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Related Concept Videos

Outliers and Influential Points01:08

Outliers and Influential Points

An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the vertical...
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A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
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Published on: December 10, 2012

Identifying influential observations in Bayesian models by using Markov chain Monte Carlo.

Dan Jackson1, Ian R White, James Carpenter

  • 1MRC Biostatistics Unit, Cambridge, UK. daniel.jackson@mrc-bsu.cam.ac.uk

Statistics in Medicine
|September 10, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces two efficient methods to approximate influence statistics in statistical modeling using Markov chain Monte Carlo (MCMC) output. These novel approaches reduce computational demands for analyzing parameter estimate sensitivity to individual observations.

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Area of Science:

  • Statistical modeling
  • Computational statistics

Background:

  • Assessing the influence of individual observations on parameter estimates is crucial in statistical modeling.
  • Re-estimating models with each observation deleted is computationally intensive, especially with Markov chain Monte Carlo (MCMC) methods.

Purpose of the Study:

  • To develop efficient methods for approximating case-deleted estimates using existing MCMC output.
  • To reduce the computational burden associated with influence diagnostics in complex statistical models.

Main Methods:

  • Proposed two novel methods to approximate case-deleted estimates from MCMC output.
  • The first method approximates influence statistics for generalized linear models (GLMs) without further likelihood evaluations.
  • The second method uses model perturbations and does not require specifying the GLM form.

Main Results:

  • Both proposed methods offer efficient approximations of case-deleted estimates.
  • The methods avoid increased computational cost with growing model complexity.
  • Evaluated against importance sampling and case deletion in logistic regression with missing covariates.

Conclusions:

  • The developed methods provide computationally efficient alternatives for influence diagnostics in MCMC-based statistical modeling.
  • These techniques are applicable in various scenarios where MCMC is employed for model fitting.
  • Practical guidance is provided for implementing these procedures.