Recently, Bayesian diagnostic classification modeling has been becoming popular in health psychology, education, and sociology. Typically information criteria are used for model selection when researchers want to choose the best model among alternative models. In Bayesian estimation, posterior predictive checking is a flexible Bayesian model…

In this thesis, I use a combination of simulations and empirical data to demonstrate that a small set of structural and functional principles - the basic tenets of predictive coding theory - succinctly accounts for a very wide range of properties in the language processing system. Predictive coding approximates hierarchical Bayesian inference via…

Bayesian network is a probabilistic graphical model that has wide applications in various domains due to its peculiarity of knowledge representation and reasoning under uncertainty. This research aims at Bayesian network structure learning and how the learned model can be used for reasoning. Learning the structure of Bayesian network from data is…

This dissertation consists of three manuscripts. The manuscripts contribute to a budding "methodological reform" currently taking place in quantitative second-language (L2) research. In the first manuscript, the researcher describes an empirical investigation on the application of two well-known effect size estimators, eta-squared (eta…

Different estimation procedures have been developed for the unidimensional three-parameter item response theory (IRT) model. These techniques include the marginal maximum likelihood estimation, the fully Bayesian estimation using Markov chain Monte Carlo simulation techniques, and the Metropolis-Hastings Robbin-Monro estimation. With each…

This simulation study compared the utility of various discrepancy measures within a posterior predictive model checking (PPMC) framework for detecting different types of data-model misfit in multidimensional Bayesian network (BN) models. The investigated conditions were motivated by an applied research program utilizing an operational complex…

Diagnostic classification models (DCMs) are structured latent class models widely discussed in the field of psychometrics. They model subjects' underlying attribute patterns and classify subjects into unobservable groups based on their mastery of attributes required to answer the items correctly. The effective implementation of DCMs depends…

Compressed sensing (CS) is an emerging signal acquisition framework that goes against the traditional Nyquist sampling paradigm. CS demonstrates that a sparse, or compressible, signal can be acquired using a low rate acquisition process. Since noise is always present in practical data acquisition systems, sensing and reconstruction methods are…

A simulation study was conducted to explore the performance of the linear logistic test model (LLTM) when the relationships between items and cognitive components were misspecified. Factors manipulated included percent of misspecification (0%, 1%, 5%, 10%, and 15%), form of misspecification (under-specification, balanced misspecification, and…

General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…

Generalized fiducial inference is a powerful tool for many difficult problems. Based on an extension of R. A. Fisher's work, we used generalized fiducial inference for two extreme value problems and a multiple comparison procedure. The first extreme value problem is dealing with the generalized Pareto distribution. The generalized Pareto…

Moving one's eyes while reading is one of the most complex everyday tasks humans face. To perform efficiently, readers must make decisions about when and where to move their eyes every 200-300ms. Over the past decades, it has been demonstrated that these fine-grained decisions are influenced by a range of linguistic properties of the text, and…

Anomaly detection is an important and indispensable aspect of any computer security mechanism. Ad hoc and mobile networks consist of a number of peer mobile nodes that are capable of communicating with each other absent a fixed infrastructure. Arbitrary node movements and lack of centralized control make them vulnerable to a wide variety of…