematically correct expressions. It begins with the definition of hierarchical models. Next, the chapter introduces four general classes of hierarchical models that have broad application in ecology. These classes can be used individually or in combination to attack virtually any research problem. Examples are used to show how to draw Bayesian networks that portray stochastic relationships between observed and unobserved quantities. The chapter furthermore shows how to use network drawings as a guide for writing posterior and joint distributions.

scholarly journals Uncertain lightweight ontologies in a product-based possibility theory framework

2017 ◽  
Vol 88 ◽  
pp. 237-258 ◽  
Author(s):  
Khaoula Boutouhami ◽  
Salem Benferhat ◽  
Faiza Khellaf ◽  
Farid Nouioua
Keyword(s):  
Possibility Theory ◽  
Theory Framework

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.

scholarly journals PredictingMycobacterium tuberculosisComplex Clades Using Knowledge-Based Bayesian Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Minoo Aminian ◽  
David Couvin ◽  
Amina Shabbeer ◽  
Kane Hadley ◽  
Scott Vandenberg ◽  
...  
Keyword(s):  
Bayesian Networks ◽  
Dna Fingerprint ◽  
Support Vector ◽  
Rule Based ◽  
Polyhedral Sets ◽  
Knowledge Based ◽  
Novel Approach ◽  
The World ◽  
Rule Set

We develop a novel approach for incorporating expert rules into Bayesian networks for classification ofMycobacterium tuberculosiscomplex (MTBC) clades. The proposed knowledge-based Bayesian network (KBBN) treats sets of expert rules as prior distributions on the classes. Unlike prior knowledge-based support vector machine approaches which require rules expressed as polyhedral sets, KBBN directly incorporates the rules without any modification. KBBN uses data to refine rule-based classifiers when the rule set is incomplete or ambiguous. We develop a predictive KBBN model for 69 MTBC clades found in the SITVIT international collection. We validate the approach using two testbeds that model knowledge of the MTBC obtained from two different experts and large DNA fingerprint databases to predict MTBC genetic clades and sublineages. These models represent strains of MTBC using high-throughput biomarkers called spacer oligonucleotide types (spoligotypes), since these are routinely gathered from MTBC isolates of tuberculosis (TB) patients. Results show that incorporating rules into problems can drastically increase classification accuracy if data alone are insufficient. The SITVIT KBBN is publicly available for use on the World Wide Web.

The Systems Theory Framework of Career Development: History and future Directions

2002 ◽  
Vol 11 (3) ◽  
pp. 63-69 ◽  
Author(s):  
Mary McMahon
Keyword(s):  
Career Development ◽  
Work Environment ◽  
Systems Theory ◽  
Future Directions ◽  
Career Theory ◽  
Development History ◽  
Rapid Changes ◽  
The World ◽  
Theory Framework ◽  
Career Practice

Since the 1980s, rapid changes in the world of work have challenged the capacity of career theory to provide adequate explanations of career and career development and the ability of traditional career practice to respond to the varied career development needs of clients in this new work environment It was against this complex and rapidly changing context that the Systems Theory Framework of career development (STF) was created. This article will review the history and development of the STF since its first publication as a contextual model in the inaugural edition of the Australian Journal of Career Development in November 1992.

REPRESENTING CONDITIONAL INDEPENDENCE RELATIONS BY VALUATION NETWORKS

1994 ◽  
Vol 02 (02) ◽  
pp. 143-165 ◽  
Author(s):  
PRAKASH P. SHENOY
Keyword(s):  
Conditional Independence ◽  
Directed Acyclic Graph ◽  
Function Theory ◽  
Possibility Theory ◽  
Belief Function ◽  
Probability Models ◽  
Graph Models ◽  
Belief Function Theory ◽  
Belief Theory ◽  
Independence Relations

Valuation networks have been proposed as graphical representations of valuation-based systems. The axiomatic framework of valuation-based systems is able to capture many uncertainty calculi including probability theory, Dempster-Shafer's belief-function theory, Spohn's epistemic belief theory, and Zadeh's possibility theory. In this paper, we show how valuation networks encode conditional independence relations. For the probabilistic case, the class of probability models encoded by valuation networks includes undirected graph models, directed acyclic graph models, directed balloon graph models, and recursive causal graph models.

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