Related papers: Solving the 100 Swiss Francs Problem

In this paper (propositional) probability logic ($PL$) is investigated from model theoretic point of view. First of all, the ultraproduct construction is adapted for $\sigma$-additive probability models, and subsequently when this class of…

Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…

An unknown positive number of items arrive at independent uniformly distributed times in the interval [0,1] to a selector, whose task is to pick online the last one. We show that under the assumption of an adversary determining the number…

We review a series of models of sociophysics introduced by Galam and Galam et al in the last 25 years. The models are divided in five different classes, which deal respectively with democratic voting in bottom up hierarchical systems,…

The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior…

In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…

The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…

Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…

Maximum-entropy distributions are shown to appear in the probability calculus as approximations of a model by exchangeability or a model by sufficiency, the former model being preferable. The implications of this fact are discussed,…

During World War II the German army used tanks to devastating advantage. The Allies needed accurate estimates of their tank production and deployment. They used two approaches to find these values: spies, and statistics. This note describes…

We study nonparametric maximum likelihood estimation for two classes of multivariate distributions that imply strong forms of positive dependence; namely log-supermodular (MTP$_2$) distributions and log-$L^\#$-concave (LLC) distributions.…

We describe some open questions related to support points in the class $S^0$ and introduce some useful techniques toward a higher dimensional Bieberbach conjecture.

The principle of rewarding a crowd for surprisingly common answers has been used in the literature for designing a number of truthful information elicitation mechanisms. A related method has also been proposed in the literature for better…

Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

For general data, the number of complex solutions to the likelihood equations is constant and this number is called the (maximum likelihood) ML-degree of the model. In this article, we describe the special locus of data for which the…

Consider the following game: You are given two indistinguishable envelopes, each containing money. One contains twice as much as the other. You may pick one envelope and keep the money it contains. Having chosen an envelope, you are given…

In this paper, we consider the revealed preferences problem from a learning perspective. Every day, a price vector and a budget is drawn from an unknown distribution, and a rational agent buys his most preferred bundle according to some…

Large language models (LLMs) increasingly help people solve problems, from debugging code to repairing machinery. This process requires generating plausible hypotheses from partial descriptions, then updating them as more information…

In an article published in 1993, P. Colmez formulated a remarkable conjecture, which asserts that the Faltings height of a CM abelian variety can be computed as a linear combination of logarithmic derivatives of Artin $L$-functions. Noting…