相关论文: Statistical Curse of the Second Half Rank

I describe the occurence of Eulerian numbers and Stirling numbers of the second kind in the combinatorics of the Statistical Curse of the Second Half Rank problem.

There seems to be an upper limit to predicting the outcome of matches in (semi-)professional sports. Recent work has proposed that this is due to chance and attempts have been made to simulate the distribution of win percentages to identify…

Across science and policy, decision-makers often need to draw conclusions about the best candidate among competing alternatives. For instance, researchers may seek to infer the effectiveness of the most successful treatment or determine…

Decision-makers often deploy the best-performing treatment from a randomized experiment, creating a winner's curse: selection favors treatments whose observed outcomes are high partly because of statistical noise, so the na\"ive estimate of…

We find a remarkable agreement between the statistics of a randomly divided interval and the observed statistical patterns and distributions found in horse racing betting markets. We compare the distribution of implied winning odds, the…

Consider the following Stochastic Score Classification Problem. A doctor is assessing a patient's risk of developing a certain disease, and can perform $n$ tests on the patient. Each test has a binary outcome, positive or negative. A…

A major challenge in data-driven decision-making is accurate policy evaluation-i.e., guaranteeing that a learned decision-making policy achieves the promised benefits. A popular strategy is model-based policy evaluation, which estimates a…

Boxing has a long-standing problem with biased judging, impacting both professional and Olympic bouts. "Robberies", where boxers are widely seen as being denied rightful victories, threaten to drive fans and athletes away from the sport. To…

Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g. uninsurable labor…

When data are right-censored, i.e. some outcomes are missing due to a limited period of observation, survival analysis can compute the "time to event". Multiple classes of outcomes lead to a classification variant: predicting the most…

We present here two examples of stochastic modelings of social phenomena. The first topic is pedestrian counter flow. Two groups of model pedestrians move in opposite directions and create congestions. It will be shown that this congestion…

We study a stochastic process that mimics single-game elimination tournaments. In our model, the outcome of each match is stochastic: the weaker player wins with upset probability q<=1/2, and the stronger player wins with probability 1-q.…

The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn…

We study the crowding of near-extreme events in the time gaps between successive finishers in major international marathons. Naively, one might expect these gaps to become progressively larger for better-placing finishers. While such an…

The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…

We consider a general class of round-robin tournament models of equally strong players. In these models, each of the $n$ players competes against every other player exactly once. For each match between two players, the outcome is a value…

Scoring rules measure the deviation between a probabilistic forecast and reality. Strictly proper scoring rules have the property that for any forecast, the mathematical expectation of the score of a forecast p by the lights of p is…

Rank-based inference methods are applied in various disciplines, typically when procedures relying on standard normal theory are not justifiable, for example when data are not symmetrically distributed, contain outliers, or responses are…

Patterns of wins and losses in pairwise contests, such as occur in sports and games, consumer research and paired comparison studies, and human and animal social hierarchies, are commonly analyzed using probabilistic models that allow one…

Where machine-learned predictive risk scores inform high-stakes decisions, such as bail and sentencing in criminal justice, fairness has been a serious concern. Recent work has characterized the disparate impact that such risk scores can…