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There have been substantial interests in investigating HIV dynamics for understanding the pathogenesis of HIV-1 infection and antiviral treatment strategies. However, it is difficult to establish a relationship between pharmacokinetics (PK) and antiviral response due to too many confounding factors related to antiviral response during the treatment process. In this article, a mechanism-based dynamic model for HIV infection with intervention by antiretroviral therapies is proposed. In this model, we directly incorporate drug concentration, adherence and drug susceptibility into a function of treatment efficacy defined as an inhibition rate of virus replication. In order to focus our attention on estimating dynamic parameters for all subjects, we investigate a Bayesian approach under a framework of the hierarchical Bayesian (mixed-effects) model. The proposed methods and models not only can help to alleviate the difficulty in identifiability, but also can flexibly deal with sparse and unbalanced longitudinal data. The viral dynamic parameters estimated from the proposed method are, thus, more accurate since the variations in PK, adherence and drug resistance have been considered in the model.

Insurance companies have to build a reserve for their future payments which is usually done by deterministic methods giving only a point estimate. In this paper two semi-stochastic methods are presented along with a more sophisticated hierarchical Bayesian model containing MCMC technique. These models allow us to determine quantiles and confidence intervals of the reserve which can be more reliable as just a point estimate. A sort of cross-validation technique is also used to test the models.

Latent, that is Incurred But Not Reported (IBNR) claims influence heavily the calculation of the reserves of an insurer, necessitating an accurate estimation of such claims. The highly diverse estimations of the latent claim amount produced by the traditional estimation methods (chain-ladder, etc.) underline the need for more sophisticated modelling. We are aimed at predicting the number of latent claims, not yet reported. This means the continuation the so called run-off triangle by filling in the lower triangle of the delayed claims matrix. In order to do this the dynamics of claims occurrence and reporting tendency is specified in a hierarchical Bayesian model. The complexity of the model building requires an algorithmic estimation method, that we carry out along the lines of the Bayesian paradigm using the MCMC technique. The predictive strength of the model against the future disclosed claims is analysed by cross validation. Simulations serve to check model stability. Bootstrap methods are also available as we have full record of the individual claims at our disposal. Those methods are used for assessing the variability of the estimated structural parameters.

The paper surveys almost two decades of progress by me and colleagues in three psychometric research areas involving the probability modeling and statistical analysis of standardized ability test data: nonparametric multidimensional latent ability structure modeling and assessment, test fairness modeling and assessment, and modeling and assessment of skills diagnosis via educational testing. In the process, it is suggested that the unidimensional scoring testing paradigm that has driven standardized ability testing research for over half a century is giving way to a new multidimensional latent ability modeling and multiple scoring paradigm that in particular explains and allows the effective detection of test bias and embraces skills-level formative assessment, opening up a plethora of challenging, exciting, and societally important research problems for psychometricians. It is hoped that this light-stepping history will interest probabilists and statisticians in exploring the field of psychometrics.

Informally, test bias occurs when an examinee is under or over evaluated by his test score in terms of the purpose of the test. Also informally, skills diagnosis refers to evaluating examinee levels of mastery (usually done dichotomously as master versus nonmaster of each skill) on a moderate number of carefully selected skills for which having student skills profiles can greatly help individual student learning and classroom level.

My strategy, strongly influenced by his probabilistic background, for producing interesting and effective psychometric research is to choose psychometric research questions from practical challenges facing educational testing. Then, I and colleagues bring to bear sophisticated probability modeling and modern statistical thought to solve these questions, making effectiveness of the resulting research in meeting the educational testing challenges the ultimate criterion for judging its worth.

It is somebody's ancient proverb that the acorn sometimes falls far from the oak tree. Y. S. Chow taught me the tools of probability limit theorem research, taught me to approach research with enthusiasm and tenacity, and provided a very supportive environment for me and his other graduate students. Although psychometrics/educational measurement is far from the probabilistic oak tree, whatever success I've had as a psychometrician has been strongly influenced by the supportive, demanding, and creative environment Y. S. creates for his students. By now I have had many Ph.D. students in psychometrics: it was the just described model of Y. S.'s for mentoring Ph.D. students that I followed with all of them.

The field of computational statistics refers to statistical methods or tools that are computationally intensive. Due to the recent advances in computing power, some of these methods have become prominent and central to modern data analysis. In this paper, we focus on several of the main methods including density estimation, kernel smoothing, smoothing splines, and additive models. While the field of computational statistics includes many more methods, this paper serves as a brief introduction to selected popular topics.

The proliferation of sequencing technologies in biomedical research has raised many new privacy concerns. These include concerns over the publication of aggregate data at a genomic scale (e.g. minor allele frequencies, regression coefficients). Methods such as differential privacy can overcome these concerns by providing strong privacy guarantees, but come at the cost of greatly perturbing the results of the analysis of interest. Here we investigate an alternative approach for achieving privacy-preserving aggregate genomic data sharing without the high cost to accuracy of differentially private methods. In particular, we demonstrate how other ideas from the statistical disclosure control literature (in particular, the idea of disclosure risk) can be applied to aggregate data to help ensure privacy. This is achieved by combining minimal amounts of perturbation with Bayesian statistics and Markov Chain Monte Carlo techniques. We test our technique on a GWAS dataset to demonstrate its utility in practice. An implementation is available at https://github.com/seanken/PrivMCMC.

The methodology of Markov basis initiated by Diaconis and Sturmfels¹ stimulated active research on Markov bases for more than ten years. It also motivated improvements of algorithms for Gröbner basis computation for toric ideals, such as those implemented in 4ti2.² However at present explicit forms of Markov bases are known only for some relatively simple models, such as the decomposable models of contingency tables. Furthermore general algorithms for Markov bases computation often fail to produce Markov bases even for moderate-sized models in a practical amount of time. Hence so far we could not perform exact tests based on Markov basis methodology for many important practical problems.

In this article we propose to use lattice bases for performing exact tests, in the case where Markov bases are not known. Computation of lattice bases is much easier than that of Markov bases. With many examples we show that the approach with lattice bases is practical. We also check that its performance is comparable to Markov bases for the problems where Markov bases are known.