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Related Concept Videos

Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

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Related Experiment Videos

Automating approximate Bayesian computation by local linear regression.

Kevin R Thornton1

  • 1Department of Ecology and Evolutionary Biology, University of California Irvine, Irvine, CA, USA. krthornt@uci.edu

BMC Genetics
|July 9, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces ABCreg, a standalone software for Approximate Bayesian Computation (ABC) using local linear regression. ABCreg automates parameter inference, simplifying complex analyses for biological data.

Related Experiment Videos

Area of Science:

  • Computational Biology
  • Statistical Genetics
  • Bioinformatics

Background:

  • Parameter inference in biology often requires computationally intensive methods.
  • Approximate Bayesian Computation (ABC) using summary statistics is a popular alternative.
  • A computationally appealing ABC method uses linear regression, but lacks automated tools.

Purpose of the Study:

  • To describe a new program for automating Approximate Bayesian Computation using local linear regression.
  • To provide a standalone, documented, and open-source tool for parameter inference.

Main Methods:

  • The ABCreg software package implements a local linear-regression approach to ABC.
  • It processes multiple datasets, offers two transformation methods, and allows user-controlled command-line options.
  • The program is simulation-agnostic, functioning with any simulation machinery.

Main Results:

  • ABCreg is a standalone, fully-documented software package.
  • It automates processing of multiple datasets and generates R-compatible output.
  • The software includes features for handling regression failures and is open-source and modular.

Conclusions:

  • ABCreg simplifies the implementation of Approximate Bayesian Computation based on local-linear regression.
  • The tool facilitates the analysis of simulated and empirical biological data.