Statistics and Computational Methods Seminar Series - Spring 2026

First speaker: Alessandra Guglielmi (Politecnico di Milano)

Title: Robust Bayesian nonparametric clustering across groups

Abstract: 
This talk is divided into two parts. In the first part, I will present a unified framework for the construction and Bayesian analysis of random probability measures with interacting atoms from a point process, encompassing both repulsive and attractive behaviours of the atoms. When such a prior is used as the mixing measure in a parametric mixture model, it yields well-separated and interpretable clusters. In the second part, I will focus on a BNP model for clustering observations across partially exchangeable groups of data. Previously proposed models achieve across-group clustering by sharing atoms in the group-specific mixing measures. However, exact atom sharing can be overly rigid when groups differ subtly, leading to a trade-off between clustering and density estimation and to the fragmentation of clusters across groups. We introduce a mixture model in which the group-specific mixing measures follow a (normalised) hierarchical shot-noise Cox process (HSNCP), a new prior that we define, based on an “attractive” point process. Our approach departs from traditional BNP models by allowing group-specific mixture distributions to have components that are not necessarily identical, but instead concentrate around shared centers through a kernel. The HSNCP model also introduces a flexible notion of cluster: a cluster corresponds not to a single mixture component, but to an atom of the “mother process”. This framework enables robust cluster estimation across groups, while maintaining accurate density estimation within groups, thereby overcoming the density–clustering trade-off of previous approaches. We present theoretical results on the prior, building on the framework introduced in the first part of the talk. We also develop an efficient conditional MCMC algorithm for posterior inference and assess the performance of the HSNCP mixture model on simulated and real datasets.

Second speaker: Michele Guindani (UCLA)

Title: Embracing Heterogeneity: Bayesian Clustering methods for neuroscience data

Abstract: 

A common practice in neuroscience is to average data across analytical units such as neurons, trials, or subjects. While averaging can improve signal, it often masks important heterogeneity in brain activity. In this talk, I will present two recent methods that employ Bayesian clustering to recover latent subpopulations and neuronal ensembles, with applications in human and animal experiments. First, I will introduce a repulsive mixture model applied to Event-Related Potential (ERP) data. ERPs are small voltage changes in the brain's electrical activity, measured by electroencephalography (EEG), that are time-locked to a specific stimulus or cognitive event. Our model assigns a projection determinantal point process (pDPP) prior to the cluster locations, which mathematically enforces separation and helps uncover these hidden neuro-cognitive subgroups. The analytical tractability of the pDPP prior leads to efficient algorithms that yield parsimonious, interpretable partitions with strong frequentist guarantees, including posterior consistency and the automatic elimination of redundant components. Second, I will describe a Bayesian semiparametric framework for calcium imaging that jointly infers neural spikes and identifies functionally coherent ensembles. We model spiking probability with latent Gaussian processes and promote anatomical coherence using a location-dependent stick-breaking prior. Applied to hippocampal recordings from a mouse navigating a circular arena, the model reveals spatially structured co-activation patterns that vary with the animal's position. Taken together, these studies demonstrate the value of Bayesian clustering techniques for uncovering structure in human ERPs and mouse calcium imaging data.

Link streaming:

https://teams.microsoft.com/meet/39653650835774?p=V1a75VXDpXYicww4P1