BAYSM 2026

Title: Recent Advances in Bayesian Inference from Privatized Data via Data Augmentation

Abstract: Analyzing data under privacy constraints is like dancing with shackles, as privacy protection requires modified analysis procedures and inevitably reduces data utility. Performing statistical inference on privatized data is even more challenging, as it requires deriving reliable insights from lower-quality data. Drawing on three recent studies, this talk presents a data augmentation Markov Chain Monte Carlo framework for Bayesian inference from privatized data. The core idea is to treat the unobserved confidential data as latent variables. We discuss an independent Metropolis-within-Gibbs sampler and a recent algorithmic improvement. We present spectral gap bounds of reversible hybrid Gibbs samplers, validating the convergence of our data augmentation algorithms. The talk concludes with a discussion of some open problems in the field.

Title: Discrete Autoregressive Switching Processes with Cumulative Shrinkage Priors for Graphical Modeling of Multivariate Time Series Data

Abstract: We propose a flexible Bayesian approach for sparse Gaussian graphical modeling of multivariate time series. We account for temporal correlation in the data by assuming that observations are characterized by an underlying and unobserved hidden discrete autoregressive process. We assume multivariate Gaussian emission distributions and capture spatial dependencies by modeling the state-specific precision matrices via graphical horseshoe priors. We characterize the mixing probabilities of the hidden process via a cumulative shrinkage prior that accommodates zero-inflated parameters for non-active components, and further incorporate a sparsity-inducing Dirichlet prior to estimate the effective number of states from the data. For posterior inference, we develop a sampling procedure that allows estimation of the number of discrete autoregressive lags and the number of states, and that cleverly avoids having to deal with the changing dimensions of the parameter space. We thoroughly investigate performance of our proposed methodology through several simulation studies. We further illustrate the use of our approach for the estimation of dynamic brain connectivity based on fMRI data collected on a subject performing a task-based experiment on latent learning.

Title: We Still Don't Understand High Dimensional Bayesian Optimization

Abstract: Bayesian optimization suffers in theory from a curse of dimensionality: the number of observations needed to optimize a black-box function growing exponentially. However, recent methods that assume smoothness or locality have made progress on problems with thousands of dimensions, well beyond what prior theory suggests is feasible. This talk discusses recent work characterizing why the curse of dimensionality may not hold in practice and new questions that emerge from this analysis. I will begin with a preliminary theoretical result characterizing a "good enough" regime of Bayesian optimization, in which coarse approximate optima can be found in polynomial time under mild smoothness or locality assumptions. The degree of the polynomial depends on the desired degree of exactness, reverting to an exponential bound for near-perfect solutions. The second half turns to a puzzling empirical finding: not only can approximate solutions be found in polynomial time, they can also be found with simple models. We show that linear models can yield near-state-of-the-art optimization performance once a geometric pathology is corrected for, despite the true objective being highly nonlinear. Together, these results suggest the need to depart from long-held intuitions about high-dimensional Bayesian optimization.

Title: Partially Exchangeable Partitions à la de Finetti: Finite and Infinite Characterizations

Abstract: We study partially exchangeable partitions in the sense of de Finetti, where invariance in law is imposed with respect to the subgroup of permutations preserving a given ordered reference partition. In both finite and infinite settings, we provide explicit characterizations of the associated partition laws, which remain valid even when de Finetti-type representations are unavailable, that is, when an underlying representation in terms of random probability measures need not exist. In particular, we prove that the multiset of counts given by the sizes of the intersections between the random partition and the reference partition is a minimal sufficient statistic for the class of partially exchangeable partition laws. We then characterize the corresponding partially exchangeable partition probability functions through symmetry and consistency conditions analogous to those of exchangeable partition probability functions. We further establish the equivalence with partially exchangeable sequences as well as with predictive laws, thereby yielding a partition-based description of these objects that does not rely on de Finetti-type representations. These results provide a general foundation for random partitions beyond the exchangeable setting. From a statistical modelling perspective, they also clarify the learning mechanisms underlying partition-based models and provide constructive tools for specifying new partially exchangeable priors without necessarily relying on de Finetti-type representations.

Title: Bayesian Multiresolution Functional Regression and Clustering via Self-Truncating Cumulative Shrinkage Processes

Abstract: We propose a Bayesian multiresolution framework for functional data analysis that captures varying levels of complexity at a local scale. As is commonly done, the model represents each function as a sum of increasingly flexible layers, with each layer defined by a basis expansion (e.g., B-splines) whose resolution increases with depth. Spike-and-slab Lasso priors enable data-driven activation of basis coefficients, allowing each layer to selectively operate on local regions of the domain and producing a principled separation between smooth and highly variable segments of the function. To enforce ordered shrinkage across layers, we introduce the Self-Truncating Cumulative Shrinkage Process (stCUSP), a prior that regulates the effective number of active layers. stCUSP extends the original Cumulative Shrinkage Process by incorporating a probabilistic self-truncation mechanism that penalizes redundant layers via spike-and-slab distributions applied to the stick-breaking variables. This promotes parsimony and interpretability while retaining the adaptive shrinkage behavior characteristic of CUSP. We plan to extend the prior to a partially exchangeable framework, enabling nested clustering of functions according to their complexity, interpreted as the number of activated layers.

Title: Sub-Cauchy Sampling: Escaping the Dark Side of the Moon

Abstract: We introduce a Markov chain Monte Carlo algorithm based on Sub-Cauchy Projection, a geometric transformation that generalizes stereographic projection by mapping Euclidean space into a spherical cap of a hyper-sphere, referred to as the complement of the dark side of the moon. We prove that our proposed method is uniformly ergodic for sub-Cauchy targets, namely targets whose tails are at most as heavy as a multidimensional Cauchy distribution, and show empirically its performance for challenging high-dimensional problems. The simplicity and broad applicability of our approach open new opportunities for Bayesian modeling and computation with heavy-tailed distributions in settings where most existing methods are unreliable.