A0497
Title: How much data is enough? Effective sample size in Bayesian graphical models
Authors: Giuseppe Arena - University of Amsterdam (Netherlands) [presenting]
Lourens Waldorp - University of Amsterdam (Netherlands)
Maarten Marsman - University of Amsterdam (Netherlands)
Abstract: In Bayesian analysis, the concept of effective sample size (ESS) applies separately to both the data and the prior, quantifying the independent information provided by the data beyond what is already encoded in an informative prior derived from a previous study. In graphical models such as Gaussian graphical models (GGMs), calculating the ESS becomes challenging due to the complexity of the model and the dependencies among parameters. While extensive prior work has introduced methods for estimating the ESS of data and prior, their use in the context of Bayesian graphical models remains relatively unexplored. The methodology for calculating the ESS of data and informative priors in GGMs is first outlined. Two common research scenarios are then considered: Planning a Bayesian analysis with a known informative prior and calibrating priors to prevent prior dominance in the posterior. In the former, the ESS quantifies the amount of data needed to balance prior influence, supporting robust inference. In the latter, the ESS is used to evaluate prior dominance, guiding the appropriate adjustments to maintain reliable posterior inference. The discussion concludes with methodological extensions for estimating the ESS in ordinal Markov random fields.
