相关论文: Goodstein revisited

In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each…

When do nonparametric Bayesian procedures ``overfit''? To shed light on this question, we consider a binary regression problem in detail and establish frequentist consistency for a certain class of Bayes procedures based on hierarchical…

We identify computability-theoretic properties enabling us to separate various statements about partial orders in reverse mathematics. We obtain simpler proofs of existing separations, and deduce new compound ones. This work is part of a…

To the frequentist who computes posteriors, not all priors are useful asymptotically: in this paper Schwartz's 1965 Kullback-Leibler condition is generalised to enable frequentist interpretation of convergence of posterior distributions…

We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit…

The classical discrete $p$-Hardy inequality establishes a sharp relationship between the $\ell^{p}$-norms of a sequence and its discrete derivative. In this paper, we generalize this inequality to discrete derivatives of arbitrary integer…

In this article we discuss the proof in the short unpublished paper appeared in the 3rd volume of Godel's Collected Works entitled "On undecidable sentences" (*1931?), which provides an introduction to Godel's 1931 ideas regarding the…

We propose a simple approach that provides accurate uncertainty quantification for Bayesian inference in misspecified or approximate models, and for generalized (Gibbs) posteriors. While existing solutions in this context are based on…

We extend the classical Bernstein technique to the setting of integro-differential operators. As a consequence, we provide first and one-sided second derivative estimates for solutions to fractional equations, including some convex fully…

We propose generalized portmanteau-type test statistics in the frequency domain to test independence between two stationary time series. The test statistics are formed analogous to the one in Chen and Deo (2004, Econometric Theory 20,…

For relational monadic formulas (the L\"owenheim class) second-order quantifier elimination, which is closely related to computation of uniform interpolants, projection and forgetting - operations that currently receive much attention in…

Prediction algorithms assign numbers to individuals that are popularly understood as individual "probabilities" -- what is the probability of 5-year survival after cancer diagnosis? -- and which increasingly form the basis for life-altering…

We define a variant of the Goodstein process based on fast-growing functions and show that it terminates, but this fact is not provable in Kripke-Platek set theory or other theories of strength the Bachmann-Howard ordinal. We moreover show…

In this paper we take closer look at recent developments for the chase procedure, and provide additional results. Our analysis allows us create a taxonomy of the chase variations and the properties they satisfy. Two of the most central…

In 1948 Hoeffding devised a nonparametric test that detects dependence between two continuous random variables X and Y, based on the ranking of n paired samples (Xi,Yi). The computation of this commonly-used test statistic takes O(n log n)…

We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…

We propose a new method to approximate the posterior distribution of probabilistic programs by means of computing guaranteed bounds. The starting point of our work is an interval-based trace semantics for a recursive, higher-order…

This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds…

We obtain the rigorous uniform asymptotics of a particular integral where a stationary point is close to an endpoint. There exists a general method introduced by Bleistein for obtaining uniform asymptotics in this situation. However, this…

Let $\hat f_n$ be the nonparametric maximum likelihood estimator of a decreasing density. Grenander characterized this as the left-continuous slope of the least concave majorant of the empirical distribution function. For a sample from the…