Dynamic Bayesian Networks with Conditional Dynamics in Edge Additions and Deletions

ABSTRACT This study presents a dynamic Bayesian network framework that facilitates intuitive, gradual edge changes. We use two conditional dynamics to model the edge additions and deletions, as well as edge selections, separately. In contrast to previous research that employed a mixture network approach—which limits the number of edge changes—or relied on structural priors to induce gradual changes—often leading to ambiguous network evolution—our model fosters more frequent and intuitive edge change dynamics. Moreover, when the maximum number of parents for the nodes in the network is , the correlation matrix can be represented by at most correlations. In contrast, conventional dynamic correlation models necessitate correlations. Consequently, the structure specified by the Bayesian network facilitates dimensionality reduction of the correlation matrix from to . Furthermore, correlations evolve sequentially according to the network structures and the topological ordering, thereby mimicking the information flow among stocks in financial markets, offering a realistic framework for modeling correlation evolution. We implement Markov chain Monte Carlo sampling to estimate the model structures and parameters, and we illustrate the model's efficacy through a portfolio selection application.