Student Poster & KNU G-Lamp Posters Information

Abstract:
General Bayesian updating (GBU) is a framework for updating prior beliefs about the parameter of interest to a posterior distribution via a loss function without imposing the distribution assumption on data. In recent years, the asymptotic distribution of the loss-likelihood bootstrap (LLB) sample has been a standard for determining the loss scale parameter which controls the relative weight of the loss function to the prior in GBU. However, the existing method fails to consider the prior distribution since it relies on the asymptotic equivalence between GBU and LLB. To address this limitation, we propose a new finite-sample-based approach to loss scale determination using the Bayesian generalized method of moments (BGMM) as a reference. We develop an efficient algorithm that determines the loss scale parameter by minimizing the Kullback-Leibler divergence between the exact posteriors of GBU and BGMM. We prove the convexity of our objective function to ensure a unique solution. Asymptotic properties of the proposed method are established to demonstrate its generalizability. We demonstrate the performance of our proposed method through a simulation study and a real data application.

Abstract:
This study introduces a modified spatial hurdle integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) model that improves prediction for spatiotemporal count data, especially in the presence of over-dispersion and zero inflation. To ensure parsimony, the model builds on existing spatial hurdle INGARCH frameworks and incorporates an empirical Bayes approach to estimate the probability of positive counts, allowing greater flexibility in modeling zero values. This study employs Bayesian inference with an adaptive Markov Chain Monte Carlo (MCMC) algorithm to estimate parameters efficiently. Simulation studies and real-world applications to weekly dengue fever case data from four provinces in Thailand and four cantons in Costa Rica demonstrate the model’s effectiveness. The improved model captures spatiotemporal dependencies more accurately and handles excess zeros more robustly than traditional spatial hurdle and zero-inflated INGARCH models. These results highlight the model’s value in improving the analysis of spatiotemporal disease patterns.

Abstract:
Accurate valuation and efficient management of ecological resources are crucial for sustainable forestry practices and ecological economics. This study introduces an innovative Bayesian statistical approach integrated with functional data analysis to precisely quantify the value of ecological products in lacquer tree . The research utilizes comprehensive field data collected from Pingli.
The proposed methodological framework combines Bayesian inference with functional modeling techniques, leveraging B-spline basis functions to capture complex ecological dynamics.
This model effectively characterizes the spatial heterogeneity of ecological services attributable to site-specific conditions and reveals temporal patterns through principal component regression. These patterns show initial decreases followed by increases in ecosystem service valuation. Additionally, a Bayesian-based correction mechanism is introduced to refine market pricing systems, significantly enhancing the accuracy of ecological valuation.
Our findings highlight the substantial potential and practical value of Bayesian functional modeling in ecological valuation.

Abstract:
This study explores a structure-based approach to assessing fairness across intersectional subgroups using Bayesian networks. A causal graph was learned from the COMPAS dataset, and the influence of a particular structural pathway—linking demographic characteristics, prior offenses, and recidivism—was examined. Conditional probabilities of recidivism were compared before and after the removal of the path, and the resulting differences, measured per subgroup, defined path-specific effects (PSE). To summarize subgroup variation, we introduce the Intersectional Fairness Score (IFS), capturing the disparity in structural impact. The proposed structure learning method incorporates prior constraints and temporal ordering to improve interpretability and bias sensitivity. Compared to conventional BIC-optimized structures, our approach reveals group-specific unfairness that may otherwise remain obscured. These results highlight the value of Bayesian structure learning as a tool for uncovering latent fairness issues in algorithmic systems.

Abstract:
Transformer models have achieved remarkable performance across various domains, including natural language processing. However, due to the permutation-invariance of multi-head attention, vanilla Transformer architectures tend to show decreased predictive performance when applied to time-series data, where positional information plays a crucial role. To address this limitation, positional encoding is added directly to the embedded input data, but this additive approach has been criticized for blending positional and semantic information, potentially causing information interference.
As an alternative, we propose several forms of positional encoding via concatenation in parallel with the embedded input. This design allows positional information and semantic content to exist in separate dimensions, thereby reducing interference. We conduct a comparative analysis against the traditional additive approach, using both time-series and language datasets. Experimental results demonstrate that the concatenation-based methods achieve stable and superior performance across both data types.

Abstract:
The Susceptible–Infectious–Recovered (SIR) model is widely used as a fundamental framework for the analysis of infectious disease transmission dynamics. Since the SIR model describes disease spread through a system of differential equations, specifying the full likelihood is difficult. The Approximate Bayesian Computation (ABC) has been proposed as a likelihood-free Bayesian inference method. However, existing ABC methods for SIR modeling have been limited to infectious diseases observed at a single location. We propose a hierarchical Bayesian SIR modeling framework that applies ABC within Gibbs sampling to address this limitation. Our framework models infection rates for multiple regions under a hierarchical structure and enables information sharing across regions without requiring an explicit likelihood function. Bayesian inference is conducted using ABC within Gibbs sampling to account for the uncertainty associated with the infection rates. Simulation studies and real-world applications demonstrate that the proposed method improves the stability and accuracy of infection rate estimation compared to existing region-wise approaches.

Abstract:
In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation.
In this paper, we view diffusion models as an implicit approach to nonparametric density estimation and study them within a statistical framework to analyze their surprising performance.
A key challenge in high-dimensional statistical inference is leveraging low-dimensional structures inherent in the data to mitigate the curse of dimensionality.
We assume that the underlying density exhibits a low-dimensional structure by factorizing into low-dimensional components, a property common in examples such as Bayesian networks and Markov random fields.
Under suitable assumptions, we demonstrate that an implicit density estimator constructed from diffusion models adapts to the factorization structure and achieves the minimax optimal rate with respect to the total variation distance.
In constructing the estimator, we design a sparse weight-sharing neural network architecture, where sparsity and weight-sharing are key features of practical architectures such as convolutional neural networks.

Abstract:
In this paper, we develop an online Bayesian inferential method for the Cox proportional hazards model with right-censored data. The proposed method is designed to analyze datasets where mini-batches of the entire data are sequentially available. As each mini-batch arrives, the method updates the current prior to the posterior distribution, which is then used as the prior for the next step. Each update consists of two steps: updating the marginal posterior of the regression coefficients using the partial likelihood and updating the remaining conditional posterior using the Poisson form Bayesian bootstrap likelihood. Our method is capable of inferring both the regression coefficients and the baseline cumulative hazard function. To the best of our knowledge, this is the first online Bayesian method for the Cox proportional hazards model. Through numerical experiments and real data analysis, we demonstrate that the proposed method outperforms existing frequentist online methods and is comparable to batch learning on the entire dataset, even when the size of mini-batches is moderately small.

Abstract:
Online learning is an inferential paradigm in which parameters are learned sequentially from data rather than from a fixed dataset, as in batch learning. Instead of training on a large dataset at once, an online learning algorithm updates parameters incrementally as new data arrive. In this talk, we assume that mini-batches from the entire dataset become available in sequential order. The Bayesian framework, which updates the belief about an unknown parameter after each mini-batch observation, is naturally suited for online learning. As each mini-batch arrives, we update the posterior distribution based on the current prior and the mini-batch observations, with the updated posterior serving as the prior for the next step. However, unless conjugacy holds, this naive Bayesian approach is rarely computationally tractable. If the model is regular, the updated posterior distribution can be approximated by a normal distribution, as justified by the Bernstein--von Mises theorem. We consider a variational approximation at each step and investigate the frequentist properties of the sequentially updated posterior at the final step. Under mild assumptions, we prove that the accumulated approx

Abstract:
Understanding cell-cell interactions in the tumor microenvironment (TME) is critical for assessing tumor progression, yet quantitative analysis has been limited. We propose a novel approach using spatial statistics to numerically capture cell interactions from pathology slides and correlate them with patient survival. We applied robust spatial summary statistics (e.g., Pair Correlation Function, K-functions) to point pattern data extracted from tumor pathology images. These spatial features were then used to predict patient survival outcomes using Functional Principal Component Analysis and a Functional Cox Proportional Hazard Model on the Lung cancer screening dataset and oral cancer image dataset. Our analysis revealed numerous statistically significant spatial predictors strongly correlated with patient survival (p < 0.05), highlighting that spatial cell-cell interactions have clinically meaningful implications for prognosis. This study highlights how robust spatial quantification of the TME can provide clinically meaningful survival predictions.

Abstract:
Interpreting the inner workings of Long Short-Term Memory (LSTM) networks is critical for transparent time-series modeling yet remains challenging. We present a unified framework that combines systematic gate ablation with gradient-based attribution to assess the relative importance of input, forget, and output gates over time. Ablation experiments highlight the pivotal role of the forget gate in preserving long-term dependencies, while attribution analysis produces a time-step-level map of each gate’s influence on the final prediction. Together, these methods offer a concise temporal profile of gate contributions, improving model interpretability and guiding the design of more efficient LSTM variants.

Abstract:
Accurate out-of-sample time series forecasting is crucial in many applications. While machine learning methods are widely used, most lack prediction intervals, limiting their ability to quantify uncertainty. This study addresses this gap by constructing one-step-ahead prediction intervals during the out-of-sample period using the wild bootstrap, Bayesian bootstrap (BB), and moving block bootstrap (MBB), tailored to SVR, random forest, LSTM, and XGBoost. Simulation studies based on a variety of time series models, such as ARMA, SARIMA, threshold models, and models with heavy-tailed distributions or GARCH-type errors, demonstrate the effectiveness of the proposed methods. The findings show that BB- and MBB-based machine learning models perform better when the data lacks a known generative structure. We further compare forecasting models for monthly suicide deaths in Japan and weekly enterovirus outpatient and inpatient visits in Taiwan using six approaches: BSTS, SARIMAX, SVR, random forest, LSTM, and XGBoost. Results show that BB and MBB outperform wild bootstrap in coverage and forecast accuracy, supporting their use in public health time series prediction.

Abstract:
The normalized difference vegetation index (NDVI) is a key metric for monitoring vegetation dynamics and detecting early signs of ecosystem changes. In particular, extreme values of NDVI are highly sensitive to external drivers such as climate change, underscoring the importance of precise analysis. However, traditional models focusing on mean values often fail to capture the distinct effects of predictors at the distributional extreme. To overcome this, quantile regression-based approaches have been increasingly adopted for modeling the extreme quantiles of NDVI. This study focuses on modeling extreme NDVI quantiles in the Indian subcontinent using a quantile additive model, accounting for nonlinear weather effects and spatiotemporal variability. The results show that all covariates have statistically significant, nonlinear influences on both tails of the NDVI distribution. Furthermore, the direction and magnitude of these effects vary between the lower and upper quantiles, highlighting the distributional heterogeneity and spatial complexity of NDVI.

Abstract:
Bayesian Reduced Rank Regression (RRR) has attracted increasing attention as a means to quantify the uncertainty of both the coefficient matrix and its rank in a multivariate linear regression framework. However, the existing Bayesian RRR approach relies on the strong assumption that the positions of independent coefficient vectors are known when the rank of the coefficient matrix is given. In contrast, the conventional RRR approach is free from this assumption since it permits the singular value decomposition (SVD) of the coefficient matrix. In this paper, we propose a Weighted Bayesian Bootstrap (WBB) approach to incorporate the SVD into the Bayesian RRR framework. The proposed Bayesian method offers an innovative way of sampling from the posterior distribution of the low-rank coefficient matrix. In addition, our WBB approach allows simultaneous posterior sampling for all ranks, which greatly improves computational efficiency. To quantify the rank uncertainty, we develop a posterior sample-based Monte Carlo method for marginal likelihood calculation. We demonstrate the superiority and applicability of the proposed method by conducting simulation studies and real data analysis.