Speaker: Ye Jin Choi
Title: K Functions for Spatial Functional Data with Phase Variation and Shapes of Planar Curves
Abstract: We model the shapes of spatially dependent functional data or boundaries of two-dimensional (2D) objects, i.e., spatially dependent shapes of parameterized curves. Functional data is often composed of two confounded sources of variation: amplitude and phase. Amplitude captures shape differences among functions while phase captures timing differences in these shape features. Similarly, boundaries of 2D objects represented as parameterized curves exhibit variation in terms of their shape, translation, scale, orientation and parameterization. We study the spatial dependence among functions or curves by first decomposing given data into the different sources of variation. The proposed framework leverages a modified definition of the trace-variogram, which is commonly used to capture spatial dependence in functional data. We propose different types of trace-variograms that capture different components of variation in functional or shape data, and use them to define a functional/shape mark-weighted K function by considering their locations in the spatial domain as random. This statistical summary then allows us to study the spatial dependence in each source of variation separately. Efficacy of the proposed framework is demonstrated through extensive simulation studies and real data applications.
Speaker: Biqing Yang
Title: Bayesian Causal Inference with Gaussian Process Priors for Treatment Effect Estimation
Abstract: With the increasing demand for observational data analysis, developing robust statistical methods to estimate causal effects has become increasingly important. We propose novel Bayesian methods that integrate both propensity and prognostic scores with Gaussian process priors to improve treatment effect estimation, particularly in scenarios where heterogeneous treatment effect estimation is of interest.
We explore two primary approaches to leverage these techniques in causal inference. The first approach develops a Bayesian semiparametric model that simultaneously incorporates propensity and prognostic scores. By leveraging Gaussian process priors, we estimate both the average treatment effect (ATE) and conditional average treatment effect (CATE) with flexibility. We also establish theoretical properties, including asymptotic consistency and the doubly robustness of the estimator, ensuring validity under a wide range of conditions. The second approach addresses scenarios with no control group or an insufficient number of control observations, extending Bayesian causal inference to external control data borrowing by integrating Gaussian process priors with a propensity-score-integrated power prior. This method enables more effective incorporation of external data while accounting for heterogeneity in treatment effects. We illustrate its effectiveness through simulation studies and an application to real-world data.
Both approaches are evaluated using extensive simulations and real-world applications, showing improved performance compared to several existing methods. While many existing methods focus solely on estimating the ATE, our findings contribute to a more comprehensive Bayesian framework for causal inference, providing theoretical insights and practical guidelines for estimating both the ATE and CATE.
