William Denault: High dimensional regression methods for inhomogeneous Poisson processes via split-variational inference

Recent advances in fine-mapping—the task of narrowing a set of highly correlated associations to putative causal variants—have shown great promise. However, most existing approaches overlook the spatial structure of molecular traits measured by sequencing assays, and to our knowledge, none are tailored to the overdispersed nature of these count data. We propose Poisson-fSuSiE, a fine-mapping method for inhomogeneous Poisson processes aimed at molecular traits from sequence-based assays.   To maintain computational efficiency, we introduce  Split Variational Inference, a variational empirical-Bayes (EB) procedure that alternates between two fast steps: (i) a convex Poisson mean update and (ii) closed-form EB updates for flexible priors on functional coefficients. Split Variational Inference applied to Poisson fSuSiE yields scalable inference while preserving uncertainty quantification. In simulations spanning diverse correlation structures, effect patterns, and overdispersed counts models, our method achieves higher power and better calibration of posterior inclusion probabilities (PIPs) and credible sets compared to transform-based alternatives. We further apply Poisson-fSuSiE  to a recently published dataset containing RNA-seq, ATAC-seq, and H3K4me1 sequencing measurements, where it identifies compact, concordant credible sets that overlap independent signals—demonstrating applicability across multiple sequencing assays.