Variational Inference of Bayesian Dynamic Generalized Additive Models for Mortality Analysis

While generalized additive models are widely used to estimate smooth nonlinear relationships between responses and covariates, their application to temporal data analysis is limited, as the smooth functions may fail to accurately capture temporal evolution in the data and may yield unstable out-of-sample predictions. To address this limitation, dynamic generalized additive models have been proposed, which comprise two components: a generalized additive component and a component of random effects that evolve according to latent stochastic processes. The model falls within the scope of non-Gaussian state space models. For posterior inference in a Bayesian perspective of the model, Markov chain Monte Carlo algorithms require many iterations to converge, particularly in cases involving high-dimensional non-Gaussian time series observations. Therefore, we employ a variational inference scheme to obtain reasonable results efficiently. Specifically for the coefficients of the spline bases and the random effects, a Gaussian variational approximation is assumed. The optimization of the evidence lower bound is performed using a coordinate ascent variational inference algorithm. The proposed variational approach is more efficient than several competing methods in the dynamic generalized additive model framework. We apply the method to study death counts as a function of observed predictors and temporally dependent multivariate random effects that incorporate dependence structures among geographical locations and among causes of death, using an Italian mortality dataset from January 2015 to December 2020.