Confidence distribution, Combining Information, and Discrepant Posterior Distribution Paradox

Music City Center 

Dr. Bill Strawderman's contributions to statistical theory have profoundly shaped modern perspectives on estimation and decision theory. I was fortunate to be his colleague and to benefit from his guidance, both academically and personally. In this memorial session, I focus on the framework of confidence distributions, which we co-developed together with Kesar Singh. This talk revisits the problem of combining information from multiple sources—frequentist, Bayesian, or otherwise—within the confidence distribution framework, and sheds light on the paradox of the discrepant posterior distribution phenomenon. By connecting these themes, we honor Strawderman's deep commitment to principled inference and methodological rigor, while also presenting recent developments moving his legacy forward. Particular attention will be given to the foundational and practical implications of these ideas for unifying Bayesian and frequentist inference approaches, especially in the context of modern statistical science, machine learning, and artificial intelligence.