title: New method to incorporate Type B uncertainty into least-squares procedures in radionuclide metrology.
abstract: We discuss a new method to incorporate Type B uncertainty into least-squares procedures. The new method is based on an extension of the likelihood function from which a conventional least-squares function is derived. The extended likelihood function is the product of the original likelihood function with additional PDFs (Probability Density Functions) that characterize the Type B uncertainties. The PDFs are considered to describe one's incomplete knowledge on correction factors being called nuisance parameters. We use the extended likelihood function to make point and interval estimations of parameters in the basically same way as the least-squares function used in the conventional least-squares method is derived. Since the nuisance parameters are not of interest and should be prevented from appearing in the final result, we eliminate such nuisance parameters by using the profile likelihood. As an example, we present a case study for a linear regression analysis with a common component of Type B uncertainty. In this example we compare the analysis results obtained from using our procedure with those from conventional methods.
authors.affiliation: University of Science & Technology (UST), Yuseong, Daejeon 305-350, Republic of Korea.
authors.forename: Jubong
authors.initials: J
authors.lastname: Han
authors.affiliation: Korea Research Institute of Standards and Science (KRISS), Yuseong, Daejeon 305-340, Republic of Korea. Electronic address: lee@kriss.re.kr.
authors.forename: K B
authors.initials: KB
authors.lastname: Lee
authors.affiliation: Korea Research Institute of Standards and Science (KRISS), Yuseong, Daejeon 305-340, Republic of Korea.
authors.forename: Jong-Man
authors.initials: JM
authors.lastname: Lee
authors.affiliation: Korea Research Institute of Standards and Science (KRISS), Yuseong, Daejeon 305-340, Republic of Korea.
authors.forename: Tae Soon
authors.initials: TS
authors.lastname: Park
authors.affiliation: Korea Research Institute of Standards and Science (KRISS), Yuseong, Daejeon 305-340, Republic of Korea.
authors.forename: J S
authors.initials: JS
authors.lastname: Oh
authors.affiliation: Korea Research Institute of Standards and Science (KRISS), Yuseong, Daejeon 305-340, Republic of Korea.
authors.forename: Pil-Jei
authors.initials: PJ
authors.lastname: Oh
keywords: Bayesian statistics; Least-squares analysis; Likelihood function; Type B uncertainty