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The Bradley-Terry model has previously been used in both Bayesian and frequentist interpretations to evaluate the strengths of sports teams based on win-loss game results. It has also been extended to handle additional possible results such…

The Bradley-Terry model assigns probabilities for the outcome of paired comparison experiments based on strength parameters associated with the objects being compared. We consider different proposed choices of prior parameter distributions…

A common problem faced in statistical inference is drawing conclusions from paired comparisons, in which two objects compete and one is declared the victor. A probabilistic approach to such a problem is the Bradley-Terry model, first…

The Bradley-Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behaviour, chess…

This paper deals with the estimation of the unknown distribution of hidden random variables from the observation of pairwise comparisons between these variables. This problem is inspired by recent developments on Bradley-Terry models in…

Two new Bayesian methods for estimating and predicting in-game home team win probabilities are proposed. The first method has a prior that adjusts as a function of lead differential and time elapsed. The second is an adjusted version of the…

Ranking a vector of alternatives on the basis of a series of paired comparisons is a relevant topic in many instances. A popular example is ranking contestants in sport tournaments. To this purpose, paired comparison models such as the…

Pairwise comparison data are widely used to infer latent rankings in areas such as sports, social choice, and machine learning. The Bradley-Terry model provides a foundational probabilistic framework but inherently assumes transitive…

We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry…

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…

In this paper, we propose a Bayesian predictive density estimator to predict the time until the r-th goal is scored in a hockey game, using ancillary information such as their performances in the past, points and specialists' opinions. To…

Estimating the predictive uncertainty of a Bayesian learning model is critical in various decision-making problems, e.g., reinforcement learning, detecting adversarial attack, self-driving car. As the model posterior is almost always…

Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…

Many applications, e.g. in content recommendation, sports, or recruitment, leverage the comparisons of alternatives to score those alternatives. The classical Bradley-Terry model and its variants have been widely used to do so. The…

Prediction and modelling of competitive sports outcomes has received much recent attention, especially from the Bayesian statistics and machine learning communities. In the real world setting of outcome prediction, the seminal \'{E}l\H{o}…

We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced…

We consider Bayesian estimation of a $p\times p$ precision matrix, when $p$ can be much larger than the available sample size $n$. It is well known that consistent estimation in such ultra-high dimensional situations requires regularization…

Variable selection techniques have become increasingly popular amongst statisticians due to an increased number of regression and classification applications involving high-dimensional data where we expect some predictors to be unimportant.…

We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent…

Ranking items based on pairwise comparisons is common, from using match outcomes to rank sports teams to using purchase or survey data to rank consumer products. Statistical inference-based methods such as the Bradley-Terry model, which…