Mathematical and applied statistics
Research focus
The Peer review has evaluated this group as Average
1. Bayesian statistics [J1, J8, J9, J13, J14, P17, BC19, BC21]. The formulation and analysis of interesting distributions for random probability measures, to be used as prior distributions in Bayesian non parametrics, is still a very active area of research in mathematical statistics. The research has been focused on extensions and generalizations of the Dirichlet process, on processes with independent increments, and on neutral to the right priors. Functionals of a random probability measure identify features of a population that are often interesting to estimate. Making inference on these features is possible if one is able to elicit and compute the prior and posterior distribution for the respective functionals starting from suitable assesments on the prior distribution of the random probability measure. However, these distributions are often unknown, or, if known, they have analytic expressions which are too difficult to evaluate. Some practical applications concern survival analysis: the determination of the distribution of expected lifetimes or the predictive distribution of the survival time in the regression model called "accelerated failure time” (AFT). The implementation of prior distributions for Bayesian nonparametric inference sets a need for robustness analysis, i.e. a study of the sensitivity of the inferential results with respect to changes in the choice of the prior. The robustness analysis is concerned with determination of extreme values of posterior functionals letting the prior vary in a specified class of probability measures. 2. Randomly reinforced urn systems [J2, J3, J4, J5, J6, J7, BC20] Urn models have always been the object of special interest in Bayesian non parametric literature as intuitive metaphors for the construction and the characterization of both the model and the prior distribution. In this research, systems of randomly reinforced urns have been considered for: a) Formulating Bayesian models and priors for partially exchangeable data. Interacting reinforced urn systems are very flexible representations that accommodate known mathematical models, with applications, for instance, in economics and biology. They are based on the idea of reinforcement which allows their extension to situations where dependence is an important issue. By considering particular systems of interacting reinforced urn systems, prior distributions are devised for mixutres of Markov processes and continuous time semi-Markov processes. b) Studying and implementing a class of response adaptive design for clinical trials. The focus is on a control problem for modelling experiments performed to compare treatments. Observations accrue sequentially; when a new statistical unit enters the experiment, the experimenter faces the control problem of allocating the unit to a treatment based on information generated by past observations and relative to the unknown response distributions. The experimenter simultaneous goals are to collect evidence for determining the superior treatment and to maximize the number of units in the experiment that receive the superior treatment; moreover, as part of the problem constraints, the experimenter's allocation strategy must be random. This control problem is encountered in industrial applications, but it is more easily illustrated within the framework of clinical trials where it is motivated by ethical reasons. Allocation strategies have been searched that are optimal in the sense of asymptotically targetting the treatment with highest response utility, the main example being based on a randomly reinforced urn that generalizes the classical Polya scheme. 83 3. Classification and pattern recognition for quality control [J10, P16, P18]. Quality regulation in electricity distribution has received significant attention in recent years, following a widespread adoption of performance-based regulation in the form of a price cap. Regulators design incentive mechanism specifically targeted at the quality of supply, assuming the form of financial penalties and rewards for the distribution company. A common problem encountered in implementing this incentive mechanism is the definition and treatment of major events. The research focus has been on statistical classification methods aimed at a criterion for the definition of major event days followed by the construction of methodologies for their identification.
Dipartimento di afferenza
Docenti afferenti
Full Professors
Secchi Piercesare
Associate Professors
Ladelli Lucia
Guglielmi Alessandra
Assistant Professors
Paganoni Anna Maria
Battistini Egidio
Epifani Ilenia