15 papers
Modal Exchangeability: Centered Symmetry and the Credal Architecture of Kripke Frames
Daniel Zantedeschi
We ask what happens when the index set carries modal structure, with possibilities organized into a Kripke frame. We define modal exchangeability as invariance under accessibility-…
Mini-Batch Covariance, Diffusion Limits, and Oracle Complexity in Stochastic Gradient Descent: A Sampling-Design Perspective
Daniel Zantedeschi, Kumar Muthuraman
Stochastic gradient descent (SGD) is central to simulation optimization, stochastic programming, and online M-estimation, where sampling effort is a decision variable. We study the…
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…
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.…
Kakeya Conjecture and Conditional Kolmogorov Complexity
Nicholas G. Polson, Daniel Zantedeschi
This paper develops an information-theoretic framework for algorithmic complexity under regular identifiable fibering. The central question is: when a decoder is given information…
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 with No Shame: Admissibility Geometries of Predictive Inference
Nicholas G. Polson, Daniel Zantedeschi
Modern predictive systems combine predictors, sequential monitors, prediction sets, and online strategies, each with a different certificate of optimality. We study four criterion-…
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…
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…
Entropy-Regularized Inference: A Predictive Approach
Nicholas G. Polson, Daniel Zantedeschi
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat…
Bayesian Prediction under Moment Conditioning
Nicholas G. Polson, Daniel Zantedeschi
Moment restrictions specify a class of laws, not a predictive model. We obtain one by conditioning an independent sample from a reference law on its empirical moments, and define p…
De Finetti + Sanov = Bayes: Exchangeable Prediction under Moment Constraints
Nicholas G. Polson, Daniel Zantedeschi
We study exchangeable prediction when empirical-moment constraints define each active finite horizon N. The relevant law is the de Finetti mixture conditioned on E_N = {Phat_N in E…