scholarly journals Chain Graph Models to Elicit the Structure of a Bayesian Network

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Federico M. Stefanini
Keyword(s):  
Graphical Models ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Graph Model ◽  
Structural Features ◽  
Chain Graph ◽  
Graph Models ◽  
Degree Of Belief ◽  
Statistical Background ◽  
A Chain

Bayesian networks are possibly the most successful graphical models to build decision support systems. Building the structure of large networks is still a challenging task, but Bayesian methods are particularly suited to exploit experts’ degree of belief in a quantitative way while learning the network structure from data. In this paper details are provided about how to build a prior distribution on the space of network structures by eliciting a chain graph model on structural reference features. Several structural features expected to be often useful during the elicitation are described. The statistical background needed to effectively use this approach is summarized, and some potential pitfalls are illustrated. Finally, a few seminal contributions from the literature are reformulated in terms of structural features.

Bayesian Applications in Auditory Research

2019 ◽  
Vol 62 (3) ◽  
pp. 577-586 ◽  
Author(s):  
Garnett P. McMillan ◽  
John B. Cannon
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Interim Analysis ◽  
Iterative Process ◽  
Bayes Theorem ◽  
Sound Therapy ◽  
The Many ◽  
Auditory Research

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592

The interpretation of unsolvable λ-terms in models of untyped λ-calculus

1998 ◽  
Vol 63 (4) ◽  
pp. 1529-1548 ◽  
Author(s):  
Rainer Kerth
Keyword(s):  
Graph Model ◽  
Stable Model ◽  
Graph Models ◽  
Stable Models

AbstractOur goal in this paper is to analyze the interpretation of arbitrary unsolvable λ-terms in a given model of λ-calculus. We focus on graph models and (a special type of) stable models. We introduce the syntactical notion of a decoration and the semantical notion of a critical sequence. We conjecture that any unsolvable term β-reduces to a term admitting a decoration. The main result of this paper concerns the interconnection between those two notions: given a graph model or stable model , we show that any unsolvable term admitting a decoration and having a non-empty interpretation in generates a critical sequence in the model.In the last section, we examine three classical graph models, namely the model of Plotkin and Scott, Engeler's model and Park's model . We show that and do not contain critical sequences whereas does.

scholarly journals Synthesis and crystal structures of a bis(3-hydroxy-cyclohex-2-en-1-one) and two hexahydroquinoline derivatives

2020 ◽  
Vol 76 (2) ◽  
pp. 125-131
Author(s):  
Scott A. Steiger ◽  
Chun Li ◽  
Christina Gates ◽  
Nicholas R. Natale
Keyword(s):  
Hydrogen Bonds ◽  
Title Compound ◽  
Crystal Packing ◽  
Structural Features ◽  
Boat Conformation ◽  
Two Dimensional ◽  
Aryl Group ◽  
Dimensional Network ◽  
A Chain ◽  
Intramolecular Hydrogen

The title compound I, 2,2′-[(2-nitrophenyl)methylene]bis(3-hydroxy-5,5-dimethylcyclohex-2-enone), C23H27NO6, features a 1,3-ketone–enol conformation which is stabilized by two intramolecular hydrogen bonds. The most prominent intermolecular interactions in compound I are C—H...O hydrogen bonds, which link molecules into a two-dimensional network parallel to the (001) plane and a chain perpendicular to (1\overline{1}1). Both title compounds II, ethyl 4-(4-hydroxy-3,5-dimethoxyphenyl)-2,7,7-trimethyl-5-oxo-1,4,5,6,7,8-hexahydroquinoline-3-carboxylate, C23H29NO6, and III, ethyl 4-(anthracen-9-yl)-2,7,7-trimethyl-5-oxo-1,4,5,6,7,8-hexahydroquinoline-3-carboxylate, C29H29NO3, share the same structural features, such as a shallow boat conformation of the dihydropyridine group and an orthogonal aryl group attached to the dihydropyridine. Intermolecular N—H...O bonding is present in the crystal packing of both compound II and III.

A Discrete Chain Graph Model for 3d+t Cell Tracking with High Misdetection Robustness

2012 ◽  
pp. 144-157 ◽  
Author(s):  
Bernhard X. Kausler ◽  
Martin Schiegg ◽  
Bjoern Andres ◽  
Martin Lindner ◽  
Ullrich Koethe ◽  
...  
Keyword(s):  
T Cell ◽  
Cell Tracking ◽  
Graph Model ◽  
Chain Graph

scholarly journals Estimating the Gumbel-Barnett copula parameter of dependence

2018 ◽  
Vol 41 (1) ◽  
pp. 53-73 ◽  
Author(s):  
Jennyfer Portilla Yela ◽  
José Rafael Tovar Cuevas
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Empirical Evaluation ◽  
Bayesian Estimator ◽  
Dependence Structure ◽  
Type I ◽  
Copula Parameter

In this paper, we developed an empirical evaluation of four estimation procedures for the dependence parameter of the Gumbel-Barnett copula obtained from a Gumbel type I distribution. We used the maximum likelihood, moments and Bayesian methods and studied the performance of the estimates, assuming three dependence levels and 20 different sample sizes. For each method and scenario, a simulation study was conducted with 1000 runs and the quality of the estimator was evaluated using four different criteria. A Bayesian estimator assuming a Beta(a,b) as prior distribution, showed the best performance regardless the sample size and the dependence structure.

Graph methods for the investigation of metabolic networks in parasitology

Parasitology ◽  
2010 ◽  
Vol 137 (9) ◽  
pp. 1393-1407 ◽  
Author(s):  
LUDOVIC COTTRET ◽  
FABIEN JOURDAN
Keyword(s):  
Metabolic Network ◽  
Large Scale ◽  
Metabolic Networks ◽  
Graph Model ◽  
New Drugs ◽  
Mathematical Methods ◽  
Graph Models ◽  
Metabolic Network Reconstruction ◽  
Network Analyses ◽  
Genome Scale

SUMMARYRecently, a way was opened with the development of many mathematical methods to model and analyze genome-scale metabolic networks. Among them, methods based on graph models enable to us quickly perform large-scale analyses on large metabolic networks. However, it could be difficult for parasitologists to select the graph model and methods adapted to their biological questions. In this review, after briefly addressing the problem of the metabolic network reconstruction, we propose an overview of the graph-based approaches used in whole metabolic network analyses. Applications highlight the usefulness of this kind of approach in the field of parasitology, especially by suggesting metabolic targets for new drugs. Their development still represents a major challenge to fight against the numerous diseases caused by parasites.

Bayesian Analysis of a 2 × 2 Contingency Table with Both Completely and Partially Cross-Classified Data

1985 ◽  
Vol 10 (1) ◽  
pp. 31-43 ◽  
Author(s):  
Philip J. Smith ◽  
Sung C Choi ◽  
Erdogan Gunel
Keyword(s):  
Experimental Design ◽  
Bayesian Analysis ◽  
Bayesian Methods ◽  
Incomplete Data ◽  
Prior Distribution ◽  
Contingency Table ◽  
Response Variable ◽  
Testing Hypotheses ◽  
Test Conditions ◽  
First Response

A frequently used experimental design is one in which the experimental units are measured twice (e.g., under different test conditions). When the response variable is dichotomous, the equality of the two proportions is usually assessed by a test due to McNemar (1947) . However, in addition to obtaining this complete data where two responses are available for each unit, incomplete data may be available also: In this case observations are available on the first response alone for some units and additional observations are available on the second response alone for other units. In this paper Bayesian methods are presented for estimating and testing hypotheses regarding the two success probabilities in light of both the complete and incomplete data. A method by which the prior distribution may be assessed is sketched and a numerical example to illustrate the method is presented.

scholarly journals Structural features of the first component of human complement, C1, as revealed by surface iodination

1982 ◽  
Vol 203 (1) ◽  
pp. 185-191 ◽  
Author(s):  
C L Villiers ◽  
S Chesne ◽  
M B Lacroix ◽  
G J Arlaud ◽  
M G Colomb
Keyword(s):  
Sucrose Gradient ◽  
Structural Features ◽  
Complement Component ◽  
Monomeric Form ◽  
Human Complement ◽  
Equal Distribution ◽  
A Chain ◽  
Sucrose Gradient Ultracentrifugation ◽  
Label Distribution ◽  
Human Complement Component

Lactoperoxidase-catalysed surface iodination and sucrose-gradient ultracentrifugation were used to investigate the structure of human complement component C1. 1. Proenzymic subcomponents C1r and C1s associated to form a trimeric C1r2-C1s complex (7.6 S) in the presence of EDTA, and a tetrameric Clr2-C1s2 complex (9.1 S) in the presence of Ca2+. Iodination of the 9.1 S complex led to a predominant labelling of C1r (70%) over C1s (30%), essentially located in the b-chain moiety of C1r and in the a-chain moiety of C1s. 2. Reconstruction of proenzymic soluble C1 (15.2 S) from C1q, C1r and C1s was partially inhibited when C1s labelled in its monomeric form was used and almost abolished when iodinated C1r was used. Reconstruction of fully activated C1 was not possible, whereas hybrid C1q-C1r2-C1s2 complex was obtained. 3. Iodination of proenzymic or activated C1 bound to IgG-ovalbumin aggregates led to an equal distribution of the radioactivity between C1q and C1r2-C1s2. With regard to C1q, the label distribution between the three chains was similar whether C1 was in its proenzymic or activated form. Label distribution in the C1r2-C1s2 moiety of C1 was the same as that obtained for isolated C1r2-C1s2, and this was also true for the corresponding activated components. However, two different labelling patterns were found, corresponding to the proenzyme and the activated states.

Finding a chain graph in a bipartite permutation graph

2016 ◽  
Vol 116 (9) ◽  
pp. 569-573 ◽  
Author(s):  
Masashi Kiyomi ◽  
Yota Otachi
Keyword(s):  
Chain Graph ◽  
Permutation Graph ◽  
A Chain
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