Mathematics – Statistics Theory
Scientific paper
2006-09-04
Mathematics
Statistics Theory
24 pages, 1 figure
Scientific paper
In the Bayesian analysis of contingency table data, the selection of a prior distribution for either the log-linear parameters or the cell probabilities parameter is a major challenge. Though the conjugate prior on cell probabilities has been defined by Dawid and Lauritzen (1993) for decomposable graphical models, it has not been identified for the larger class of graphical models Markov with respect to an arbitrary undirected graph or for the even wider class of hierarchical log-linear models. In this paper, working with the log-linear parameters used by GLIM, we first define the conjugate prior for these parameters and then derive the induced prior for the cell probabilities: this is done for the general class of hierarchical log-linear models. We show that the conjugate prior has all the properties that one expects from a prior: notational simplicity, ability to reflect either no prior knowledge or a priori expert knowledge, a moderate number of hyperparameters and mathematical convenience. It also has the strong hyper Markov property which allows for local updates within prime components for graphical models.
Liu Jinnan
Massam Hélène
No associations
LandOfFree
The conjugate prior for discrete hierarchical log-linear models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The conjugate prior for discrete hierarchical log-linear models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The conjugate prior for discrete hierarchical log-linear models will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-727330