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Presumption of Innocence, Probable Cause, and Prior Probability—Bayes Meets Due Process

Presumption of Innocence, Probable Cause, and Prior Probability—Bayes Meets Due Process

This webinar is on-demand and available immediately.

In the wake of Daubert, the 2009 National Research Council (NRC) Report and the 2016 President’s Council of Advisors on Science and Technology (PCAST) Report, forensic science service providers have grappled with the best ways to move away from unqualified testimony like, “match to the exclusion of all others,” “zero error rate,” and “scientific certainty.”1,2

Bayes’ Theorem could be a useful construct for communicating accuracy and the limits of forensic science results. However, the key concepts are often misunderstood and unsettled issues about how to use Bayes’ Formula in the judicial setting remain.

For the uninitiated, this presentation will serve to review the fundamentals of Bayes’ Formula. The notation, basic concepts, and principles of conditional probability will be reviewed to allow for a careful discussion of several challenges for using this formula in the judicial and forensic science service provider settings.

The tension between prior probability and presumption of innocence will be explored by looking at the history of the presumption of innocence in Coffin v. United States, State v. Skipper, and U.S. v. Shonubi.3-5 Does a presumption of innocence mean the prior probability must be fixed at zero? What if the suspect is part of a closed population set (e.g., one of only 100 prisoners who could have committed a crime)?6

The notion of probable cause in Beck v. Ohio, and the 4th Amendment to the United States Constitution will be examined to determine if physical evidence presented to a forensic science service provider is different from a randomly selected item and, therefore, has a different prior probability of matching a crime scene sample or being an illegal substance, etc. The highly desired but often elusive posterior probability will be explained with special attention to Positive Predictive Value (PPV) and common mistakes in the literature.7,8

Finally, the likelihood ratio will be inspected. This mathematical term requires the scientist to populate both a numerator and denominator with values. What constitutes acceptable sources for these numbers is a source of debate in the development of forensic science standards. Do they need to originate from rigorous probability distributions, or can they be estimated, or even based, on an examiner’s subjective, qualitative assessment?9

Strategies for direct and cross examination of expert witnesses will be presented that answer three questions: (1) how can the forensic science results be presented in the best light, (2) how can fair concerns about accuracy and error rates be raised, and (3) how can this material be covered without confusing judges and juries?10-12


Presenter: Jeff Salyards, PhD, MFS



  1. National Research Council. 2009. Strengthening Forensic Science in the United States: A Path Forward. Washington, DC: The National Academies Press.
  2. President’s Council of Advisors on Science and Technology (PCAST). Report to the President: Forensic Science in Criminal Courts: Ensuring Scientific Validity of Feature-Comparison Methods. (2016). Washington, DC: Executive Office of the President of the United States.
  3. Allen, Ronald J. et al. Probability and proof in State v. Skipper: an internet exchange. Jurimetrics J. 35 (1994): 277. 
  4. Friedman, Richard D. A presumption of innocence, not of even odds. Stanford Law Review (2000): 873-887.
  5. Thompson, William C. et al. The role of prior probability in forensic assessments. Frontiers in genetics 4 (2013): 220.
  6. Di Bello, Marcello. Trial by statistics: Is a high probability of guilt enough to convict? Mind 128.512 (2019): 1045-1084. 
  7. Caliebe, Amke et al. Likelihood ratio and posterior odds in forensic genetics: Two sides of the same coin. Forensic Science International: Genetics 28 (2017): 203-210.
  8. Taroni, Franco, and Alex Biedermann. Inadequacies of posterior probabilities for the assessment of scientific evidence. Law, Probability and Risk 4.1-2 (2005): 89-114.
  9. Lund, Steven P., and Hari Iyer. Likelihood ratio as weight of forensic evidence: a closer look. Journal of Research of the National Institute of Standards and Technology 122 (2017): 1.
  10. Dale, Reid. On Rational Jurisprudence: A Problem in Bayesian Confirmation Theory. arXiv preprint arXiv:2209.12896 (2022).
  11. Garrett, Brandon L., William E. Crozier, and Rebecca Grady. Error rates, likelihood ratios, and jury evaluation of forensic evidence.
Price: $0.00