Statistical Inference for Models with Intractable Normalizing Constants

In this dissertation, we have proposed two new algorithms for statistical inference for models with intractable normalizing constants: the Monte Carlo Metropolis-Hastings algorithm and the Bayesian Stochastic Approximation Monte Carlo algorithm. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. At each iteration, it replaces the unknown normalizing constant ratio by a Monte Carlo estimate. Although the algorithm violates the detailed balance condition, it still converges, as shown in the paper, to the desired target distribution under mild conditions. The BSAMC algorithm works by simulating from a sequence of approximated distributions using the SAMC algorithm. A strong law of large numbers has been established for BSAMC estimators under mild conditions. One significant advantage of our algorithms over the auxiliary variable MCMC methods is that they avoid the requirement for perfect samples, and thus it can be applied to many models for which perfect sampling is not available or very expensive. In addition, although the normalizing constant approximation is also involved in BSAMC, BSAMC can perform very robustly to initial guesses of parameters due to the powerful ability of SAMC in sample space exploration. BSAMC has also provided a general framework for approximated Bayesian inference for the models for which the likelihood function is intractable: sampling from a sequence of approximated distributions with their average converging to the target distribution. With these two illustrated algorithms, we have demonstrated how the SAMCMC method can be applied to estimate the parameters of ERGMs, which is one of the typical examples of statistical models with intractable normalizing constants. We showed that the resulting estimate is consistent, asymptotically normal and asymptotically efficient. Compared to the MCMLE and SSA methods, a significant advantage of SAMCMC is that it overcomes the model degeneracy problem. The strength of SAMCMC comes from its varying truncation mechanism, which enables SAMCMC to avoid the model degeneracy problem through re-initialization. MCMLE and SSA do not possess the re-initialization mechanism, and tend to converge to a solution near the starting point, so they often fail for the models which suffer from the model degeneracy problem

Impacts of Innovation School System in Korea: A Latent Space Item Response Model with Neyman-Scott Point Process

South Korea's educational system has faced criticism for its lack of focus on critical thinking and creativity, resulting in high levels of stress and anxiety among students. As part of the government's effort to improve the educational system, the innovation school system was introduced in 2009, which aims to develop students' creativity as well as their non-cognitive skills. To better understand the differences between innovation and regular school systems in South Korea, we propose a novel method that combines the latent space item response model (LSIRM) with the Neyman-Scott (NS) point process model. Our method accounts for the heterogeneity of items and students, captures relationships between respondents and items, and identifies item and student clusters that can provide a comprehensive understanding of students' behaviors/perceptions on non-cognitive outcomes. Our analysis reveals that students in the innovation school system show a higher sense of citizenship, while those in the regular school system tend to associate confidence in appearance with social ability. We compare our model with exploratory item factor analysis in terms of item clustering and find that our approach provides a more detailed and automated analysis

A Bayesian Adaptive Phase I/II Clinical Trial Design with Late-onset Competing Risk Outcomes

Early-phase dose-finding clinical trials are often subject to the issue of late-onset outcomes. In phase I/II clinical trials, the issue becomes more intractable because toxicity and efficacy can be competing risk outcomes such that the occurrence of the first outcome will terminate the other one. In this paper, we propose a novel Bayesian adaptive phase I/II clinical trial design to address the issue of late-onset competing risk outcomes. We use the continuation-ratio model to characterize the trinomial response outcomes and the cause-specific hazard rate method to model the competing-risk survival outcomes. We treat the late-onset outcomes as missing data and develop a Bayesian data augmentation method to impute the missing data from the observations. We also propose an adaptive dose-finding algorithm to allocate patients and identify the optimal biological dose during the trial. Simulation studies show that the proposed design yields desirable operating characteristics

Factors Influencing Residual Pleural Opacity in Tuberculous Pleural Effusion

Tuberculous pleural effusion (TPE) leads to residual pleural opacity (RPO) in a significant proportion of cases. The aim of this study was to investigate which TPE patients would have RPO following the treatment. This study was performed prospectively for a total of 60 TPE patients, who underwent pleural fluid analysis on the initial visit and chest radiographs and computed tomography (CT) scans before and after the administration of antituberculous medication. At the end of antituberculous medication, the incidence of RPO was 68.3% (41/60) on CT with a range of 2-50 mm. Compared with the non-RPO group, the RPO group had a longer symptom duration and lower pleural fluid glucose level. On initial CT, loculation, extrapleural fat proliferation, increased attenuation of extrapleural fat, and pleura-adjacent atelectasis were more frequent, and parietal pleura was thicker in the RPO group compared with the non-RPO group. By multivariate analysis, extrapleural fat proliferation, loculated effusion, and symptom duration were found to be predictors of RPO in TPE. In conclusion, RPO in TPE may be predicted by the clinico-radiologic parameters related to the chronicity of the effusion, such as symptom duration and extrapleural fat proliferation and loculated effusion on CT