SBSS Student Paper Award II

Spatial transcriptomics has gained tremendous popularity as it allows researchers to map gene expression directly onto tissue architecture, preserving spatial context and providing high-resolution insights into cellular interactions and biological processes within their native environments. In talk, we introduce a novel Bayesian nonparametric framework, Dirichlet process mixture of random spanning trees (DP-RST), designed to detect an unknown number of non-convex clusters in complex spatial domains. The model's two-layer partitioning effectively addresses challenges posed by the intricate spatial organization of tissue samples, such as non-convex clusters and irregular spatial boundaries of the samples itself. We apply DP-RST to a mouse colonic dataset during healing from inflammatory damage, revealing meaningful clusters associated with different stages of tissue repair. Differential gene expression analysis highlights key genes with spatially distinct patterns, revealing the compartmentalization of immune, metabolic, and regenerative processes during mucosal healing. 

In randomized controlled trials, using an ordinal outcome is often more statistically efficient than using a binary composite outcome. The treatment effect on an ordinal outcome is frequently described as the odds ratio from a proportional odds model; however, this summary measure lacks transparency when proportional odds is violated. We propose transparent treatment effect summary measures for ordinal outcomes, including 'weighted mean' risk differences and 'weighted geometric mean' odds ratios and relative risks, along with Bayesian estimators based on non-proportional odds models that facilitate covariate adjustment with marginalization via the Bayesian bootstrap. We propose weighting schemes that ensure inference is invariant to whether the ordinal outcome is ordered from best to worst versus worst to best, and invariant to the insertion of a outcome level with zero probability. Using computer simulation, we show that comparative testing based on the proposed treatment effect summary measures performs well relative to the traditional proportional odds approach. We provide an analysis using the proposed framework of the COVID-OUT trial which exhibits evidence of non-proportional odds effects. 

Multivariate Hawkes Processes (MHPs) model complex temporal dynamics among event sequences on multiple dimensions. Typically, strong parametric assumptions are made about the excitation functions of MHP, motivating the need for modeling flexible excitation patterns. Further, different excitation functions across dimensions often have strong similarities. Motivated by reasons above, we propose MHP based on dependent Dirichlet process (MHP-DDP), a hierarchical nonparametric Bayesian modeling approach for MHP. MHP-DDP flexibly estimates the excitation function via a mixture of scaled Beta distributions, and borrows strengths across dimensions by modeling such mixing distribution as a mixture of a shared Dirichlet process (DP) and a group-specific idiosyncratic DP. We develop a Markov chain Monte Carlo (MCMC) algorithm for implementation. We also conduct simulations to compare MHP-DDP to benchmark methods where total or no information is borrowed. We show that MHP- DDP outperforms the benchmark methods in terms of lower estimation error for the MCMC algorithm. Finally, we apply our method to an example in finance, where we study the order flow in the limit order book (LOB) records. 

Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize "data-level dependence'' in analysis of extreme events, we propose a mixture model that achieves flexible dependence properties and allows high-dimensional inference for extremes of spatial processes. We modify the popular random scale construction that multiplies a Gaussian random field by a single radial variable; we allow the radial variable to vary smoothly across space and add non-stationarity to the Gaussian process. As the level of extremeness increases, this single model exhibits both asymptotic independence at long ranges and either asymptotic dependence or independence at short ranges. We make joint inference on the dependence model and a marginal model using a copula approach within a Bayesian hierarchical model. Three different simulation scenarios show close to nominal frequentist coverage rates. Lastly, we apply the model to a dataset of extreme summertime precipitation over the central United States. We find that the joint tail of precipitation exhibits non-stationary dependence structure that cannot be captured by limiting extreme value models or current state-of-the-art sub-asymptotic models. 

In astronomical observations, the estimation of distances from parallaxes is a challenging task due to the inherent measurement errors and the non-linear relationship between the parallax and the distance.
This study leverages ideas from robust Bayesian inference to tackle these challenges, investigating a broad class of prior densities for estimating distances with a reduced bias and variance. Through theoretical analysis, simulation experiments, and the application to data from the Gaia Data Release 1 (GDR1), we demonstrate that heavy-tailed priors provide more reliable distance estimates, particularly in the presence of large fractional parallax errors. Theoretical results highlight the "curse of a single observation", where the likelihood dominates the posterior, limiting the impact of the prior. Nevertheless, heavy-tailed priors can delay the explosion of posterior risk, offering a more robust framework for distance estimation. The findings suggest that reciprocal invariant priors, with polynomial decay in their tails, such as the Half-Cauchy and Product Half-Cauchy, are particularly well-suited for this task, providing a balance between bias reduction and variance control.