Abstract
In this article we consider Bayesian inference for partially observed Andersson-Madigan-Perlman (AMP) Gaussian chain graph (CG) models. Such models are of particular interest in applications such as biological networks and financial time series. The model itself features a variety of constraints which make both prior modeling and computational inference challenging. We develop a framework for the aforementioned challenges, using a sequential Monte Carlo (SMC) method for statistical inference. Our approach is illustrated on both simulated data as well as real case studies from university graduation rates and a pharmacokinetics study.
Highlights
Two common approaches to probabilistically describe conditional dependence structures are based on undirected graphs (Markov networks) and directed acyclic graphs (DAG) (Bayesian networks), e.g. [25]
Chain graphs were first introduced in the late eighties, most research has focused on Bayesian networks and Gaussian Graphical Models
We introduce a sequential Monte Carlo (SMC) method as in [10] that improves upon Markov chain Monte Carlo (MCMC)-based methods in this context
Summary
Two common approaches to probabilistically describe conditional dependence structures are based on undirected graphs (Markov networks) and directed acyclic graphs (DAG) (Bayesian networks), e.g. [25]. Two common approaches to probabilistically describe conditional dependence structures are based on undirected graphs (Markov networks) and directed acyclic graphs (DAG) (Bayesian networks), e.g. Whilst a directed edge works as in DAGs when it comes to representing independence, the undirected edge can be understood in different ways, giving rise to the different interpretations This implies that chain graphs can represent every independence model achievable by any DAG, whereas the opposite does not hold. Based upon the likelihood method in [13] we develop a new Bayesian model for latent AMP chain graphs. This model can incorporate covariate information, if available.
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