7 papers · 1 filter
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…
E-Values, Bayes Risk, Dual Role of Markov's Inequality
Nicholas G. Polson, Daniel Zantedeschi
Two approaches to hypothesis testing, e-value testing and Bayes risk minimisation, both invoke Markov's inequality to control error probabilities. They differ in which distribution…
A New Look at Bayesian Testing
Jyotishka Datta, Nicholas G. Polson, Vadim Sokolov +1
We identify the critical deviation scale governing Bayesian evidence accumulation in regular parametric testing. Under integrated Bayes risk with zero-one loss, the risk-optimal re…
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…
Bayes Risk for Goodness of Fit Tests
Nicholas G. Polson, Vadim Sokolov, Daniel Zantedeschi
We develop a unified framework for goodness-of-fit (GOF) testing through the lens of Bayes risk. Classical GOF procedures are commonly calibrated either at fixed significance level…
Conformal Prediction = Bayes?
Jyotishka Datta, Nicholas G. Polson, Vadim Sokolov +1
Conformal prediction (CP) is widely presented as distribution-free predictive inference with finite-sample marginal coverage under exchangeability. We argue that CP is best underst…