A Robust Framework for Bayesian Nonparametric Model Misspecification Detection

Thesis Abstract

In modern statistical practice, Bayesian nonparametric (BNP) methods offer flexible alternatives to parametric models, yet practical deployment is hindered by model misspecification risks and computational challenges. This study addresses the problem by developing a robust framework for detecting and mitigating BNP model misspecification in applied inference, with particular emphasis on posterior reliability and predictive validity across diverse data-generating processes. The aim is to construct a theoretically grounded, computationally tractable framework that signals misspecification, adapts priors and kernels accordingly, and preserves interpretability of results under uncertainty. Specific objectives are (i) to formalize diagnostic criteria for BNP misspecification using a blend of posterior predictive checks, discrepancy measures, and information-theoretic divergence; (ii) to integrate robustifying mechanisms—such as coarsened likelihoods, tempered transitions, and adaptive Dirichlet process priors—to sustain inference under misspecified components; (iii) to establish model-averaging and nonparametric sensitivity analysis procedures that quantify the impact of misspecification on predictive intervals and decision outcomes; (iv) to validate the framework through extensive simulations under controlled misspecification scenarios and real-world datasets from epidemiology and econometrics; and (v) to provide pragmatic guidelines for practitioners on diagnostic interpretation and computational implementation. The methodological core combines Bayesian nonparametric theory with robust statistics and computational Bayesian methods. A hierarchical BNP model, built on a Dirichlet process mixture with adaptive concentration parameters, is augmented with misspecification-detection layers based on posterior predictive p-values, energy distance discrepancies, and the ?? likelihood ratio statistic adapted to nonparametric priors. The research adopts a mixed-methods design with two strands a simulation study and an empirical study. The population consists of synthetic data generated from known and unknown mixtures, and real datasets including a public health time series of infectious disease counts (n = 5,000 observations) and a cross-sectional macroeconomic dataset (n = 10,000 observations). The sample sizes are chosen to ensure stable estimation of nonparametric components and to stress-test diagnostic procedures. Data collection instruments are secondary data sources and simulated data generators calibrated to reflect realistic misspecification patterns, while ensuring reproducibility through open-source code and reproducible seeds. Validity and reliability are addressed through calibration of simulation settings, replication across multiple misspecification levels, and cross-validation of diagnostic metrics. The analysis plan employs Markov chain Monte Carlo (MCMC) with parallel tempering to sample from posterior distributions, along with variational Bayes as a scalable alternative for large datasets. Model specification follows a BNP regression framework where the error structure is modeled as a Dirichlet process mixture, coupled with a robustification layer that employs coarsened observation models and tempered likelihoods. Diagnostics rely on a composite misspecification index combining posterior predictive checks, k-nearest neighbor discrepancy measures, and cross-validated predictive loss. Sensitivity analyses examine the influence of prior choices on the detection of misspecification and on posterior inferences. Expected findings indicate that the proposed framework reliably detects misspecification across a spectrum of data-generating processes, and that robustification mechanisms temper overconfidence in predictive intervals while maintaining calibration under both correct specification and misspecification. The framework is anticipated to improve out-of-sample predictive performance and yield more honest uncertainty quantification compared to standard BNP applications without diagnostic checks. The contribution to knowledge lies in (i) providing a unified diagnostic-robust BNP framework that explicitly links misspecification signals to adaptive modeling choices, (ii) advancing practical tools for robust BNP inference that integrate theory and computation, and (iii) delivering actionable guidelines for practitioners on when and how to adjust BNP models in response to diagnostic indicators. The study concludes with recommendations for adopting diagnostic-driven BNP workflows in applied research, including criteria for switching to more flexible priors, implementing model averaging, and reporting misspecification diagnostics alongside inference results.