Filippo Ascolani received his PhD in Statistics at Bocconi University in 2024 and he is starting as an Assistant Professor in the Department of Statistical Science at Duke University. Previously he obtained a B.Sc. in Mathematics and a M.Sc. in Stochastics and Data Science from University of Torino, Italy. His main research interests lie in Bayesian nonparametric inference for data displaying complex dependence structures, with an emphasis on the associated theoretical properties. Currently, he is also working on the theory of Bayesian computation and scalable Markov Chain Monte Carlo methods.

This will be one of three Lawrence D. Brown PhD Student Award winners’ talks in a special session at the 11th World Congress in Probability and Statistics in Bochum, Germany, August 12–16, 2024. (See below for how to apply for next year’s award.)

Nonparametric priors with full-range borrowing of information

Real phenomena often exhibit a high level of heterogeneity: datasets may often refer to different features, populations, or, in general, may be recorded under different experimental, though related, conditions. Such situations entail significant opportunities for borrowing information across different samples and groups of data.

It is, then, apparent that modeling the dependence structure across heterogeneous data is crucial for any statistical inference, since it directly impacts the borrowing of information. In a Bayesian framework this is done through models for partially exchangeable data, where only observations belonging to the same group can be permuted without affecting the overall distribution. Despite the extensive advances over the last two decades, most available proposals in the Bayesian nonparametric framework allow only for borrowing information by reinforcement. Indeed, the usual procedure consists of shrinking the estimates for different samples towards each other: shrinkage is justified by the fact that distributions of different, but related, populations are expected to be similar in terms of shape and/or location. However many phenomena, e.g. analysis of the returns of different financial assets or survival times and abundances of competitive species, may naturally lead to negative correlation between the samples.

In this work we derive a new class of dependent nonparametric priors that can induce correlations of any sign. We show that the constraint of positive correlation in most of the available methods is due to the sharing of atoms between random measures modelling the group-specific distributions: analogously, we show that going beyond this assumption allows for a more flexible idea of borrowing of information. This is achieved thanks to a novel concept, termed hyper-tie, that generalizes the standard notion of tie arising in exchangeable models and represents a direct and simple measure of dependence.

Our proposal is based on the normalization of Completely Random Vectors, which are random elements whose realizations are vectors of discrete finite measures. In particular, we leverage their amenable analytical tractability to derive explicit distributional properties, which allows us to tune the dependence both within and across groups. Moreover, we obtain a characterization of the posterior distribution and devise algorithms for posterior inference. We illustrate our model by analyzing the relation between stocks and bonds over the same temporal frame and in the problem of clustering multivariate responses with missing entries.

This a joint work with Beatrice Franzolini, Antonio Lijoi and Igor Prünster.

Apply for next year’s PhD Student Award

The IMS Lawrence D. Brown PhD Student Award is open for applications. The deadline is May 1, 2024. Eligible applicants compete to be one of three speakers at an invited session as part of the IMS Annual Meeting (the 2025 Joint Statistical Meetings, in Nashville, USA, August 2–7, 2025). The award includes reimbursement for travel and meeting registration fee
(up to $2,000 for each recipient).

The award was created in memory of Lawrence D. Brown (1940–2018), professor of statistics at The Wharton School, University of Pennsylvania, who was an enthusiastic and dedicated mentor to many graduate students. For application details see: https://imstat.org/ims-awards/ims-lawrence-d-brown-ph-d-student-award/