The characterization of Monte Carlo errors for the quantification of the value of forensic evidence

References

• European Network of Forensic Science Institutes. ENFSI guideline for evaluative reporting in forensic science. Strengthening the evaluation of forensic results across Europe (STEOFRAE); 2015.
   Google Scholar
• National Research Council Committee on Identifying the Needs of the Forensic Sciences Community. Strengthening forensic science in the United States: a path forward. Washington (DC): The National Academies Press; 2009.
   Google Scholar
• Aitken C, Roberts P, Jackson G. Fundamentals of probability and statistical evidence in criminal proceedings; guidance for judges, lawyers, forensic scientists and expert witnesses. 1st ed. London: Royal Statistical Society's Working Group on Statistics and the Law; 2010.
   Google Scholar
• Aitken C, Taroni F. Statistics and the evaluation of evidence for forensic scientists. 2nd ed. Chichester: John Wiley and Sons, Ltd.; 2004.
   Google Scholar
• Cook R, Evett IW, Jackson G, et al. A hierarchy of propositions: deciding which level to address in casework. Sci Justice. 1998;38(4):231–239. doi: 10.1016/S1355-0306(98)72117-3
   Web of Science ®Google Scholar
• Cereda G. Bayesian approach to LR assessment in case of rare type match: careful derivation and limits. Report No.: arXiv:1502.02406v9. University of Lausanne/Leiden University; 2016.
   Google Scholar
• Cereda G. Impact of model choice on LR assessment in case of rare haplotype match (Frequentist Approach). Scand J Statist. 2016. doi: 10.1111/sjos.12250
   Google Scholar
• Lunn D, Jackson C, Best N, et al. The BUGS book: a practical introduction to Bayesian analysis. Texts in Statistical Science. Boca Raton (FL): CRC Press; 2013.
   Google Scholar
• Han C, Carlin BP. MCMC methods for computing Bayes factors: a comparative review. J Amer Statist Assoc. 2001;96:1122–1132. doi: 10.1198/016214501753208780
   Web of Science ®Google Scholar
• Taroni F, Bozza S, Biedermann A, et al. Dismissal of the illusion of uncertainty in the assessment of a likelihood ratio. Law Probab Risk. 2016;15(1):1–16. doi: 10.1093/lpr/mgv008
   Web of Science ®Google Scholar
• Curran JM, Buckleton JS, Triggs CM, et al. Assessing uncertainty in DNA evidence caused by sampling effects. Sci Justice. 2002;42(1):29–37. doi: 10.1016/S1355-0306(02)71794-2
   PubMed Web of Science ®Google Scholar
• Buckleton J, Triggs CM, Walsh SJ, editors. Forensic DNA evidence interpretation. Boca Raton (FL): CRC Press; 2005.
   Google Scholar
• Morrison GS. Measuring the validity and reliability of forensic likelihood-ratio systems. Sci Justice. 2011;51:91–98. doi: 10.1016/j.scijus.2011.03.002
   PubMed Web of Science ®Google Scholar
• Sjerps MJ, Alberink I, Bolck A, et al. Uncertainty and LR: to integrate or not to integrate, that's the question. Law Probab Risk. 2016;15(1):23–29. doi: 10.1093/lpr/mgv005
   Web of Science ®Google Scholar
• Beecham GW, Weir BS. Confidence interval of the likelihood ratio associated with mixed stain DNA evidence. J Forensic Sci. 2011;56(S1):166–171. doi: 10.1111/j.1556-4029.2010.01600.x
   Web of Science ®Google Scholar
• Morrison GS, Enzinger E. What should a forensic practitioner's likelihood ratio be? Sci Justice. 2016;56(5):374–379. doi: 10.1016/j.scijus.2016.05.007
   PubMed Web of Science ®Google Scholar
• Curran JM. Admitting to uncertainty in the LR. Sci Justice. 2016;56(5):380–382. doi: 10.1016/j.scijus.2016.05.005
   PubMed Web of Science ®Google Scholar
• Ommen DM, Saunders CP, Neumann C. An argument against presenting interval quantifications as a surrogate for the value of evidence. Sci Justice. 2016;56(5):383–387. doi: 10.1016/j.scijus.2016.07.001
   PubMed Web of Science ®Google Scholar
• Berger CEH, Slooten K. The LR does not exist. Sci Justice. 2016;56(5):388–391. doi: 10.1016/j.scijus.2016.06.005
   PubMed Web of Science ®Google Scholar
• Biedermann A, Bozza S, Taroni F, et al. Reframing the debate: a question of probability, not of likelihood ratio. Sci Justice. 2016;56(5):392–396. doi: 10.1016/j.scijus.2016.05.008
   PubMed Web of Science ®Google Scholar
• van den Hout A, Alberink I. Posterior distributions for likelihood ratios in forensic science. Sci Justice. 2016;56(5):397–401. doi: 10.1016/j.scijus.2016.06.011
   PubMed Web of Science ®Google Scholar
• Taylor D, Hicks T, Champod C. Using sensitivity analyses in Bayesian networks to highlight the impact of data paucity and direct future analyses: a contribution to the debate on measuring and reporting the precision of likelihood ratios. Sci Justice. 2016;56(5):402–410. doi: 10.1016/j.scijus.2016.06.010
   PubMed Web of Science ®Google Scholar
• Kass RE, Raftery AE. Bayes factors. J Amer Statist Assoc. 1995;90(430):773–795. doi: 10.1080/01621459.1995.10476572
   Web of Science ®Google Scholar
• Newton MA, Raftery AE. Approximate Bayesian inference with the weighted likelihood bootstrap. J R Stat Soc Ser B Methodol. 1994;56(1):3–48.
   Google Scholar
• Tanner MA. Tools for statistical inference: methods for the exploration of posterior distributions and likelihood functions. 3rd ed. New York (NY): Springer; 1996.
   Google Scholar
• Geweke J. Bayesian inference in econometric models using Monte Carlo integration. Econometrica. 1989;57(6):1317–1339. doi: 10.2307/1913710
   Web of Science ®Google Scholar
• Serfling RJ. Approximation theorems of mathematical statistics. Wiley Series in Probability and Statistics. New York: John Wiley and Sons, Ltd.; 1980.
   Google Scholar
• Neal R. The harmonic mean of the likelihood: worst Monte Carlo method ever; 2008 [cited 2014 May 15]. Available from: http://radfordneal.wordpress.com/2008/08/17/the-harmonic-mean-of-the-likelihood-worst-monte-carlo-method-ever/
   Google Scholar
• Aitken CGG, Lucy D. Evaluation of trace evidence in the form of multivariate data. J Roy Statist Soc Ser C. 2004;53(1):109–122. doi: 10.1046/j.0035-9254.2003.05271.x
   Web of Science ®Google Scholar
• Dataset from the Journal of the Royal Statistical Society: Series C; 2004 [cited 2016 Apr 20]. Available from: http://onlinelibrary.wiley.com/store/10.1111/(ISSN)1467-9876/asset/homepages/glass-data.txt?v=1&s=e9bb566557f519b28a40918e8016affc52981802&isAguDoi&false
   Google Scholar
• Ferguson TS. Mathematical statistics: a decision theoretic approach. New York: Academic Press; 1967.
   Google Scholar
• Gelman A, Carlin JB, Stern HS, et al. Bayesian data analysis. 3rd ed. Texts in Statistical Science. Boca Raton (FL): CRC Press; 2014.
   Google Scholar
• Izenman AJ. Modern multivariate statistical techniques: regression, classification, and manifold learning. New York: Springer Texts in Statistics; 2013.
   Google Scholar
• Anderson TW. An introduction to multivariate statistical analysis. 3rd ed. Hoboken (NJ): John Wiley and Sons, Ltd.; 2003.
   Google Scholar
• Miller JJ. Asymptotic properties of maximum likelihood estimates in the mixed model of the analysis of variance. Ann Statist. 1977;5(4):746–762. doi: 10.1214/aos/1176343897
   Web of Science ®Google Scholar
• Dettman JR, Cassabaum AA, Saunders CP, et al. Forensic discrimination of copper wire using trace element concentrations. Anal Chem. 2014;86:8176–8182. doi: 10.1021/ac5013514
   PubMed Web of Science ®Google Scholar
• Hadfield JD. MCMC methods for multi-response generalised linear mixed models: the MCMCglmm R package. J Statist Softw. 2010;33(2):1–22. doi: 10.18637/jss.v033.i02
   PubMed Web of Science ®Google Scholar
• Hepler AB, Saunders CP, Davis LJ, et al. Score-based likelihood ratios for handwriting evidence. Forensic Sci Int. 2012;219(1):129–140. doi: 10.1016/j.forsciint.2011.12.009
   PubMed Web of Science ®Google Scholar
• Berger JO, Bernardo JM, Sun D. The formal definition of reference priors. Ann Statist. 2009;37(2):905–938. doi: 10.1214/07-AOS587
   Web of Science ®Google Scholar
• Robert CP. The Bayesian choice: from decision-theoretic foundations to computational implements. Springer Texts in Statistics. New York: Springer; 2001.
   Google Scholar
• Flury B. A first course in multivariate statistics. Springer Texts in Statistics. New York: Springer-Verlag; 1997.
   Google Scholar
• Saunders CP. Empirical processes for estimated projections of multivariate normal vectors with applications to E.D.F. and correlation type goodness of fit tests [dissertation]. University of Kentucky; 2006.
   Google Scholar
• Fisher RA. Statistical methods for research workers. 5th ed. Edinburgh: Oliver and Boyd; 1934.
   Google Scholar