Cecilia Balocchi

Matrix-Assisted Laser Desorption/Ionization Mass Spectrometry Imaging (MSI) is a powerful technique for spatially resolved molecular profiling and cancer biomarker discovery. Recent advances, including a novel multiomics workflow, enable multiple rounds of MSI on the same tissue section, extracting diverse molecular classes, such as lipids, N-glycans, and peptides, while preserving spatial resolution. This innovation is particularly valuable for studies with limited tissue sample availability, such as rare diseases or small tumors. However, the resulting data are high-dimensional and spatially structured, with the various molecular types sharing the same pixel grid. To address these challenges, we propose Poseidon, a Bayesian nonparametric nested biclustering model that simultaneously segments the common tissue pixels and clusters molecular signals within each molecular class, leveraging the shared spatial structure. A separately exchangeable framework is first considered, and then extended to handle spatial data via Markov random fields. For scalability, we implement an efficient mean-field variational inference algorithm tailored for multi-dataset analysis. After validating the efficacy of our method on simulated scenarios, we demonstrate its applicability in a real-world case study, where multiomics measurements were performed on kidney tissue affected by clear cell renal cell carcinoma. The nested, hierarchical structure of Poseidon, combined with its principled inferential framework, allows the extraction of meaningful biological insights, such as clear tissue segmentation and biomarker detection.

The linear varying coefficient models posits a linear relationship between an outcome and covariates in which the covariate effects are modeled as functions of additional effect modifiers. Despite a long history of study and use in statistics and econometrics, state-of-the-art varying coefficient modeling methods cannot accommodate multivariate effect modifiers without imposing restrictive functional form assumptions or involving computationally intensive hyperparameter tuning. In response, we introduce VCBART, which flexibly estimates the covariate effect in a varying coefficient model using Bayesian Additive Regression Trees. With simple default settings, VCBART outperforms existing varying coefficient methods in terms of covariate effect estimation, uncertainty quantification, and outcome prediction. We illustrate the utility of VCBART with two case studies: one examining how the association between later-life cognition and measures of socioeconomic position vary with respect to age and socio-demographics and another estimating how temporal trends in urban crime vary at the neighborhood level. An R package implementing VCBART is available at https://github.com/skdeshpande91/VCBART.

Implements a faster and more expressive version of Bayesian Additive Regression Trees that, at a high level, approximates unknown functions as a weighted sum of binary regression tree ensembles. Supports fitting (generalized) linear varying coefficient models that posits a linear relationship between the inverse link and some covariates but allows that relationship to change as a function of other covariates. Additionally supports fitting heteroscedastic BART models, in which both the mean and log-variance are approximated with separate regression tree ensembles. A formula interface allows for different splitting variables to be used in each ensemble. For more details see Deshpande (2025) and Deshpande et al. (2024) .

Fits linear varying coefficient (VC) models, which assert a linear relationship between an outcome and several covariates but allow that relationship (i.e., the coefficients or slopes in the linear regression) to change as functions of additional variables known as effect modifiers, by approximating the coefficient functions with Bayesian Additive Regression Trees. Implements a Metropolis-within-Gibbs sampler to simulate draws from the posterior over coefficient function evaluations. VC models with independent observations or repeated observations can be fit. For more details see Deshpande et al. (2024) .

Species-sampling problems (SSPs) refer to a vast class of statistical problems calling for the estimation of (discrete) functionals of the unknown species composition of an unobservable population. A common feature of SSPs is their invariance with respect to species labeling, which is at the core of the Bayesian nonparametric (BNP) approach to SSPs under the popular Pitman-Yor process (PYP) prior. In this paper, we develop a BNP approach to SSPs that are not “invariant” to species labeling, in the sense that an ordering or ranking is assigned to species’ labels. Inspired by the population genetics literature on age-ordered alleles’ compositions, we study the following SSP with ordering: given an observable sample from an unknown population of individuals belonging to species (alleles), with species’ labels being ordered according to weights (ages), estimate the frequencies of the first r order species’ labels in an enlarged sample obtained by including additional unobservable samples. By relying on an ordered PYP prior, we obtain an explicit posterior distribution of the first r order frequencies, with estimates being of easy implementation and computationally efficient. We apply our approach to the analysis of genetic variation, showing its effectiveness in estimating the frequency of the oldest allele, and then we discuss other potential applications.

Given an observed sample from a population of individuals belonging to species, "species-sampling" problems (SSPs) call for estimating some features of the unknown species composition of additional unobservable samples from the same population. Within SSPs, the problems of estimating coverage probabilities, the number of unseen species and coverages of prevalences have emerged in the past three decades for being the subject of numerous methodological and applied works, mostly in biological sciences but also in statistical machine learning, electrical engineering, theoretical computer science, information theory and forensic statistics. In this paper, we focus on these popular SSPs, and present an overview of their Bayesian nonparametric (BNP) analysis under the Pitman--Yor process (PYP) prior. While reviewing the literature, we improve on computation and interpretability of existing posterior inferences, typically expressed through complicated combinatorial numbers, by establishing novel posterior representations in terms of simple compound Binomial and Hypergeometric distributions. We also consider the problem of estimating the discount and scale parameters of the PYP prior, showing a property of Bayesian consistency with respect to estimation through the hierarchical Bayes and empirical Bayes approaches, that is: the discount parameter can be estimated consistently, whereas the scale parameter cannot be estimated consistently, thus advising caution in posterior inference. We conclude our work by discussing some generalizations of SSPs, mostly in the field of biological sciences, which deal with "feature-sampling", multiple populations of individuals sharing species and classes of Markov chains.

Accurate estimation of the change in crime over time is a critical first step toward better understanding of public safety in large urban environments. Bayesian hierarchical modeling is a natural way to study spatial variation in urban crime dynamics at the neighborhood level, since it facilitates principled “sharing of information” between spatially adjacent neighborhoods. Typically, however, cities contain many physical and social boundaries that may manifest as spatial discontinuities in crime patterns. In this situation, standard prior choices often yield overly smooth parameter estimates, which can ultimately produce mis-calibrated forecasts. To prevent potential over-smoothing, we introduce a prior that partitions the set of neighborhoods into several clusters and encourages spatial smoothness within each cluster. In terms of model implementation, conventional stochastic search techniques are computationally prohibitive, as they must traverse a combinatorially vast space of partitions. We introduce an ensemble optimization procedure that simultaneously identifies several high probability partitions by solving one optimization problem using a new local search strategy. We then use the identified partitions to estimate crime trends in Philadelphia between 2006 and 2017. On simulated and real data, our proposed method demonstrates good estimation and partition selection performance. Supplementary materials for this article are available online.