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Related Concept Videos

Graphical Representation of Inequalities01:28

Graphical Representation of Inequalities

The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all points...
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Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...
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Related Experiment Video

Updated: May 17, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

Directed acyclic graphs with edge-specific bounds.

Tyler J Vanderweele1, Zhiqiang Tan

  • 1Department of Epidemiology, Harvard School of Public Health, 677 Huntington Avenue, Boston, Massachusetts 02115, U.S.A., tvanderw@hsph.harvard.edu.

Biometrika
|October 11, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces bounded edges in causal graphs to quantify causal effects with unmeasured confounding. This new framework provides methods for estimating treatment effects even when all variables are not observed.

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Area of Science:

  • Causal inference
  • Graphical models
  • Epidemiology

Background:

  • Estimating causal effects is crucial in many scientific fields.
  • Unmeasured confounding poses a significant challenge in observational studies.
  • Existing methods often struggle with unobserved variables.

Purpose of the Study:

  • To define and introduce the concept of a bounded edge within the causal directed acyclic graph (DAG) framework.
  • To generalize the notion of signed edges using bounds on survivor probability ratios.
  • To develop methods for propagating bounds and estimating causal effects under unmeasured confounding.

Main Methods:

  • Definition of a bounded edge based on ratios of survivor probabilities.
  • Derivation of rules for the propagation of these bounds within a causal DAG.
  • Application of bounded edge properties to derive bounds on causal effects in the presence of unmeasured confounders.

Main Results:

  • A novel definition of bounded edges is established, extending existing causal graph concepts.
  • Rules for the propagation of bounds are derived, enabling systematic analysis.
  • The framework successfully derives bounds on causal effects despite unmeasured confounding.

Conclusions:

  • Bounded edges provide a powerful tool for causal inference in the presence of unmeasured confounding.
  • The developed theory and methods offer a robust approach to estimating causal effects.
  • The approach is illustrated by estimating the effect of antihistamine treatment on asthma.