Journal of Data Science

Historical data or real-world data are often available in clinical trials, genetics, health care, psychology, environmental health, engineering, economics, and business. The power priors have emerged as a useful class of informative priors for a variety of situations in which historical data are available. In this paper, an overview of the development of the power priors is provided. Various variations of the power priors are derived under a binomial regression model and a normal linear regression model. The development of software on the power priors is also briefly reviewed. Throughout this paper, the data from the Kociba study and the National Toxicology Program study as well as the data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) study are used to demonstrate the derivations of the power priors and their variations. Detailed analyses of the data from these studies are carried out to further demonstrate the usefulness of the power priors and their variations in these real applications. Finally, the directions of future research on the power priors are discussed.

The Corona Virus Disease 2019 (COVID-19) emerged in Wuhan, China in December 2019. In order to control the epidemic, the Chinese government adopted several public health measures. To study the influence of these measures on the transmissibility of COVID-19 in the city of Wuhan and other cities in the Hubei province, China, we establish generalized semi-varying coefficient models for the number of new diagnosed cases and estimate the varying coefficient for the covariates by the spline method. Since the pandemic was most severe in Wuhan, we fitted separate models for Wuhan and the remaining 16 cities in Hubei. Estimators for the incubation periods, the real-time transmission rates, and the real-time reproduction numbers were obtained. The results demonstrate that the changes in the real-time transmission rate in Wuhan and other cities in Hubei are almost simultaneous. Futher, public health interventions such as restriction of traffic, adjustment of the diagnosed standard, deployment of medical resources, and improvement of nucleic acid testing capacity, had positive effects on reducing the transmission of COVID-19.

Abstract: This paper investigates the return, volatility, and trading on the Shanghai Stock Exchange with high-frequency intraday five-minute Shanghai Stock Exchange Composite Index (SHCI) data. The random walk hypothesis is rejected, indicating there are predictable components in the index. We adopt a time-inhomogeneous diffusion model using log penalized splines (log P-splines) to estimate the volatility. A GARCH volatility model is also fitted for comparison. A de-volatilized series are obtained by using the de-volatilization technique of Zhou (1991) that resample the data into different de-volatilized series with more desired properties for trading. A trading program based on local trends extracted with a State Space model is then implemented on the de-volatilized five-minute SHCI return series for profit. Volatility estimates from both models are found to be competitive for the purpose of trading.

Abstract: This paper provides a Bayesian approach to estimating the interest rate term structures of Treasury and corporate debt with a penalized spline model. Although the literature on term structure modeling is vast, to the best of our knowledge, all methods developed so far belong to the frequentist school. In this paper, we develop a two-step estimation procedure from a Bayesian perspective. The Treasury term structure is first estimated with a Bayesian penalized spline model. The smoothing parameter is naturally embedded in the model as a ratio of posterior variances and does not need to be selected as in the frequentist approach. The corporate term structure is then estimated by adding a credit spread to the estimated Treasury term structure, incorporating knowledge of the positive credit spread into the Bayesian model as an informative prior. In contrast to the frequentist method, the small sample size of the corporate debt poses no particular difficulty to the proposed Bayesian approach.

Abstract: This paper estimates the interest rate term structures of Treasury and individual corporate bonds using a robust criterion. The Treasury term structure is estimated with Bayesian regression splines based on nonlinear least absolute deviation. The number and locations of the knots in the regression splines are adaptively chosen using the reversible jump Markov chain Monte Carlo method. Due to the small sample size, the individual corporate term structure is estimated by adding a positive parametric credit spread to the estimated Treasury term structure using a Bayesian approach. We present a case study of U.S. Treasury STRIPS (Separate Trading of Registered Interest and Principal of Securities) and AT&T bonds from April 1994 to December 1996. Compared with several existing term structure estimation approaches, the proposed method is robust to outliers in our case study.