Fabrizio Ruggeri’s research while affiliated with Istituto di Matematica Applicata e Tecnologie Informatiche, Italian National Research Council and other places

Adversarial Risk Analysis (ARA) can be a more realistic and practical alternative to traditional game theoretic or decision theoretic approaches for modeling strategic decision‐making in the presence of an adversary. ARA relies on quantifying the decision‐maker's (DM's) uncertainties about the adversary's strategic thinking, choices and utilities via probability distributions to identify the optimal solution for the DM. ARA solution will be sensitive to the choices of prior distributions used for modelling the expert beliefs. Yet, to date, no mathematical results to characterize the robustness of the ARA solution to the misspecification of one or more prior distributions exist. Prior elicitation is known to be challenging. We present the very first mathematical results on the global robustness of the ARA solution. We use the distorted band class of priors and establish the conditions under which an ordering on the ARA solution can be established when modelling the first‐price sealed‐bid auctions using the nonstrategic play and level‐ thinking solution concepts. We illustrate these results using numerical examples and discuss further areas of research.

Robust Bayesian analysis has been mainly devoted to detecting and measuring robustness to the prior distribution. Indeed, many contributions in the literature aim to define suitable classes of priors which allow the computation of variations of quantities of interest while the prior changes within those classes. The literature has devoted much less attention to the robustness of Bayesian methods to the likelihood function due to mathematical and computational complexity, and because it is often arguably considered a more objective choice compared to the prior. In this contribution, a new approach to Bayesian local robustness to the likelihood function is proposed and extended to robustness to the prior and to both. This approach is based on the notion of distortion function introduced in the literature on risk theory, and then successfully adopted to build suitable classes of priors for Bayesian global robustness to the prior. The novel robustness measure is a local sensitivity measure that turns out to be very tractable and easy to compute for certain classes of distortion functions. Asymptotic properties are derived and numerical experiments illustrate the theory and its applicability for modelling purposes.

Forecasting the volume of emergency events is important for resource utilization in emergency medical services (EMS). This became more evident during the COVID-19 outbreak when emergency event forecasts used by various EMS at that time tended to be inaccurate due to fluctuations in the number, type, and geographical distribution of these events. The motivation for this study was to develop a statistical model capable of predicting the volume of emergency events for Lombardy’s regional EMS called AREU at different time horizons. To accomplish this goal, we propose a negative binomial additive autoregressive model with smoothing splines, which can predict over-dispersed counts of emergency events one, two, five, and seven days ahead. In the model development stage, a large set of covariates was considered, and the final model was selected using a cross-validation procedure that takes into account the observations’ temporal dependence. Comparisons of the forecasting performance using the mean absolute percentage error showed that the proposed model outperformed the model used by AREU, as well as other widely used forecasting models. Consequently, AREU decided to adopt the new model for its forecasting purposes.

In this paper, we propose a method for wavelet denoising of signals contaminated with Gaussian noise when prior information about the ${L^{2}}$-energy of the signal is available. Assuming the independence model, according to which the wavelet coefficients are treated individually, we propose simple, level-dependent shrinkage rules that turn out to be Γ-minimax for a suitable class of priors. The proposed methodology is particularly well suited in denoising tasks when the signal-to-noise ratio is low, which is illustrated by simulations on a battery of some standard test functions. Comparison to some commonly used wavelet shrinkage methods is provided.

The zero‐truncated Poisson distribution is a useful model for integer‐valued random phenomena when a value of 0 is unobservable or simply out of domain. Alternative names are conditional Poisson distribution or positive Poisson distribution.