1,390 research outputs found
Ranked nodes: A simple and effective way to model qualitative judgements in large-scale Bayesian Networks
Comment: Expert Elicitation for Reliable System Design
Comment: Expert Elicitation for Reliable System Design [arXiv:0708.0279]Comment: Published at http://dx.doi.org/10.1214/088342306000000529 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A hybrid Bayesian network for medical device risk assessment and management
ISO 14971 is the primary standard used for medical device risk management.
While it specifies the requirements for medical device risk management, it does
not specify a particular method for performing risk management. Hence, medical
device manufacturers are free to develop or use any appropriate methods for
managing the risk of medical devices. The most commonly used methods, such as
Fault Tree Analysis (FTA), are unable to provide a reasonable basis for
computing risk estimates when there are limited or no historical data available
or where there is second-order uncertainty about the data. In this paper, we
present a novel method for medical device risk management using hybrid Bayesian
networks (BNs) that resolves the limitations of classical methods such as FTA
and incorporates relevant factors affecting the risk of medical devices. The
proposed BN method is generic but can be instantiated on a system-by-system
basis, and we apply it to a Defibrillator device to demonstrate the process
involved for medical device risk management during production and
post-production. The example is validated against real-world data
Stacking Factorizing Partitioned Expressions in Hybrid Bayesian Network Models
Hybrid Bayesian networks (HBN) contain complex conditional probabilistic
distributions (CPD) specified as partitioned expressions over discrete and
continuous variables. The size of these CPDs grows exponentially with the
number of parent nodes when using discrete inference, resulting in significant
inefficiency. Normally, an effective way to reduce the CPD size is to use a
binary factorization (BF) algorithm to decompose the statistical or arithmetic
functions in the CPD by factorizing the number of connected parent nodes to
sets of size two. However, the BF algorithm was not designed to handle
partitioned expressions. Hence, we propose a new algorithm called stacking
factorization (SF) to decompose the partitioned expressions. The SF algorithm
creates intermediate nodes to incrementally reconstruct the densities in the
original partitioned expression, allowing no more than two continuous parent
nodes to be connected to each child node in the resulting HBN. SF can be either
used independently or combined with the BF algorithm. We show that the SF+BF
algorithm significantly reduces the CPD size and contributes to lowering the
tree-width of a model, thus improving efficiency
Representations of matroids
The concept of matroids was originally introduced by Whitney and Van
der Waerden in the 1930's to generalise the notion of linear dependence in
a vector space; certain axioms satisfied by this relation were observed to
be satisfied by other types of â dependenceâ relations, such as algebraic
dependence and â cycleâ dependence in a graph. Consequently a matroid was
defined to be a set with an abstract dependence relation satisfying these
axioms. One of the most natural questions to ask is whether every such
â matroid' is representable in the obvious sense in a vector space. The
answer is of course no (otherwise matroid theory would be equivalent to
linear algebra) although in the early years of the subject examples of
non-representable matroids were not easily obtainable. In this thesis we
continue the work of Inglcton (in [20]) and Vamos (in [35,36]) on the
representation problem, buiding up to an algebraic treatment in the
important last chapter
- âŚ