Statistical methods for jointly estimating the decay constant of 40K and the age of a dating standard

被引:57
作者
Kwon, JY [1 ]
Min, KW
Bickel, PJ
Renne, PR
机构
[1] Univ Calif Berkeley, Dept Stat, Berkeley, CA 94720 USA
[2] Univ Calif Berkeley, Dept Earth & Planetary Sci, Berkeley, CA 94720 USA
[3] Berkeley Geochronol Ctr, Berkeley, CA USA
来源
MATHEMATICAL GEOLOGY | 2002年 / 34卷 / 04期
基金
美国国家科学基金会;
关键词
errors-in-variables; nonlinear regression; maximum likelihood; bootstrap; Bonferroni confidence regions;
D O I
10.1023/A:1015035228810
中图分类号
P [天文学、地球科学];
学科分类号
07 ;
摘要
To simultaneously evaluate the decay constant of K-40 (lambda) and the age of a standard (t(std)) using isotopic data from geologic materials, we applied a series of statistical methods. The problem of estimating the most probable intercept of many nonlinear curves in lambda, and t(std) space is formulated by an errors-in-variables nonlinear regression model. Then a maximum likelihood method is applied to the model for a point estimate, which is equivalent to the nonlinear least square method when measurement error distributions are Gaussian. Uncertainties and confidence regions of the estimates can be approximated using three methods: the asymptotic normal approximation, the parametric bootstrap method and Bonferroni confidence regions. Five pairs of published data for samples with ages from 2 ka to 4.5 Ga were used to estimate lambda and the age of Fish Canyon sanidine (t(FCs)), The statistical procedure yields most probable estimates of lambda (5.4755 +/- 0.0170 x 10(-10) (1sigma)/year) and t(FCs) (28.269 +/- 0.0661 (1sigma) Ma) which are in between previously published values. These results indicate the power of our approach to provide improved constraints on these parameters, although the preliminary nature of some of the input data require further review before the values can be adopted.
引用
收藏
页码:457 / 474
页数:18
相关论文
共 26 条
[1]   The NUBASE evaluation of nuclear and decay properties [J].
Audi, G ;
Bersillon, O ;
Blachot, J ;
Wapstra, AH .
NUCLEAR PHYSICS A, 1997, 624 (01) :1-124
[2]   Intercalibration of 40Ar/39Ar dating standards [J].
Baksi, AK ;
Archibald, DA ;
Farrar, E .
CHEMICAL GEOLOGY, 1996, 129 (3-4) :307-324
[3]  
Bickel PJ., 2001, MATH STAT BASIC IDEA
[4]  
Carroll RJ., 1995, MEASUREMENT ERROR NO
[5]  
Efron B., 1993, INTRO BOOTSTRAP, V1st ed., DOI DOI 10.1201/9780429246593
[6]   ENERGY-LEVELS OF A = 21-44 NUCLEI .5. [J].
ENDT, PM ;
VANDERLE.C .
NUCLEAR PHYSICS A, 1973, A214 (OCT29) :1-625
[7]  
GOPEL C, 1992, METEORITICS, V27, P226
[8]  
Huber P. J., 1981, ROBUST STAT
[9]   PRECISION MEASUREMENT OF HALF-LIVES AND SPECIFIC ACTIVITIES OF U-235 AND U-238 [J].
JAFFEY, AH ;
FLYNN, KF ;
GLENDENIN, LE ;
BENTLEY, WC ;
ESSLING, AM .
PHYSICAL REVIEW C, 1971, 4 (05) :1889-+
[10]  
LANPHER MA, 1998, GEOL ASS CANADA, V23, P102