Bayes and the Law

“…As to the implication of our argument for legal decision making in general, we want to stress that we do not argue that criminal cases should be approached with a complete Bayesian analysis. In our view, and that of many others, a likelihood-ratio analysis of one or even several pieces of evidence does not imply a full Bayesian approach including the estimation of prior odds, even though likelihood ratios also occur in Bayesian analyses (de Keijser and Elffers, 2012;Dienes, 2008;Fenton et al, 2016;Royall, 1997). However, we do advocate that judges (and juries) adopt a scenario approach in that they do not simply accumulate evidence against the suspect, but analyse every piece of evidence as to its fit in competing scenario's, even without trying to actually quantify these fits with likelihoods.…”

“…Our calculation implicitly conditions on the fact that at least one expert is right, but allows for the possibility that only some subset of the experts in I is right even if I ∈ Compat; we place positive probability on M I even if I is a strict subset of some I ∈ Compat. This method of combining experts' judgments is similar in spirit to the method proposed by Dawid (1987) and Fenton et al (2016). This completes our description of how to combine experts' causal judgments.…”

“…The ability to discriminate species through the application of ZooMS provides an opportunity to test competing propositions about Neandertal selection of ribs for functional purposes (H 0 : opportunism vs. H A : selection of larger ribs). We employ Bayesian reasoning to quantify the relative support for competing hypotheses in light of the observed faunal distributions and ZooMS results 57,58 . Our statistical framework incorporates both a strong alternative H As , implying that Neandertals had relatively (2020) 10:7746 | https://doi.org/10.1038/s41598-020-64358-w www.nature.com/scientificreports www.nature.com/scientificreports/ fixed preferences for ribs of larger-bodied ungulates, and a weak alternative H Aw , implying less rigid preferences (Supplementary Note).…”

“…The relative support for H A vs. H 0 is quantified by the posterior odds: where E represents a set of empirical observations (Supplementary Note). This form of reasoning appears in legal and forensic contexts where, for example, it must be decided whether crime scene evidence better supports the prosecution or defense 57,58 . P(E | H 0 ) is the likelihood of the sample under H 0 , calculated using the multinomial formula with probabilities given by the relative frequencies of all rib fragments in an assemblage.…”

“…As to the implication of our argument for legal decision making in general, we want to stress that we do not argue that criminal cases should be approached with a complete Bayesian analysis. In our view, and that of many others, a likelihood-ratio analysis of one or even several pieces of evidence does not imply a full Bayesian approach including the estimation of prior odds, even though likelihood ratios also occur in Bayesian analyses (de Keijser and Elffers, 2012;Dienes, 2008;Fenton et al, 2016;Royall, 1997). However, we do advocate that judges (and juries) adopt a scenario approach in that they do not simply accumulate evidence against the suspect, but analyse every piece of evidence as to its fit in competing scenario's, even without trying to actually quantify these fits with likelihoods.…”

“…Our calculation implicitly conditions on the fact that at least one expert is right, but allows for the possibility that only some subset of the experts in I is right even if I ∈ Compat; we place positive probability on M I even if I is a strict subset of some I ∈ Compat. This method of combining experts' judgments is similar in spirit to the method proposed by Dawid (1987) and Fenton et al (2016). This completes our description of how to combine experts' causal judgments.…”

“…The ability to discriminate species through the application of ZooMS provides an opportunity to test competing propositions about Neandertal selection of ribs for functional purposes (H 0 : opportunism vs. H A : selection of larger ribs). We employ Bayesian reasoning to quantify the relative support for competing hypotheses in light of the observed faunal distributions and ZooMS results 57,58 . Our statistical framework incorporates both a strong alternative H As , implying that Neandertals had relatively (2020) 10:7746 | https://doi.org/10.1038/s41598-020-64358-w www.nature.com/scientificreports www.nature.com/scientificreports/ fixed preferences for ribs of larger-bodied ungulates, and a weak alternative H Aw , implying less rigid preferences (Supplementary Note).…”

“…The relative support for H A vs. H 0 is quantified by the posterior odds: where E represents a set of empirical observations (Supplementary Note). This form of reasoning appears in legal and forensic contexts where, for example, it must be decided whether crime scene evidence better supports the prosecution or defense 57,58 . P(E | H 0 ) is the likelihood of the sample under H 0 , calculated using the multinomial formula with probabilities given by the relative frequencies of all rib fragments in an assemblage.…”

“…As to the implication of our argument for legal decision making in general, we want to stress that we do not argue that criminal cases should be approached with a complete Bayesian analysis. In our view, and that of many others, a likelihood-ratio analysis of one or even several pieces of evidence does not imply a full Bayesian approach including the estimation of prior odds, even though likelihood ratios also occur in Bayesian analyses (de Keijser and Elffers, 2012;Dienes, 2008;Fenton et al, 2016;Royall, 1997). However, we do advocate that judges (and juries) adopt a scenario approach in that they do not simply accumulate evidence against the suspect, but analyse every piece of evidence as to its fit in competing scenario's, even without trying to actually quantify these fits with likelihoods.…”

“…Our calculation implicitly conditions on the fact that at least one expert is right, but allows for the possibility that only some subset of the experts in I is right even if I ∈ Compat; we place positive probability on M I even if I is a strict subset of some I ∈ Compat. This method of combining experts' judgments is similar in spirit to the method proposed by Dawid (1987) and Fenton et al (2016). This completes our description of how to combine experts' causal judgments.…”

“…The ability to discriminate species through the application of ZooMS provides an opportunity to test competing propositions about Neandertal selection of ribs for functional purposes (H 0 : opportunism vs. H A : selection of larger ribs). We employ Bayesian reasoning to quantify the relative support for competing hypotheses in light of the observed faunal distributions and ZooMS results 57,58 . Our statistical framework incorporates both a strong alternative H As , implying that Neandertals had relatively (2020) 10:7746 | https://doi.org/10.1038/s41598-020-64358-w www.nature.com/scientificreports www.nature.com/scientificreports/ fixed preferences for ribs of larger-bodied ungulates, and a weak alternative H Aw , implying less rigid preferences (Supplementary Note).…”

“…The relative support for H A vs. H 0 is quantified by the posterior odds: where E represents a set of empirical observations (Supplementary Note). This form of reasoning appears in legal and forensic contexts where, for example, it must be decided whether crime scene evidence better supports the prosecution or defense 57,58 . P(E | H 0 ) is the likelihood of the sample under H 0 , calculated using the multinomial formula with probabilities given by the relative frequencies of all rib fragments in an assemblage.…”