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math.ST2026
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…
math.ST2026
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…
math.ST2026
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…