Premium
SEMIPARAMETRIC REGRESSION AND GRAPHICAL MODELS
Author(s) -
Wand M. P.
Publication year - 2009
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2009.00538.x
Subject(s) - graphical model , semiparametric regression , markov chain monte carlo , inference , mathematics , bayesian inference , bayesian probability , spline (mechanical) , computer science , markov chain , bayesian network , regression , econometrics , artificial intelligence , statistics , structural engineering , engineering
Summary Semiparametric regression models that use spline basis functions with penalization have graphical model representations. This link is more powerful than previously established mixed model representations of semiparametric regression, as a larger class of models can be accommodated. Complications such as missingness and measurement error are more naturally handled within the graphical model architecture. Directed acyclic graphs, also known as Bayesian networks, play a prominent role. Graphical model‐based Bayesian ‘inference engines’, such as bugs and vibes , facilitate fitting and inference. Underlying these are Markov chain Monte Carlo schemes and recent developments in variational approximation theory and methodology.