Title（标题）：Confidence Distribution and a Frequentist Approach to Incorporate

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Speaker（汇报人）：Prof. Minge Xie

Department of Statistics，Rutgers University

Time（功夫）：2011年9月15日（周四）下午2:00 — 3:00

Place（地址）：拉斯维加斯9888新楼217教室

Abstract（提要）：Incorporating external information, such as prior information and expert opinions, can play an important role in statistical design, analysis and interpretation of results. Seeking effective schemes for incorporating prior information with the primary outcomes of interest has drawn increasing attention in many applications. Most methods currently used for combining prior information with data are Bayesian. We demonstrate using a binomial clinical trial example that they sometimes may encounter a problem and a counterintuitive “outlying posterior phenomenon,” especially when informative prior distribution is skewed.

In this talk, we present an alternative frequentist framework of combining information using confidence distributions (CDs), and illustrate it through an example of incorporating expert opinions with information from clinical trial data. A CD uses a distribution function to estimate a parameter of interest. Some researchers have suggested that a CD is a “frequentist analogue of a Bayesian posterior,” although the notion of CD, especially in its asymptotic form, is much broader. In this talk, we present a formal definition of CDs and demonstrate promising potentials of the CD concept, as an effective tool in statistical inference. The proposed alternative frequentist framework of combining information using CDs not only unifies most existing meta-analysis approaches, but also leads to development of new approaches. In particular, we develop a frequentist approach to combine surveys of expert opinions with binomial clinical trial data, and illustrate it using data from a collaborative research with Johnson & Johnson Pharmaceuticals.

The development may also have applications in financial industry and other fields, where prior knowledge and historical information are much valued and need to be incorporated with current data.