Modeling Relevance

Lempert, Richard

doi:10.2307/1288024

Cited by 132 publications

(55 citation statements)

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“…when γ1 = γ2 =0, however equation (5) implies that this cannot occur unless P(E2|E1) = P(E2|H)P(H|E1) + P(E2|A)P(A|E1) (9) If we define a third parameter λ by λ = P(E2|E1) --P(E2|H)P(H|E1) --P(E2|A)P(A|E1) where --1 ≤ λ ≤ 1 (10) we can relate the three parameters that govern the degree of conditional dependence by:…”

Section: [P(e2|e1) -P(e2|h)]p(e1|h) (8a) and γ2 = [P(e2|e1) -P(e2|a)]mentioning

confidence: 99%

“…1--4 In addition, some aspects of the fallacies that can arise from incorrectly assuming independence have been discussed in relation to general types of forensic evidence. 5,6 A primary concern is that investigators or jurors will overestimate the combined weight of two pieces of evidence offered in support of a common hypothesis because their mutual dependencies will go unrecognized. Understanding this statistical phenomenon takes on additional significance in theories of forensic evidence because recent treatments of context bias have been based on modeling such bias as an induced form of conditional dependence.…”

Section: Introductionmentioning

confidence: 99%

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Conditional Dependence in Microbial Forensic Assays - A Primer

Velsko

2013

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SummaryThis report provides an introduction to the topic of conditional dependence in the context of microbial forensic assays. Conditional dependence between two items of evidence E1 and E2 occurs when they are both used to support a hypothesis, but E1 affects the probability of E2 and vice versa. Ignoring this dependence can lead to very large errors in estimating the diagnosticity of the combined evidence. To introduce readers to this concept, a number of definitions of conditional dependence that have been used by authors in the past have been collected together and compared. Formal mathematical relationships that constrain conditional dependence are summarized. There are several specific scenarios in which unrecognized conditional dependence can arise in microbial forensic contexts. This report provides some notional examples that illustrate dramatic effects of conditional dependence on the weight of microbial forensic evidence, and discusses the relevance of these observations for the validation of microbial forensic assays. A two--parameter model that describes the transition between various limiting forms of conditional dependence relations is provided in an appendix.

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Section: [P(e2|e1) -P(e2|h)]p(e1|h) (8a) and γ2 = [P(e2|e1) -P(e2|a)]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Conditional Dependence in Microbial Forensic Assays - A Primer

Velsko

2013

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“…I've stated it this way because there are interesting disagreements about both the relationship between rationality and obligation (e.g., between objectivists who think that there can be obligations to refrain from doing things that we're rationally required to do and authors who think that rationality and obligation are more intimately connected) and about the normative significance of expected value (e.g., between non-consequentialists who think that we should sometimes follow principles when we know that doing so stands in the way of promoting some good and those who think that we should use the tools of decision-theory to determine what to do). [] defends a version of this argument and we can find seeds of it in Lempert (1977). larger number of guilty criminals" is not at all to say that society does, or should, embrace a policy that juries, conscious of the magnitude of their doubts in a particular case, ought to convict in the face of this acknowledged and quantified uncertainty.…”

Section: Tribe and Reasonable Doubtmentioning

confidence: 99%

Truth, knowledge, and the standard of proof in criminal law

Littlejohn

2017

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Could it be right to convict and punish defendants using only statistical evidence? In this paper, I argue that it is not and explain why it would be wrong. This is difficult to do because there is a powerful argument for thinking that we should convict and punish defendants using statistical evidence. It looks as if the relevant cases are cases of decision under risk and it seems we know what we should do in such cases (i.e., maximize expected value). Given some standard assumptions about the values at stake, the case for convicting and punishing using statistical evidence seems solid. In trying to show where this argument goes wrong, I shall argue (against Lockeans, reliabilists, and others) that beliefs supported only by statistical evidence are epistemically defective and (against Enoch, Fisher, and Spectre) that these epistemic considerations should matter to the law. To solve the puzzle about the role of statistical evidence in the law, we need to revise some commonly held assumptions about epistemic value and defend the relevance of epistemology to this practical question.

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“…One way to determine the probative value of any piece of evidence E (such as a footprint matching that of the defendant found at the crime scene) is to use the likelihood ratio (LR) [22] [3]. This is the probability of E given the prosecution hypothesis (e.g., 'defendant guilty') divided by the probability of E given the alternative, complementary defence hypothesis (e.g, 'defendant not guilty').…”

Section: Introductionmentioning

confidence: 99%

When ‘neutral’ evidence still has probative value (with implications from the Barry George Case)

et al. 2014

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The likelihood ratio (LR) is a probabilistic method that has been championed as a 'simple rule' for evaluating the probative value of forensic evidence in court. Intuitively, if the LR is greater than one then the evidence supports the prosecution hypothesis; if the LR is less than one it supports the defence hypothesis, and if the LR is equal to one then the evidence favours neither (and so is considered 'neutral' -having no probative value). It can be shown by Bayes' theorem that this simple relationship only applies to pairs of hypotheses for which one is the negation of the other (i.e. to mutually exclusive and exhaustive hypotheses) and is not applicable otherwise. We show how easy it can be -even for evidence experts -to use pairs of hypotheses that they assume are mutually exclusive and exhaustive but are not, and hence to arrive at erroneous conclusions about the value of evidence using the LR. Furthermore, even when mutually exclusive and exhaustive hypotheses are used there are extreme restrictions as to what can be concluded about the probative value of evidence just from a LR. Most importantly, while the distinction between source-level hypotheses (such as defendant was/was not at the crime scene) and offence-level hypotheses (defendant is/is not guilty) is well known, it is not widely understood that a LR for evidence about the former generally has no bearing on the LR of the latter. We show for the first time (using Bayesian networks) the full impact of this problem, and conclude that it is only the LR of the offence level hypotheses that genuinely determine the probabitive value of the evidence. We investigate common scenarios in which evidence has a LR of one but still has significant probative value (i.e. is not neutral as is commonly assumed). As illustration we consider the ramifications of these points for the case of Barry George. The successful appeal against his conviction for the murder of Jill Dando was based primarily on the argument that the firearm discharge residue (FDR) evidence, assumed to support the prosecution hypothesis at the original trial, actually had an LR equal to one and hence was 'neutral'. However, our review of the appeal transcript shows numerous examples of the problems with the use of hypotheses identified above. We show that if one were to follow the arguments recorded in the Appeal judgment verbatim, then contrary to the Appeal conclusion, the probative value of the FDR evidence may not have been neutral as was concluded.

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Modeling Relevance

Cited by 132 publications

References 0 publications

Conditional Dependence in Microbial Forensic Assays - A Primer

Conditional Dependence in Microbial Forensic Assays - A Primer

Truth, knowledge, and the standard of proof in criminal law

When ‘neutral’ evidence still has probative value (with implications from the Barry George Case)

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