Estimating Products in Forensic Identification Using DNA Profiles

Abstract In many areas, such as reliability and forensic identification, it is of interest to estimate a product of unknown parameters, each of which is estimated from test data. The maximum likelihood estimator usually used in both applications is approximately unbiased but has an asymmetric sampling distribution, particularly when the sample size is not large. Consequently, most estimates understate the parameter value, often substantially, and this may be a serious drawback if “overoptimism” is highly undesirable. Further, widely used methods of interval estimation based on confidence limits suffer from a range of theoretical and computational problems. Alternative methods of estimation are developed and discussed, based on frequentist, Bayesian, and likelihood approaches.

[1]  Peter Donnelly,et al.  Inference in Forensic Identification , 1995 .

[2]  B S Weir.  Population genetics in the forensic DNA debate. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

[3]  D. Hartl,et al.  Population genetics in forensic DNA typing. , 1991, Science.

[4]  N E Morton,et al.  Genetic structure of forensic populations. , 1992, American journal of human genetics.

[5]  Robert J. Buehler,et al.  Confidence Intervals for the Product of Two Binomial Parameters , 1957 .

[6]  L. N. Bol’shev,et al.  Interval Estimates in the Presence of Nuisance Parameters , 1966 .

[7]  C Buffery,et al.  Allele frequency distributions of four variable number tandem repeat (VNTR) loci in the London area. , 1991, Forensic science international.

[8]  T. O. Lewis,et al.  Estimating lower confidence limits on system reliability using a Monte-Carlo technique on binomial data , 1988 .

[9]  Albert Madansky,et al.  APProximate Confidence Limits for the Reliability of Series and Parallel Systems , 1965 .

[10]  M. Springer,et al.  Bayesian confidence limits for the product of N binomial parameters , 1966 .

[11]  N. Singpurwalla,et al.  Methods for Statistical Analysis of Reliability and Life Data. , 1975 .

[12]  Robert J. Buehler,et al.  SOME VALIDITY CRITERIA FOR STATISTICAL INFERENCES , 1959 .

[13]  Ian W. Evett,et al.  Some aspects of the Bayesian approach to evidence evaluation , 1989 .

[14]  H. F. Martz,et al.  A Comparison of Three Methods for Calculating Lower Confidence Limits on System Reliability Using Binomial Component Data , 1985, IEEE Transactions on Reliability.

[15]  M. R. Srinivasan,et al.  Evaluation of standard error and confidence interval of estimated multilocus genotype probabilities, and their implications in DNA forensics. , 1993, American journal of human genetics.

[16]  Martin Crowder,et al.  Statistical Analysis of Reliability Data , 1991 .

[17]  B Budowle,et al.  Fixed-bin analysis for statistical evaluation of continuous distributions of allelic data from VNTR loci, for use in forensic comparisons. , 1991, American journal of human genetics.

[18]  A. Winterbottom,et al.  Transformations Improving Maximum Likelihood Confidence Intervals for System Reliability , 1978 .

[19]  P Gill,et al.  Databases, quality control and interpretation of DNA profiling in the Home Office Forensic Science Service , 1991, Electrophoresis.

[20]  D J Balding,et al.  DNA profile match probability calculation: how to allow for population stratification, relatedness, database selection and single bands. , 1994, Forensic science international.

[21]  Robert G. Easterling,et al.  Approximate Confidence Limits for System Reliability , 1972 .

[22]  Martin Crowder,et al.  Statistical Analysis of Reliability Data , 1991 .