Related papers: Evaluating probabilistic forecasts of football mat…
We characterise the unbiasedness of the score function, viewed as an inference function for a class of finite mixture models. The models studied represent the situation where there is a stratification of the observations in a finite number…
Premier League is known as one of the most competitive football league in the world, hence there are many goals are scored here every match. Which are the factors that affect to the number of goal scored in each match? We use Poisson…
Predicting outcomes in sports is important for teams, leagues, bettors, media, and fans. Given the growing amount of player tracking data, sports analytics models are increasingly utilizing spatially-derived features built upon player…
In this paper, we present betting strategy of a football game using probability theory. We know all betting houses offer slightly unfair odds towards the player. Here we discuss a simple way to figure out which betting house is offering…
Uncertainty associated with statistical problems arises due to what has not been seen as opposed to what has been seen. Using probability to quantify the uncertainty the task is to construct a probability model for what has not been seen…
Propensity score matching is commonly used to draw causal inference from observational survival data. However, its asymptotic properties have yet to be established, and variance estimation is still open to debate. We derive the statistical…
Knowing when a classifier's prediction can be trusted is useful in many applications and critical for safely using AI. While the bulk of the effort in machine learning research has been towards improving classifier performance,…
The probabilistic serial (PS) rule is one of the most prominent randomized rules for the assignment problem. It is well-known for its superior fairness and welfare properties. However, PS is not immune to manipulative behaviour by the…
Professional team sports provide an excellent domain for studying the dynamics of social competitions. These games are constructed with simple, well-defined rules and payoffs that admit a high-dimensional set of possible actions and…
Authors often struggle to interpret peer review feedback, deriving false hope from polite comments or feeling confused by specific low scores. To investigate this, we construct a dataset of over 30,000 ICLR 2021-2025 submissions and compare…
Time-to-event forecasts are essential when decisions depend on event timing. This article develops a framework for evaluating such forecasts when the event has not yet occurred or is not predicted within the forecast horizon. We introduce a…
In this work, we investigate the reliability of the probabilistic binary forecast. We mathematically prove that a necessary, but not sufficient, condition for achieving a reliable probabilistic forecast is maximizing the Peirce skill score…
The quality of probabilistic forecasts is crucial for decision-making under uncertainty. While proper scoring rules incentivize truthful reporting of precise forecasts, they fall short when forecasters face epistemic uncertainty about their…
All proper scoring rules incentivize an expert to predict \emph{accurately} (report their true estimate), but not all proper scoring rules equally incentivize \emph{precision}. Rather than treating the expert's belief as exogenously given,…
Many proper scoring rules such as the Brier and log scoring rules implicitly reward a probability forecaster relative to a uniform baseline distribution. Recent work has motivated weighted proper scoring rules, which have an additional…
This paper studies algorithmic fairness when the protected attribute is location. To handle protected attributes that are continuous, such as age or income, the standard approach is to discretize the domain into predefined groups, and…
We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but…
Language-model agents increasingly emit uncertainty signals throughout a trajectory, but existing agentic UQ evaluations often conflate ranking usefulness with probabilistic truthfulness. AUROC, AUPRC, risk-coverage, Trajectory ECE, and…
Calibration is a classical notion from the forecasting literature which aims to address the question: how should predicted probabilities be interpreted? In a world where we only get to observe (discrete) outcomes, how should we evaluate a…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define several notions of randomness associated with interval, rather than precise,…