Post by Università Bocconi

How can #statisticalModels better reflect the complexity of real-world data? #Bayesian statistics is widely used across fields such as medicine, economics, and #ArtificialIntelligence because it allows researchers to update prior beliefs as new #data becomes available. The core of this process is the #posteriorDistribution, which describes uncertainty after observing data. However, calculating the exact posterior is often computationally infeasible, especially in complex or high-dimensional models. Francesco Pozza, Daniele Durante, and Botond Szabo (all from Bocconi’s Department of Decision Sciences and the Bocconi Institute for Data Science and Analytics research center) introduce a new method to improve #BayesianInference by addressing a long-standing limitation in posterior approximations. To make these methods practical, statisticians typically rely on simplified approximations. Most existing techniques assume that posterior distributions are symmetric and bell-shaped. Yet real-world posteriors are frequently asymmetric or skewed. When symmetry is imposed where it does not exist, approximations can become less accurate and introduce bias. Rather than replacing existing approaches with more computationally expensive alternatives, the authors propose a different strategy: starting from a standard symmetric approximation and systematically “perturbing” it to incorporate skewness. The result is a #method that remains mathematically tractable while significantly improving accuracy. Importantly, the approach does not require additional optimization steps, making it efficient and broadly applicable across different models. The study combines theoretical guarantees with practical evidence. The authors show that the skewed approximations are provably optimal within their class and improve performance both in finite samples and large-data settings. Numerical experiments and real-world applications confirmed that introducing asymmetry consistently enhanced the characterization of complex posterior distributions. The broader implication is methodological. Instead of discarding established statistical tools, the research upgrades them to better reflect the realities they are designed to represent. By integrating asymmetry in a principled way, the method brings #StatisticalModeling closer to the complexity of modern data environments.