Tutor: Tommaso Rigon
Politecnico di Milano - Mathematical Engineering - Bayesian Statistics
Università degli Studi di Milano-Bicocca
2025-09-26
Short Bio
My name is Tommaso Rigon and I am a Senior Assistant Professor (RTD-B).
University of Milano-Bicocca, Department of Economics, Management and Statistics (DEMS), Milan, Italy.
- Senior Assistant Professor (RTD-B), 2023 - Present
- Junior Assistant Professor (RTD-A), 2020 - 2023
Duke University, Department of Statistical Science, Durham (NC), U.S.A.
- Postdoctoral Associate, 2020 - 2020
- Research Associate, 2019 - 2020
Education
- Ph.D. in Statistical Sciences, Bocconi University, Milan, Italy.
- M.Sc. in Statistical Sciences, University of Padova, Padua, Italy.
- B.Sc. in Statistics, Economics & Finance, University of Padova, Padua, Italy.
Hyperbolic secant regression
Background
Let Y_1,\dots,Y_n be independent random variable distributed according to a hyperbolic secant distribution, whose density is f(y_i; \theta_i) = \frac{\exp\{\theta_i y_i - \log{\cos(\theta_i)} \}}{2 \cosh(\pi y_i / 2)}, \qquad y_i \in \mathbb{R}, \; \theta_i \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right). This distribution is discussed in Morris (1982) and is an instance of highly tractable exponential family having a quadratic variance function.
This distribution can be employed to build a novel generalized linear model (GLM), which automatically incorporates heteroskedasticity and exhibits heavier tails than the Gaussian law.
There are multiple application areas for such a regression technique, including (but not limited to) financial data.
Objectives and expectations
Research gap
A systematic Bayesian investigation of such a GLM is entirely lacking. In principle, this GLM framework can be combined with modern Bayesian tools for regression, such as:
- Variable selection and regularization, e.g., shrinkage priors or spike-and-slab priors.
- Random effects (parametric and nonparametric).
- Generalized Additive Models (GAMs), e.g., Gaussian Processes.
Overdispersion may require novel generalized Bayes techniques (Agnoletto et al. 2025).
A Polya-gamma data augmentation scheme may be applicable by adapting the results in Polson et al. (2013). If not, Hamiltonian Monte Carlo (HMC) remains a feasible option.
Expected outcome
The group is expected to implement and develop 2–3 of the research gaps outlined above.
I expect the group to be proficient in R programming (knowledge of C++ is a strong asset, though probably not essential). Most of the work will focus on the practical implementation of these ideas.
