19 papers
Martingale Posterior Predictive Coherence: Hausdorff Moment Hierarchy
Nicholas G. Polson, Daniel Zantedeschi
For an exchangeable Bernoulli sequence with de Finetti mixing measure Pi, the k-step predictive probability P(X_{n+1}=...=X_{n+k}=0 | F_n) equals the posterior expectation E[(1-the…
An Old Look at Empirical Bayes
Nicholas G. Polson, Vadim O. Sokolov, Daniel Zantedeschi
Dennis Lindley once said that there is only one thing worse than a frequentist, and that is an empirical Bayesian. The quip has the air of caricature, but its technical content is…
Horseshoe Priors and MDP
Nick Polson, Vadim Sokolov, Daniel Zantedeschi
Carvalho (2010) established two foundational theorems for the horseshoe prior: tight two-sided logarithmic bounds on the marginal density near the origin (Theorem~1.1), and a super…
Bell's Inequality, Causal Bounds, and Quantum Bayesian Computation: A Unified Framework
Nick Polson, Vadim Sokolov, Daniel Zantedeschi
Bell inequalities characterize the boundary of the local-realist correlation polytope -- the set of joint probability distributions achievable by classical hidden-variable models.…
Bayes, E-values and Testing
Nicholas G. Polson, Vadim Sokolov, Daniel Zantedeschi
E-values and E-processes (nonnegative supermartingales) provide anytime-valid evidence for sequential testing via Ville's inequality, yet their connection to Bayesian reasoning, re…
Synthetic Priors
Nick Polson, Vadim Sokolov
Bayesian inference in generalized linear models requires a prior on the coefficient vector . Practitioners naturally reason about response probabilities at specific covariate v…