Graphical Models for Associations between Variables, some of which are Qualitative and some Quantitative

Lectures on Algebraic Statistics

“…The two cases are referred to as LWF or AMP chain graphs in [8], and are called 'block concentrations' and 'concentration regressions' in [99]. Here we will use the two acronyms LWF and AMP, which are the initials of the authors of the original papers: LauritzenWermuth-Frydenberg [49,68] and Andersson-Madigan-Perlman [8].…”

A conditional linear Gaussian network to assess the impact of several agronomic settings on the quality of Tuscan Sangiovese grapes

“…A Conditional Linear Gaussian Network (CLGN: Lauritzen and Wermuth, 1989) is defined on a set of variables = { 1 , … , }, each being either continuous with domain on the real numbers or qualitative with a finite number of values, and is composed of:…”

“…CLGNs were firstly proposed by Lauritzen and Wermuth (1989), but the core idea may be traced back to path analysis (Wright, 1934). In a CLGN, a multivariate Gaussian distribution on multiple outcomes is assumed conditionally to treatments, and it is factored into linear regression models.…”

Parallel Importance Sampling in Conditional Linear Gaussian Networks

“…A Conditional Linear Gaussian Network is a hybrid Bayesian network where the joint distribution is a conditional linear Gaussian (CLG) [11]. In the CLG model, the conditional distribution of each discrete variable X D ∈ X given its parents is a multinomial, whilst the conditional distribution of each continuous variable Z ∈ X with discrete parents X D ⊆ X and continuous parents X C ⊆ X, is given as a normal density by…”

“…Our goal is to analyse the performance of probabilistic inference in hybrid Bayesian networks in scenarios where data come in streams at high speed, and therefore a quick response is required. Because of that, we will focus our analysis on conditional linear Gaussian (CLG) models [10,11], instead of more expressive alternatives such as mixtures of exponentials [12], mixtures of polynomials [18] and mixtures of truncated basis functions in general [9], as inference in the latter models is in general more time consuming [15].…”