Integrating Out Nuisance Parameters for Computationally More Efficient Bayesian Estimation: An Illustration and Tutorial

Martin Hecht*, Christian Gische, Daniel Vogel, Steffen Zitzmann

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Citations (Scopus)
1 Downloads (Pure)

Abstract

Bayesian estimation has become very popular. However, run time of Bayesian models is often unsatisfactorily high. In this illustration, we show how to reduce run time by (a) integrating out nuisance model parameters and by (b) reformulating the model based on covariances and means. The core concept is to use the sample scatter matrix which is in our case Wishart distributed with the model-implied covariance matrix as the scale matrix. To illustrate this approach, we choose the popular multi-level null (intercept-only) model, provide a step-by-step instruction on how to implement this model in a multi-purpose Bayesian software, and show how structural equation modeling techniques can be employed to bypass mathematically challenging derivations. A simulation study showed that run time is considerably reduced and an empirical example illustrates our approach. Further, we show how the JAGS sampling progress can be monitored and stopped automatically when convergence and precision criteria are reached.

Original languageEnglish
Pages (from-to)483-493
Number of pages11
JournalStructural Equation Modeling
Volume27
Issue number3
Early online date24 Sep 2019
DOIs
Publication statusPublished - 2020

Keywords

  • Bayesian analysis
  • multi-level modeling
  • nuisance parameters
  • run time optimization
  • sampler monitoring
  • structural equation modeling
  • TOO
  • MODEL

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