arXiv subjects

Nicola Torelli

Publications and source records attributed to Nicola Torelli.

11 recordsLinked to original sources

arXiv2026

Leicester's Tale: Another Perspective on the EPL 2015/16 Through Expected Goals (xG) Modelling

Probabilistic modeling is an effective tool for evaluating team performance and predicting outcomes in sports. However, an important question that hasn't been fully explored is whether these models can reliably reflect actual performance while assigning meaningful probabilities to rare results that differ greatly from expectations. In this study, we create an inference-based probabilistic framework built on expected goals (xG). This framework converts shot-level event data into season-level simulations of points, rankings, and outcome probabilities. Using the English Premier League 2015/16 season as a data, we demonstrate that the framework captures the overall structure of the league table. It correctly identifies the top-four contenders and relegation candidates while explaining a significant portion of the variance in final points and ranks. In a full-season evaluation, the model assigns a low probability to extreme outcomes, particularly Leicester City's historic title win, which stands out as a statistical anomaly. We then look at the ex ante inferential and early-diagnostic role of xG by only using mid-season information. With first-half data, we simulate the rest of the season and show that teams with stronger mid-season xG profiles tend to earn more points in the second half, even after considering their current league position. In this mid-season assessment, Leicester City ranks among the top teams by xG and is given a small but noteworthy chance of winning the league. This suggests that their ultimate success was unlikely but not entirely detached from their actual performance. Our analysis indicates that expected goals models work best as probabilistic baselines for analysis and early-warning diagnostics, rather than as certain predictors of rare season outcomes.

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arXiv2025

Copula-Based Clustering of Financial Time Series via Evidence Accumulation

Understanding the dependence structure of asset returns is fundamental in risk assessment and is particularly relevant in a portfolio diversification strategy. We propose a clustering approach where evidence accumulated in a multiplicity of classifications is achieved using classical hierarchical procedures and multiple copula-based dissimilarity measures. Assets that are grouped in the same cluster are such that their stochastic behavior is similar during risky scenarios, and riskaverse investors could exploit this information to build a risk-diversified portfolio. An empirical demonstration of such a strategy is presented by using data from the EURO STOXX 50 index.

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arXiv2025

Bayesian weighted discrete-time dynamic models for association football prediction

In recent years, great emphasis has been placed on the prediction of association football. Due to this, several studies have proposed different types of statistical models to predict the outcome of a football match. However, most existing approaches usually assume that the offensive and defensive abilities of teams remain static over time. We introduce a Bayesian dynamic approach for football goal based models that uses period-specific commensurate priors to flexibly weight the evolution of attacking and defensive abilities. Our approach assigns separate, time varying precisions for each ability and period, controlled via spike and slab hyperpriors. This adaptive shrinkage borrows information about teams' strength when past and current performance aligns and allows rapid adjustments when teams experience substantial changes (e.g., transfer windows or coaching changes). We integrate this framework into six standard goal based models evaluating predictive performance using data from the last five seasons of the German Bundesliga, English Premier League, and Spanish La Liga. Compared with the other discrete time dynamic models, our adaptive approach yields better predictive performance. The proposed methodology has also been implemented in the free and open source R package footBayes.

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arXiv2025

Eliciting prior information from clinical trials via calibrated Bayes factor

In the Bayesian framework power prior distributions are increasingly adopted in clinical trials and similar studies to incorporate external and past information, typically to inform the parameter associated to a treatment effect. Their use is particularly effective in scenarios with small sample sizes and where robust prior information is actually available. A crucial component of this methodology is represented by its weight parameter, which controls the volume of historical information incorporated into the current analysis. This parameter can be considered as either fixed or random. Although various strategies exist for its determination, eliciting the prior distribution of the weight parameter according to a full Bayesian approach remains a challenge. In general, this parameter should be carefully selected to accurately reflect the available prior information without dominating the posterior inferential conclusions. To this aim, we propose a novel method for eliciting the prior distribution of the weight parameter through a simulation-based calibrated Bayes factor procedure. This approach allows for the prior distribution to be updated based on the strength of evidence provided by the data: The goal is to facilitate the integration of historical data when it aligns with current information and to limit it when discrepancies arise in terms, for instance, of prior-data conflicts. The performance of the proposed method is tested through simulation studies and applied to real data from clinical trials.

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arXiv2024

Alternative ranking measures to predict international football results

Over the last few years, there has been a growing interest in the prediction and modelling of competitive sports outcomes, with particular emphasis placed on this area by the Bayesian statistics and machine learning communities. In this paper, we have carried out a comparative evaluation of statistical and machine learning models to assess their predictive performance for the 2022 FIFA World Cup and for the 2023 CAF Africa Cup of Nations by evaluating alternative summaries of past performances related to the involved teams. More specifically, we consider the Bayesian Bradley-Terry-Davidson model, which is a widely used statistical framework for ranking items based on paired comparisons that have been applied successfully in various domains, including football. The analysis was performed including in some canonical goal-based models both the Bradley-Terry-Davidson derived ranking and the widely recognized Coca-Cola FIFA ranking commonly adopted by football fans and amateurs.

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arXiv2021

pivmet: Pivotal Methods for Bayesian Relabelling and k-Means Clustering

The identification of groups' prototypes, i.e. elements of a dataset that represent different groups of data points, may be relevant to the tasks of clustering, classification and mixture modeling. The R package pivmet presented in this paper includes different methods for extracting pivotal units from a dataset. One of the main applications of pivotal methods is a Markov Chain Monte Carlo (MCMC) relabelling procedure to solve the label switching in Bayesian estimation of mixture models. Each method returns posterior estimates, and a set of graphical tools for visualizing the output. The package offers JAGS and Stan sampling procedures for Gaussian mixtures, and allows for user-defined priors' parameters. The package also provides functions to perform consensus clustering based on pivotal units, which may allow to improve classical techniques (e.g. k-means) by means of a careful seeding. The paper provides examples of applications to both real and simulated datasets.

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arXiv2018

Combining historical data and bookmakers'odds in modelling football scores

Modelling football outcomes has gained increasing attention, in large part due to the potential for making substantial profits. Despite the strong connection existing between football models and the bookmakers' betting odds, no authors have used the latter for improving the fit and the predictive accuracy of these models. We have developed a hierarchical Bayesian Poisson model in which the scoring rates of the teams are convex combinations of parameters estimated from historical data and the additional source of the betting odds. We apply our analysis to a nine-year dataset of the most popular European leagues in order to predict match outcomes for their tenth seasons. In this paper, we provide numerical and graphical checks for our model.

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arXiv2017

Mixture Data-Dependent Priors

We propose a two-component mixture of a noninformative (diffuse) and an informative prior distribution, weighted through the data in such a way to prefer the first component if a prior-data conflict arises. The data-driven approach for computing the mixture weights makes this class data-dependent. Although rarely used with any theoretical motivation, data-dependent priors are often used for different reasons, and their use has been a lot debated over the last decades. However, our approach is justified in terms of Bayesian inference as an approximation of a hierarchical model and as a conditioning on a data statistic. This class of priors turns out to provide less information than an informative prior, perhaps it represents a suitable option for not dominating the inference in presence of small samples. First evidences from simulation studies show that this class could also be a good proposal for reducing mean squared errors.

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arXiv2017

Bayesian semiparametric modelling of contraceptive behavior in India via sequential logistic regressions

Family planning has been characterized by highly different strategic programs in India, including method-specific contraceptive targets, coercive sterilization, and more recent target-free approaches. These major changes in family planning policies over time have motivated a considerable interest towards assessing the effectiveness of the different programs, while understanding which subsets of the population have not been properly addressed. Current studies consider specific aspects of the above policies, including, for example, the factors associated with the choice of alternative contraceptive methods other than sterilization, for women using contraceptives. Although these analyses produce relevant insights, they fail to provide a global overview of the different family planning policies, and the determinants underlying the contraceptive choices. Motivated by this consideration, we propose a Bayesian semiparametric model relying on a reparameterization of the multinomial probability mass function via a set of conditional Bernoulli choices. The sequential binary structure is defined to be consistent with the current family planning policies in India, and coherent with a reasonable process characterizing the contraceptive choices. This combination of flexible representations and careful reparameterizations allows a broader and interpretable overview of the different policies and contraceptive preferences in India, within a single model.

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arXiv2016

Maxima Units Search (MUS) algorithm: methodology and applications

An algorithm for extracting identity submatrices of small rank and pivotal units from large and sparse matrices is proposed. The procedure has already been satisfactorily applied for solving the label switching problem in Bayesian mixture models. Here we introduce it on its own and explore possible applications in different contexts.

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arXiv2016

Relabelling in Bayesian mixture models by pivotal units

In this paper a simple procedure to deal with label switching when exploring complex posterior distributions by MCMC algorithms is proposed. Although it cannot be generalized to any situation, it may be handy in many applications because of its simplicity and very low computational burden. A possible area where it proves to be useful is when deriving a sample for the posterior distribution arising from finite mixture models when no simple or rational ordering between the components is available.

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