English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In contingency table analysis, sparse data is frequently encountered for evenmodest numbers of variables, resulting in non-existence of maximum likelihoodestimates. A common solution is to obtain regularized estimates of theparameters of a log-linear model. Bayesian methods provide a coherent approachto regularization, but are often computationally intensive. Conjugate priorsease computational demands, but the conjugate Diaconis-Ylvisaker priors for theparameters of log-linear models do not give rise to closed form credibleregions, complicating posterior inference. Here we derive the optimal Gaussianapproximation to the posterior for log-linear models with Diaconis-Ylvisakerpriors, and provide convergence rate and finite-sample bounds for theKullback-Leibler divergence between the exact posterior and the optimalGaussian approximation. We demonstrate empirically in simulations and a realdata application that the approximation is highly accurate, even in relativelysmall samples. The proposed approximation provides a computationally scalableand principled approach to regularized estimation and approximate Bayesianinference for log-linear models.

Optimal Gaussian approximations to the posterior for log-linear models with Diaconis-Ylvisaker priors