weight of evidence chapter structure

[rfl-urbaniak]

• real life legal example where the notion of weight would be useful, perhaps with some intuitions about this notion (to match formal requirements to be mentioned or discussed later), and explanation of why the classical approach won't do.
• Take a step back, simple tutorial
• Get back to this case, explain how you'd model it, and how the notion of weight applies
• go through a few other cases, paying attention to why the notion would be useful, how our approach works, perhaps also pump intuitions about the formal requirements that we will discuss
• go over a range of other proposals, starting with formal requirements (this should ride on repeated intuition building present in previous examples), and then explain how the other notions work and why they wouldn't work as desired when applied to the legal cases we brought up

[marcellodibello]

Section 1: Statement of the problem

Given that a (possibly very complex) body of evidence E supports G to some extent---say very strongly---how would that support change in light of Eplus? Sometimes investigators may fail to collect evidence at the scene or made mistakes about keeping the trace evidence, etc. See tin box case. We should not throw up our arms and say "the police make a mistake and thus we should not convict." That some evidence is missing can be a problem, but does it automatically raise a reasonable doubt about guilt? We need to assess to what extent the missing evidence would have changed the outcome of the decision. Could be harmless error. Can probability, at least sometimes---say in cases involving quantitive evidence---help us make such determinations?

(Side note: how does this square with Bayesian motto that one should always look at the evidence one has, and not at evidence one could have? Here it seems we are advocating that some decisions be based on evidence we do not have. )

(Side note: this formulation of the problem must complemtn formulation of the problem in chapter about highere order probability. How is the problem formulated in that chapter? Suggestion: sometimes in two cases the guilt probability can be high, but in one we feel the evidence is strong and in the other the evidence seems weak. How to explain that difference? Go higher order.)

Section 2: Resilience

One possible answer is simply in terms of resilience. If P(G | E)>t, than what about P(G | E & Eplus)? Show why resilience does not work. Instead of the comparing P(G | E) and P(G | E & Eplus), go higher order. Also keep i mind values Eplus is known, could incriminating or exculpating. How to weight probabilities of these two possibilities? Always pick the possibility most favorable to defendant?

Section 3: Higher order approach to weight (or resilience)

State account formally as difference betwen prior (without Eplus) and posterior (with Eplus) higher-order distribution of P(G | E) and P(G | E & Eplus).

(side question: how dioes Dahlma approach to weight fi in here? " In our model, sufficient informativeness is a cost-benefit-analysis of further investigations that involves a prediction of the possibility that such investigations will produce evidence that switches the decision from conviction to acquittal. Critics of the Bayesian approach to legal evidence have claimed that ‘weight’ cannot be captured in a Bayesian model. Contrary to this claim, our model shows how sufficient informativeness can be modelled as a second order probability." See: https://lucris.lub.lu.se/ws/portalfiles/portal/140710068/Dahlman_Nordgaard_Information_Economics_in_the_Criminal_Standard_of_Proof_LPR_elektroniskt_s_rtryck_.pdf

Section 4: application to legal cases