ENFSI 24 th September 2014 The value of trace evidence. Dr. David Lucy d.lucy@lancaster.ac.uk Lancaster University ENFSI - 2014 – p.1/38
Epistemology Epistemology - theories of knowledge, or , how we can know things. • What distinguishes a scientific knowledge from other forms of knowledge is: how we come to know something is equally important to what it is we know. • The sciences appeal to observation and to logic as guides to truth, or at least to identify falsehood. Both physical sciences and law share a reliance on epistemology. ENFSI - 2014 – p.2/38
Epistemology In science: • We do not allow “arguments by authority”, • those are truths the truth value of which depends upon the person saying it. The same is not really true in law: • Eyewitness testimony is a very valuable source of legal evidence. • Not really authority in the same way. ENFSI - 2014 – p.3/38
Epistemology In science: • Most of our scientific knowledge is from others, • a very small amount of our scientific knowledge is at first hand. • Have to have trust those others are communicating actual observations. In law: • Hearsay (secondhand) evidence is forbidden, • Information illegally obtained is not allowed as evidence. ENFSI - 2014 – p.4/38
Epistemology In a physical science: • We can simply repeat our experiments, • in principal we can repeat our observations infinitely Irrespective of what a single set of observations might indicate, a large number of repeats will eventually lead to a consensus, and provisionally this consensus will represent the truth with the current information. In science a thoroughgoing epistemology is not really needed to practice science. ENFSI - 2014 – p.5/38
Forensic science Legal sciences are “historical” sciences: • Not usually possible to any level of replication, • each case is unique, an ontological singularity, • not repeated in principal, not just difficult, impossible. This means that legal epistemology must emphasise method. In the absence of replication to avoid falsehood the only devices we have are our scientific principles of knowledge acquisition. ENFSI - 2014 – p.6/38
Comparison problem The “comparison problem” is the archetypal problem of forensic science: • Where some trace is left at the scene of a crime. • Some similar trace has been found to be associated with a suspect. To what extent do the observations from the suspects item convince one that the crimescene item and suspect item are one and the same. Addresses source level propositions. Applies to some extent to all members of WG. ENFSI - 2014 – p.7/38
Glass ENFSI - 2014 – p.8/38
Glass ENFSI - 2014 – p.9/38
Glass With glass the observables can be: • refractive index, • major, minor and trace element measurements, • isotopic measurements - being done for bullet leads (Knut & KRIPOS). All the above are termed continuous measurements: • do not fit in categories. Looking at two sub-samples of observations of refractive index from a single glass jar. ENFSI - 2014 – p.10/38
Glass RI Glass refractive indicies for a jar (Greg’s data): 20 jar 63 − subsample 1 probability density jar 63 − subsample 2 15 ( × 1000) 10 5 1.5176 1.5178 1.5180 1.5182 RI ENFSI - 2014 – p.11/38
Proximity The closeness of observation: • All the observations from sub -sample one fit within sub-sample two, • sub-sample one and sub-sample two can be said to match. The p -value is 0 . 6757 which is the probability of seeing this difference in the means of the two sub-samples were they truly from a population with a single mean. Is this a good measure of whether the sub-samples are from the same glass item? ENFSI - 2014 – p.12/38
Proximity An easily conceived illustration: • A friend collects coloured marbles - stores them in bags. • each bag has marbles of only one colour. • there may be more than one bag containing marbles of each colour. • A marble has dropped out of a bag - the marble is red - you select a bag and sample a marble - that marble is red. To what extent does the observation that both marbles are red support the notion that the marble came from that particular bag? ENFSI - 2014 – p.13/38
Proximity Complete match of "red" Does this mean that the marble came from bag three? ENFSI - 2014 – p.14/38
Proximity Probability marble came from bag three is one. ENFSI - 2014 – p.15/38
Proximity ? Probability marble came from bag three is one third ( 1 3 ). ENFSI - 2014 – p.16/38
Proximity Similarity of observation on its own: • Gives no idea as to identity. Dissimilarity of observation: • Can be used to reject in cases where observation is unambiguous. • Does not apply in any logical manner where observations are continuous. Need knowledge of population to make any legitimate probabilistic inference about identity of source. ENFSI - 2014 – p.17/38
Continuous observations Have just seen how proximity of observation gives little evidence for identity of source: • this simplified the case by considering discreete observations, • that is: marble was red, blue, turquoise etc. • As the marble from the bag was red, and the recovered marble red, then we had an absolute “match”. To what extent is the notion of a match in this sense a real expectation with truly continuous observations? ENFSI - 2014 – p.18/38
Glass RI Glass refractive indicies for two jars (Greg’s data): 15 jar 63 probability density jar 71 10 ( × 1000) 5 1.5178 1.5180 1.5182 RI ENFSI - 2014 – p.19/38
RI variation Why the variation in RI observation? • Is Greg a poor observer? no, • is the GRIM process imprecise? a bit, • do the observation conditions change? they do. If the conditions better, and a more precise GRIM apparatus purchased, would the observations of RI from a single piece of glass be all the same? Unlikely! ENFSI - 2014 – p.20/38
Glass RI Can we logically exclude values occurring with low probability? 15 jar 63 probability density jar 71 10 ( × 1000) 5 p=1 × 10 − 8 1.5178 1.5180 1.5182 RI ENFSI - 2014 – p.21/38
Uncertainty in observation sample 1 sample 2 sample 3 Finite samples will always give different observations: stochastic process. ENFSI - 2014 – p.22/38
Uncertainty in observation Kinetic theory implies variation in repeated sampling from the same item: • variation is a consequence of the material, • has a stochastic origin. • regardless of the precision of apparatus, The consequences are that for a continuously varying quantity an exact match for two samples taken from the same item is very unlikely. ENFSI - 2014 – p.23/38
Summary so far Thus far two salient facts have emerged for comparison problems: 1. proximity alone can give little idea of identity, 2. for continuous variables, an exact match from two sub -samples of the same item is very unlikely. Both the above are from deep principle - not just in practice. What do we do about this? Can we live with the uncertainties? ENFSI - 2014 – p.24/38
Likelihood Repeated sampling of jar 63 leads to a “distribution”. 15 probability density 10 0.04 ( × 1000) 5 1.51780 1.51790 1.51800 1.51810 RI ENFSI - 2014 – p.25/38
Likelihood Probabilities need care: • there is a 4% probability of observing a RI between 1.517899 and 1.517905. • Given that all the observations are taken from jar 63, • or can say “conditioned on” the observation being from jar 63. It is all too easy to say that there is a 4% probability that a RI between 1.517899 and 1.517905 is from jar 63 - This is utterly wrong. ENFSI - 2014 – p.26/38
Likelihood If you wanted to know the probability that you had Jar 63 were you to observe a RI between 1.517899 and 1.517905, then: • you would have to observe a large sample (population) of RIs between 1.517899 and 1.517905, • then count how many of those were from Jar 63. • Which as an empirical experiment you cannot do. When thinking about probabilities we have to be very precise about what events in the world the probability refers to. ENFSI - 2014 – p.27/38
Likelihood Sampling from some of the other glass objects: 12 probability density 10 ( × 1000) 8 6 0.02 4 2 1.5176 1.5180 1.5184 RI ENFSI - 2014 – p.28/38
Likelihood Both Jar 63 and other items: 12 probability density 10 Jar 63 ( × 1000) 8 6 other glass items 4 2 1.5176 1.5180 1.5184 RI ENFSI - 2014 – p.29/38
Likelihood ratio For a point just take ratio of heights: 12211.5 12 probability density 10 Jar 63 ( × 1000) 8 6 other glass items 4 2624.68 2 1.5176 1.5180 1.5184 RI ENFSI - 2014 – p.30/38
Likelihood ratios This is why statisticians use likelihood ratios: • they’re simple, • they focus on the probabilities of the observations, • they do not try to calculate probabilities for which you cannot make any direct observations. By considering a likelihood ratio we automatically take into account the likelihood of the measurements given some comparative material and the populational items. We also evaluate evidence - not propositions. ENFSI - 2014 – p.31/38
Multivariate Most continuous observations are multivariate: 1.05 4.8 1.00 67.65 0.95 207 Pb/ 206 Pb 0.90 0.85 0.80 other bullets bullet PMC 0.75 35 36 37 38 39 35 36 37 38 39 208 Pb/ 204 Pb 208 Pb/ 204 Pb ENFSI - 2014 – p.32/38
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