Yuhui Chen

Accelerated hazards model based on parametric families generalized with Bernstein polynomials

A transformed Bernstein polynomial that is centered at standard parametric families, such as Weibull or log-logistic, is proposed for use in the accelerated hazards model. This class provides a convenient way towards creating a Bayesian nonparametric prior for smooth densities, blending the merits of parametric and nonparametric methods, that is amenable to standard estimation approaches. For example optimization methods in SAS or R can yield the posterior mode and asymptotic covariance matrix. This novel nonparametric prior is employed in the accelerated hazards model, which is further generalized to time-dependent covariates. The proposed approach fares considerably better than previous approaches in simulations; data on the effectiveness of biodegradable carmustine polymers on recurrent brain malignant gliomas is investigated.

A new type of Bayesian nonparametric control charts for individual measurements

As a screening process, control chart has been widely used in many fields where a monitoring process is required for quality improvement. Most commonly used control charts with data measured on a continuous scale usually assume the underlying process follows a certain parametric distribution, such as normal. As such, the charts might lack in-control robustness and might not be sensitive to an out-of-control state if the underlying process is not as the assumed. To this point, a new type of Bayesian nonparametric control charts is derived upon a recently developed nonparametric prior named the transformed Bernstein polynomial prior (TBPP). This new chart automatically inherits the merits of TBPP and thus can efficiently adjust an initial guess on the underlying process to approach to the true one. Its robustness property makes it suitable to various types of monitoring processes.

Semiparametric regression control charts

Control charts are screening processes that have been widely used in many areas where monitoring product quality is required. Many methods have been proposed to construct charts with different types of data. A common point in most existing methods is to monitor the quality variable only. However, in many situations, the quality variable depends on other covariates, such as environmental factors. Thus, without adjusting charts by taking the effect of covariates into consideration, the traditional charts typically have a poor performance when the quality variable is highly dependent on covariates. To this point, we propose a new type of semiparametric regression control charts by integrating a regression model into a traditional control chart. The quality monitoring process stems from a newly developed nonparametric prior called the transformed Bernstein polynomial prior (TBPP), which provides a convenient and robust way to implement the pattern recognition by assuming the unknown pattern is centered at a standard, commonly used parametric family, such as the normal. Then, by adding details via the data, any departure from the initial parametric guess will be captured and used for adjustment on estimation to guarantee robustness. In addition, this new type of control charts also inherits the merit of the smoothness property of the TBPP and thus provides an efficient estimation procedure through optimization. In practice, the proposed method is, therefore, suitable to screening a process where a large data set is presented.

Flexible parametrization of variance functions for quantal response data derived from counts

ABSTRACT Although the Poisson model has been widely used to fit count data, a well-known drawback is that the Poisson mean equals its variance. Many alternative models for counts that are overdispersed relative to Poisson have been developed to solve this issue, including the negative binomial model. In this article, the negative binomial model with a four-parameter logistic mean is proposed to handle these types of counts, with variance that flexibly depends on the mean. Various parameterizations for the variance are considered, including extra-Poisson variability modeled as an exponentiated B-spline. Thus, the proposed model ably captures the leveling off of the mean, i.e., the “lazy-S” shape often encountered for overdispersed dose–response counts, simultaneously taking into account both overdispersion and natural mortality. Two real datasets illustrate the merits of the proposed approach: media colony counts after tuberculosis decontamination, and the number of monkeys killed by Ache hunters over several hunting trips in the Paraguayan tropical forest.

Copula regression models for discrete and mixed bivariate responses

Estimation of the dependencies between bivariate discrete or mixed responses can be difficult. In this article, we propose a copula-based model with latent variables associated with discrete margins to account for correlations between bivariate discrete responses. Furthermore, we generalize this strategy for jointly modeling the dependencies between mixed responses in regression mixed models. The proposed method allows the adoption of flexible discrete margins and copula functions for various types of data. Maximum likelihood is used for model estimation; particularly, the estimation for bivariate responses in copula-based regression mixed models can be implemented using the SAS PROC NLMIXED procedure via adaptive Gaussian quadrature. In addition, a mixed model with non-Gaussian random effects can also be easily fitted using the same SAS procedure after reformulating the likelihood function by multiplying and dividing by a Gaussian density. Simulation results show good performance for bivariate discrete or mixed outcomes ranging from noncorrelated to highly correlated responses. An analysis of student performance in California schools shows a drastic improvement in estimation precision from the joint model versus two independent fits.