A copula method for modeling directional dependence of genes

Kim, Jong Min; Jung, Yoonsung; Sungur, Engin A.; Han, Kap Hoon; Park, Changyi; Sohn, Insuk

doi:10.1186/1471-2105-9-225

Cited by 62 publications

(37 citation statements)

References 22 publications

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“…The dependence structure of a composite response can be fully described using the marginal distributions of each variable and the association between them. Copulas have historically been popular in the fields of financial analysis (Melchiori, 2003), biological system modeling (Kim et al, 2008), and more recently applied to driver injury modeling in vehicle crashes (Yasmin, Eluru, Pinjari, & Tay, 2014). They offer a promising approach for describing the interdependence between elements of drivers' responses.…”

Section: Modeling Toolset: Copulas and Monte Carlo Simulationmentioning

confidence: 99%

From Few to Many: Using Copulas and Monte Carlo Simulation to Estimate Safety Consequences

Venkatraman

Lee

Schwarz

2015

Proceedings of the 8th International Driving Symposium on Human Factors in Driver Assessment, Training, and Vehicle Design: Dri

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Summary:With the introduction of more advanced vehicle technology, it is paramount to assess its safety benefit. Advanced driver assistance systems (ADAS) can reduce crashes and mitigate crash severity, if designed appropriately. Driver behavior models are integral to the ADAS design process, complementing time and resource intensive human participant experiments. We introduce a method to model driver responses to forward collision events by quantifying multivariate behavior with copulas and Monte Carlo simulation. This approach capitalizes on the data from small samples of crash events observed in naturalistic or simulator studies. Copulas summarize data by capturing the underlying joint distribution of variables, and Monte Carlo methods can be used to repeatedly sample from these distributions. A driver model can be parameterized with these samples, and run on a desktop driving simulation environment.

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Section: Modeling Toolset: Copulas and Monte Carlo Simulationmentioning

confidence: 99%

From Few to Many: Using Copulas and Monte Carlo Simulation to Estimate Safety Consequences

Venkatraman

Lee

Schwarz

2015

Proceedings of the 8th International Driving Symposium on Human Factors in Driver Assessment, Training, and Vehicle Design: Dri

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“…Attempts to relax such linearity assumptions include entropy networks (Hausser and Strimmer 2009;Meyer et al 2007) and copula-based approaches (Kim et al 2008).…”

Section: Other Graphical Modelsmentioning

confidence: 99%

Introduction to Graphical Modelling

Scutari

Strimmer²

2011

Handbook of Statistical Systems Biology

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The aim of this chapter is twofold. In the first part (Sections 12.1, 12.2 and 12.3) we will provide a brief overview of the mathematical and statistical foundations of graphical models, along with their fundamental properties, estimation and basic inference procedures. In particular we will develop Markov networks (also known as Markov random fields) and Bayesian networks, which are the subjects of most past and current literature on graphical models. In the second part (Section 12.4) we will review some applications of graphical models in systems biology. Graphical Structures and Random VariablesGraphical models are a class of statistical models which combine the rigour of a probabilistic approach with the intuitive representation of relationships given by graphs. They are composed by two parts:1. a set X = {X 1 , X 2 , . . . , X p } of random variables describing the quantities of interest. The statistical distribution of X is called the global distribution of the data, while the components it factorises into are called local distributions.2. a graph G = (V, E) in which each vertex v ∈ V, also called a node, is associated with one of the random variables in X (they are usually referred to interchangeably). Edges e ∈ E, also called links, are used to express the dependence structure of the data (the set of dependence relationships among Graph representations meet our earlier requirements of explicitness, saliency, and stability. The links in the graph permit us to express directly and quantitatively the dependence relationships, and the graph topology displays these relationships explicitly and preserves them, under any assignment of numerical parameters.The nature of the link outlined above between the dependence structure of the data and its graphical representation is given again by Pearl (1988) in terms of conditional independence (denoted with ⊥ ⊥ P ) and graphical separation (denoted with ⊥ ⊥ G ).Definition 12.1.1 A graph G is a dependency map (or D-map) of the probabilistic dependence structure P of X if there is a one-to-one correspondence between the random variables in X and the nodes V of G, such that for all disjoint subsets A, B, C of X we have Similarly, G is an independency map (or I-map) of P ifG is said to be a perfect map of P if it is both a D-map and an I-map, that is (12.3) and in this case P is said to be isomorphic to G.Note that this definition does not depend on a particular characterisation of graphical separation, and therefore on the type of graph used in the graphical model. In fact both Markov networks (Whittaker 1990) and Bayesian networks (Pearl 1988), which are by far the two most common classes of graphical models treated in literature, are defined as minimal I-maps even though the former use undirected graphs an the latter use directed acyclic graphs. Minimality requires that, if the dependence structure P of X can be expressed by multiple graphs, we must use the one with the minimum number of edges; if any further edge is removed then the graph is no longer an I-map of P...

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“…In economics, Patton (2006) considered an extension of the theory of copulas to model asymmetric exchange rate dependency. In biomedical studies, Kim et al (2008) also utilized a copula method for modeling directional dependence of genes.…”

Section: Introductionmentioning

confidence: 99%

Application of a nested trivariate copula structure in a competing duration hazard-based vehicle transaction decision model

Rashidi

Mohammadian

2016

Transportmetrica A: Transport Science

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Vehicle ownership has been the subject of numerous transportation studies, which typically have adopted a variety of econometric frameworks at both aggregate and disaggregate choice modeling levels. These models have covered various aspects of vehicle ownership, including vehicle transaction behavior, number of vehicles held, vehicle type choice, and vehicle use. Vehicle transaction models have been developed in both static and dynamic paradigms. However, traditionally transaction timing has been overlooked in static vehicle ownership models despite the significant role that it plays in explaining vehicle ownership behavior. The decision about transaction type is typically assumed to be independently made; therefore, independent timing models are developed for each transaction type. This study aims to introduce a joint transaction type and timing model at the disaggregate level of individuals using a discrete competing proportional hazard model. The inter-correlation among multiple transaction types is modeled in this study by utilizing a set of multivariate Archimedean copula density functions to approximate the multivariate probability density function for the error terms of transaction types in a fully nested structure. ARTICLE HISTORY

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A copula method for modeling directional dependence of genes

Cited by 62 publications

References 22 publications

From Few to Many: Using Copulas and Monte Carlo Simulation to Estimate Safety Consequences

From Few to Many: Using Copulas and Monte Carlo Simulation to Estimate Safety Consequences

Introduction to Graphical Modelling

Application of a nested trivariate copula structure in a competing duration hazard-based vehicle transaction decision model

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