The article introduces the ARTIVA formalism, a statistical method for inferring time-varying gene-regulation networks from time-course expression data. Unlike conventional static models, ARTIVA simultaneously infers the topology of a regulatory network and how it changes over time. It allows for the recovery of the chronology of regulatory associations for genes involved in specific biological processes. The method uses a combination of dynamical Bayesian networks and Reversible Jump MCMC to model gene regulatory interactions and infer temporal changes in network structure. ARTIVA was tested on simulated data and applied to two biological systems: the developmental stages of Drosophila melanogaster and the response of Saccharomyces cerevisiae to benomyl poisoning. The results show that ARTIVA effectively captures temporal dependencies in biological systems and provides a detailed understanding of network dynamics. The method was evaluated using sensitivity and positive predictive value metrics, demonstrating its ability to accurately detect changepoints and regulatory associations. The application to real data, such as the Drosophila life cycle and benomyl response datasets, confirmed the effectiveness of ARTIVA in identifying time-varying regulatory networks. The algorithm is implemented in R and is suitable for analyzing time-course data with varying numbers of genes and time points. The results highlight the robustness of ARTIVA in handling complex biological data and its potential for further investigation into the dynamics of gene regulation.The article introduces the ARTIVA formalism, a statistical method for inferring time-varying gene-regulation networks from time-course expression data. Unlike conventional static models, ARTIVA simultaneously infers the topology of a regulatory network and how it changes over time. It allows for the recovery of the chronology of regulatory associations for genes involved in specific biological processes. The method uses a combination of dynamical Bayesian networks and Reversible Jump MCMC to model gene regulatory interactions and infer temporal changes in network structure. ARTIVA was tested on simulated data and applied to two biological systems: the developmental stages of Drosophila melanogaster and the response of Saccharomyces cerevisiae to benomyl poisoning. The results show that ARTIVA effectively captures temporal dependencies in biological systems and provides a detailed understanding of network dynamics. The method was evaluated using sensitivity and positive predictive value metrics, demonstrating its ability to accurately detect changepoints and regulatory associations. The application to real data, such as the Drosophila life cycle and benomyl response datasets, confirmed the effectiveness of ARTIVA in identifying time-varying regulatory networks. The algorithm is implemented in R and is suitable for analyzing time-course data with varying numbers of genes and time points. The results highlight the robustness of ARTIVA in handling complex biological data and its potential for further investigation into the dynamics of gene regulation.